The bond-algebraic approach to dualities
An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature (strong-coupling)/high temperature (weak-coupling) dualities of c...
Uloženo v:
| Vydáno v: | Advances in physics Ročník 60; číslo 5; s. 679 - 798 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Abingdon
Taylor & Francis
01.10.2011
Taylor & Francis Ltd |
| Témata: | |
| ISSN: | 0001-8732, 1460-6976 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature (strong-coupling)/high temperature (weak-coupling) dualities of classical statistical mechanics (or (Euclidean) path integrals). Its range of applications includes discrete lattice, continuum field and gauge theories. Dualities are revealed to be local, structure-preserving mappings between model-specific bond algebras that can be implemented as unitary transformations, or partial isometries if gauge symmetries are involved. This characterization permits us to search systematically for dualities and self-dualities in quantum models of arbitrary system size, dimensionality and complexity, and any classical model admitting a transfer matrix or operator representation. In particular, special dualities such as exact dimensional reduction, emergent and gauge-reducing dualities that solve gauge constraints can be easily understood in terms of mappings of bond algebras. As a new example, we show that the ℤ
2
Higgs model is dual to the extended toric code model in any number of dimensions. Non-local transformations such as dual variables and Jordan-Wigner dictionaries are algorithmically derived from the local mappings of bond algebras. This permits us to establish a precise connection between quantum dual and classical disorder variables. Our bond-algebraic approach goes beyond the standard approach to classical dualities, and could help resolve the long-standing problem of obtaining duality transformations for lattice non-Abelian models. As an illustration, we present new dualities in any spatial dimension for the quantum Heisenberg model. Finally, we discuss various applications including location of phase boundaries, spectral behavior and, notably, we show how bond-algebraic dualities help constrain and realize fermionization in an arbitrary number of spatial dimensions. |
|---|---|
| AbstractList | An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature (strong-coupling)/high temperature (weak-coupling) dualities of classical statistical mechanics (or (Euclidean) path integrals). Its range of applications includes discrete lattice, continuum field and gauge theories. Dualities are revealed to be local, structure-preserving mappings between model-specific bond algebras that can be implemented as unitary transformations, or partial isometries if gauge symmetries are involved. This characterization permits us to search systematically for dualities and self-dualities in quantum models of arbitrary system size, dimensionality and complexity, and any classical model admitting a transfer matrix or operator representation. In particular, special dualities such as exact dimensional reduction, emergent and gauge-reducing dualities that solve gauge constraints can be easily understood in terms of mappings of bond algebras. As a new example, we show that the ℤ
2
Higgs model is dual to the extended toric code model in any number of dimensions. Non-local transformations such as dual variables and Jordan-Wigner dictionaries are algorithmically derived from the local mappings of bond algebras. This permits us to establish a precise connection between quantum dual and classical disorder variables. Our bond-algebraic approach goes beyond the standard approach to classical dualities, and could help resolve the long-standing problem of obtaining duality transformations for lattice non-Abelian models. As an illustration, we present new dualities in any spatial dimension for the quantum Heisenberg model. Finally, we discuss various applications including location of phase boundaries, spectral behavior and, notably, we show how bond-algebraic dualities help constrain and realize fermionization in an arbitrary number of spatial dimensions. An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature (strong-coupling)/high temperature (weak-coupling) dualities of classical statistical mechanics (or (Euclidean) path integrals). Its range of applications includes discrete lattice, continuum field and gauge theories. Dualities are revealed to be local, structure-preserving mappings between model-specific bond algebras that can be implemented as unitary transformations, or partial isometries if gauge symmetries are involved. This characterization permits us to search systematically for dualities and self-dualities in quantum models of arbitrary system size, dimensionality and complexity, and any classical model admitting a transfer matrix or operator representation. In particular, special dualities such as exact dimensional reduction, emergent and gauge-reducing dualities that solve gauge constraints can be easily understood in terms of mappings of bond algebras. As a new example, we show that the ... Higgs model is dual to the extended toric code model in any number of dimensions. Non-local transformations such as dual variables and Jordan-Wigner dictionaries are algorithmically derived from the local mappings of bond algebras. This permits us to establish a precise connection between quantum dual and classical disorder variables. Our bond-algebraic approach goes beyond the standard approach to classical dualities, and could help resolve the long-standing problem of obtaining duality transformations for lattice non-Abelian models. As an illustration, we present new dualities in any spatial dimension for the quantum Heisenberg model. Finally, we discuss various applications including location of phase boundaries, spectral behavior and, notably, we show how bond-algebraic dualities help constrain and realize fermionization in an arbitrary number of spatial dimensions. (ProQuest: ... denotes formulae/symbols omitted.) An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature (strong-coupling)/high temperature (weak-coupling) dualities of classical statistical mechanics (or (Euclidean) path integrals). Its range of applications includes discrete lattice, continuum field and gauge theories. Dualities are revealed to be local, structure-preserving mappings between model-specific bond algebras that can be implemented as unitary transformations, or partial isometries if gauge symmetries are involved. This characterization permits us to search systematically for dualities and self-dualities in quantum models of arbitrary system size, dimensionality and complexity, and any classical model admitting a transfer matrix or operator representation. In particular, special dualities such as exact dimensional reduction, emergent and gauge-reducing dualities that solve gauge constraints can be easily understood in terms of mappings of bond algebras. As a new example, we show that the '2 Higgs model is dual to the extended toric code model in any number of dimensions. Non-local transformations such as dual variables and Jordan--Wigner dictionaries are algorithmically derived from the local mappings of bond algebras. This permits us to establish a precise connection between quantum dual and classical disorder variables. Our bond-algebraic approach goes beyond the standard approach to classical dualities, and could help resolve the long-standing problem of obtaining duality transformations for lattice non-Abelian models. As an illustration, we present new dualities in any spatial dimension for the quantum Heisenberg model. Finally, we discuss various applications including location of phase boundaries, spectral behavior and, notably, we show how bond-algebraic dualities help constrain and realize fermionization in an arbitrary number of spatial dimensions. |
| Author | Nussinov, Zohar Ortiz, Gerardo Cobanera, Emilio |
| Author_xml | – sequence: 1 givenname: Emilio surname: Cobanera fullname: Cobanera, Emilio email: ecobaner@indiana.edu organization: Department of Physics , Indiana University – sequence: 2 givenname: Gerardo surname: Ortiz fullname: Ortiz, Gerardo organization: Department of Physics , Indiana University – sequence: 3 givenname: Zohar surname: Nussinov fullname: Nussinov, Zohar organization: Department of Physics , Washington University |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24618486$$DView record in Pascal Francis |
| BookMark | eNqFkEtLxDAUhYMoOD7-gYsiiG465jZtmrgRGXyB4GZchztp4kQyzZi0iP_elhlduNDV5cJ3DofvgOy2oTWEnACdAhX0klIKombFtKAAUw5SQLlDJlBymnNZ810yGZF8ZPbJQUpvw1vVwCbkYr402SK0TY7-1SwiOp3heh0D6mXWhazp0bvOmXRE9iz6ZI6395C83N3OZw_50_P94-zmKddM8i7XheUWKPIFlZUouNa2GeYUGi0aA8ZYxqQFK4oasEIhTGPKqhRgSib4AtghOd_0Dhvee5M6tXJJG--xNaFPSnImKl4XfCBPf5FvoY_tME5JSiVwIasBOttCmDR6G7HVLql1dCuMn6ooOYhSjGXlhtMxpBSN_UGAqlGy-pasRslqI3mIXf2Kaddh50LbDSr9f-HrTdi1NsQVfoToG9Xhpw_xeyj7s-ELYTaURw |
| CODEN | ADPHAH |
| CitedBy_id | crossref_primary_10_1007_s11128_011_0346_7 crossref_primary_10_1103_PhysRevResearch_2_023353 crossref_primary_10_1007_s00220_021_04220_w crossref_primary_10_1103_PhysRevB_111_115106 crossref_primary_10_1103_PhysRevResearch_4_043003 crossref_primary_10_1103_PhysRevB_108_214429 crossref_primary_10_1016_j_aop_2018_02_017 crossref_primary_10_1103_PRXQuantum_1_010303 crossref_primary_10_1016_j_aop_2014_08_013 crossref_primary_10_1103_PhysRevResearch_5_023099 crossref_primary_10_1103_PhysRevX_15_011001 crossref_primary_10_1103_PhysRevX_14_021040 crossref_primary_10_1038_s42005_022_00946_8 crossref_primary_10_1007_JHEP01_2015_105 crossref_primary_10_1209_0295_5075_131_40006 crossref_primary_10_1103_PRXQuantum_5_040330 crossref_primary_10_1007_JHEP08_2025_009 crossref_primary_10_1103_g76f_tlvq crossref_primary_10_1103_PhysRevX_10_041018 crossref_primary_10_1103_PhysRevLett_134_130403 crossref_primary_10_1103_ctxg_k3b6 crossref_primary_10_1016_j_aop_2012_07_001 crossref_primary_10_1103_PhysRevX_12_011050 crossref_primary_10_1088_1361_648X_aa718f crossref_primary_10_1038_s41534_024_00900_2 crossref_primary_10_1007_JHEP07_2024_225 crossref_primary_10_1088_1367_2630_18_3_033011 crossref_primary_10_1103_PhysRevB_111_045142 crossref_primary_10_1103_PhysRevResearch_3_023120 crossref_primary_10_1103_PhysRevResearch_5_013086 crossref_primary_10_1103_PhysRevX_14_041069 crossref_primary_10_1016_j_nuclphysb_2018_12_029 crossref_primary_10_1007_JHEP02_2016_180 crossref_primary_10_1016_j_nuclphysb_2013_10_018 crossref_primary_10_1103_PRXQuantum_5_010338 crossref_primary_10_1016_j_aop_2019_168018 crossref_primary_10_1016_j_aop_2023_169384 crossref_primary_10_1103_PhysRevResearch_2_013135 crossref_primary_10_1016_j_nuclphysb_2014_12_026 crossref_primary_10_1103_PhysRevB_104_165140 crossref_primary_10_1103_PhysRevX_11_041008 crossref_primary_10_1103_PRXQuantum_4_020357 crossref_primary_10_1103_PRXQuantum_4_020339 crossref_primary_10_1088_1742_5468_2014_02_P02012 |
| Cites_doi | 10.1088/0022-3719/5/11/004 10.1017/CBO9780511626265 10.1103/PhysRev.131.2766 10.1007/978-93-80250-90-8 10.1103/PhysRevB.72.045137 10.1103/PhysRev.60.252 10.1016/0375-9601(84)90816-8 10.1142/2262 10.1103/PhysRevLett.46.379 10.1088/0022-3719/6/7/010 10.1103/RevModPhys.52.453 10.1103/PhysRevLett.86.1082 10.1209/0295-5075/84/36005 10.1017/S0305004100027419 10.4310/ATMP.1998.v2.n2.a2 10.1016/0003-4916(62)90232-4 10.1073/pnas.0803726105 10.1016/0031-8914(73)90381-9 10.1103/PhysRevB.71.195120 10.1103/PhysRevD.25.1587 10.1007/978-1-4757-6848-0 10.1088/0305-4470/30/18/005 10.1016/0550-3213(80)90403-4 10.1088/0034-4885/70/6/R03 10.1016/S0370-1573(99)00083-6 10.1103/RevModPhys.36.856 10.1016/0550-3213(94)90230-5 10.1103/PhysRevB.77.064302 10.1103/PhysRevLett.96.110405 10.1103/PhysRev.115.485 10.1103/PhysRev.65.117 10.4310/ATMP.1998.v2.n2.a1 10.1016/S0370-2693(98)00377-3 10.1063/1.523343 10.1103/PhysRevB.79.214440 10.1126/science.288.5465.462 10.1017/CBO9780511470783 10.56021/9780801869099 10.1063/1.1665530 10.1103/RevModPhys.17.50 10.1103/PhysRevB.24.218 10.1016/0550-3213(79)90595-9 10.1007/BF01208273 10.1103/RevModPhys.80.1083 10.1103/PhysRevLett.94.040402 10.1007/978-1-4613-0097-7 10.1103/PhysRevLett.3.296 10.1103/PhysRevB.75.144401 10.1103/RevModPhys.63.1 10.1088/1742-5468/2005/09/P09012 10.1103/PhysRevLett.94.111601 10.1103/PhysRevB.80.081104 10.1007/978-1-4612-0869-3 10.1016/0003-4916(70)90270-8 10.1093/acprof:oso/9780199577224.001.0001 10.1016/j.nuclphysb.2004.12.016 10.1016/0370-1573(74)90023-4 10.1016/j.nuclphysb.2005.04.003 10.1016/0370-2693(92)90168-4 10.1103/PhysRevB.3.3918 10.1007/BF01089192 10.1103/PhysRevB.24.5229 10.1103/PhysRevB.80.104413 10.1016/j.aop.2008.11.002 10.1201/b10273 10.1088/1751-8113/41/7/075001 10.1017/CBO9780511622625 10.1016/0550-3213(78)90153-0 10.1103/PhysRevD.19.3682 10.1016/j.aop.2006.05.007 10.1103/PhysRevD.19.3698 10.1088/0305-4470/13/4/037 10.1063/1.881616 10.1103/RevModPhys.51.659 10.1088/0305-4470/27/4/008 10.1016/S0003-4916(02)00018-0 10.1063/1.1704281 10.1088/0305-4470/20/9/043 10.1016/0550-3213(92)90269-H 10.1103/PhysRevB.82.060411 10.1016/0550-3213(78)90502-3 10.1007/BF02710808 10.1103/PhysRevLett.93.047003 10.1103/PhysRevD.72.054509 10.1070/PU1982v025n04ABEH004537 10.1142/0983 10.1016/0550-3213(94)90093-0 10.1103/PhysRevB.2.723 10.1016/S0550-3213(00)00770-7 10.1016/0550-3213(78)90382-6 10.1063/1.1665111 10.1088/0305-4470/16/12/004 10.1016/0370-2693(79)91269-3 10.1103/PhysRevLett.63.322 10.1103/PhysRevLett.104.020402 10.1016/j.physletb.2004.10.042 10.1017/CBO9780511600722 10.1515/9780691221274 10.1142/9789812799838 10.1016/0003-4916(78)90252-X 10.1103/PhysRevLett.92.107902 10.1063/1.522914 10.1103/PhysRevLett.61.2376 10.1016/j.aop.2005.10.005 10.1016/0370-2693(77)90076-4 10.2307/1968693 10.1103/PhysRevD.21.2316 10.1007/978-3-662-03937-3 10.1016/0370-2693(95)00777-I 10.1103/PhysRevLett.96.110404 10.1103/PhysRevD.25.1103 10.1016/j.aop.2010.11.002 10.1007/978-3-662-04589-3 10.1142/9789812832870 10.1088/1751-8113/40/49/006 10.1016/0550-3213(85)90350-5 10.1103/PhysRevE.51.1004 10.1103/PhysRevD.75.085020 10.1088/0953-8984/20/27/275233 10.1143/PTP.56.1454 10.1103/PhysRevD.19.3715 10.1103/PhysRevD.10.2445 10.1016/0370-1573(76)90052-1 10.1103/PhysRevD.17.2637 10.1088/0305-4470/38/21/001 10.1017/CBO9780511813870 10.1143/PTP.6.907 10.1103/PhysRevD.11.395 10.1088/1126-6708/2005/05/066 10.1103/PhysRevB.35.8865 10.1007/BF01213610 |
| ContentType | Journal Article |
| Copyright | Copyright Taylor & Francis Group, LLC 2011 2015 INIST-CNRS Copyright Taylor & Francis Ltd. 2011 |
| Copyright_xml | – notice: Copyright Taylor & Francis Group, LLC 2011 – notice: 2015 INIST-CNRS – notice: Copyright Taylor & Francis Ltd. 2011 |
| DBID | AAYXX CITATION IQODW 7U5 8FD L7M |
| DOI | 10.1080/00018732.2011.619814 |
| DatabaseName | CrossRef Pascal-Francis Solid State and Superconductivity Abstracts Technology Research Database Advanced Technologies Database with Aerospace |
| DatabaseTitle | CrossRef Technology Research Database Advanced Technologies Database with Aerospace Solid State and Superconductivity Abstracts |
| DatabaseTitleList | Technology Research Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Physics |
| EISSN | 1460-6976 |
| EndPage | 798 |
| ExternalDocumentID | 2497688851 24618486 10_1080_00018732_2011_619814 619814 |
| Genre | Feature |
| GroupedDBID | -DZ -~X .7F .QJ 0BK 0R~ 23M 2DF 30N 4.4 5GY 5VS AAENE AAGDL AAHIA AAJMT AALDU AAMIU AAPUL AAQRR ABCCY ABFIM ABHAV ABLIJ ABPAQ ABPEM ABRLO ABTAI ABXUL ABXYU ACGEJ ACGOD ACNCT ACTIO ADCVX ADGTB ADPDO ADXPE AEISY AENEX AEOZL AEPSL AEYOC AFDUV AFKVX AFRVT AGDLA AGMYJ AHDZW AIJEM AIPZZ AIYEW AJWEG AKBVH AKOOK ALMA_UNASSIGNED_HOLDINGS ALQZU AQRUH AQTUD AVBZW AWYRJ BLEHA C5L CAG CCCUG CE4 CS3 D0L DGEBU DKSSO EAU EBS EJD E~A E~B GTTXZ H13 HF~ HZ~ H~P IPNFZ J.P KYCEM M4Z NA5 NZ- O9- P2P PQQKQ RIG RNANH RNS ROSJB RTWRZ S-T SNACF TASJS TBQAZ TDBHL TEX TFL TFT TFW TN5 TTHFI TUROJ TWF UPT UT5 UU3 WH7 ZGOLN ~02 ~S~ 07S 1TA 6TJ 8WZ A6W AANMX AATVF AAYXX ABCES ABEFU ABGQB ABZIJ ACKDS ACLZH ADIYS AETEA AFFNX AFGMD AHWVO AI. ASQZU BVUPT C09 CITATION COF DGEYW DWNMW EBKLY ECKKI EXXQB H~9 JHRKR LJTGL MVM NUSFT QSQFL TAZ TCJPB TFMCV UC4 UU9 V3L VH1 VOH ZY4 ADYSH IQODW XOL 7U5 8FD L7M |
| ID | FETCH-LOGICAL-c396t-c2f6f10a6b095826ccfd9812cafaee1eef339f1f8271a5a88ede45481e4386b13 |
| IEDL.DBID | TFW |
| ISICitedReferencesCount | 94 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000295451600001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0001-8732 |
| IngestDate | Fri Sep 05 10:24:06 EDT 2025 Sat Jul 26 00:55:16 EDT 2025 Mon Jul 21 09:13:13 EDT 2025 Sat Nov 29 04:24:40 EST 2025 Tue Nov 18 21:51:02 EST 2025 Mon Oct 20 23:33:42 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Keywords | Quantum system Dimensionality Symmetry property Path integral Heisenberg model Strong coupling High temperature Quantum size effect Structural models Continuum Local structure Classical mechanics Phase boundaries Lattice field theory Lattice model Transfer matrix method Statistical mechanics Classical theory Mathematical physics Gauge field theory Quantum theory Crystal structure |
| Language | English |
| License | CC BY 4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c396t-c2f6f10a6b095826ccfd9812cafaee1eef339f1f8271a5a88ede45481e4386b13 |
| Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23 |
| PQID | 900916895 |
| PQPubID | 53051 |
| PageCount | 120 |
| ParticipantIDs | proquest_miscellaneous_963856726 pascalfrancis_primary_24618486 proquest_journals_900916895 crossref_primary_10_1080_00018732_2011_619814 informaworld_taylorfrancis_310_1080_00018732_2011_619814 crossref_citationtrail_10_1080_00018732_2011_619814 |
| PublicationCentury | 2000 |
| PublicationDate | 10/1/2011 |
| PublicationDateYYYYMMDD | 2011-10-01 |
| PublicationDate_xml | – month: 10 year: 2011 text: 10/1/2011 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Abingdon |
| PublicationPlace_xml | – name: Abingdon |
| PublicationTitle | Advances in physics |
| PublicationYear | 2011 |
| Publisher | Taylor & Francis Taylor & Francis Ltd |
| Publisher_xml | – name: Taylor & Francis – name: Taylor & Francis Ltd |
| References | CIT0074 Kittel C. (CIT0075) 1987 CIT0073 CIT0076 CIT0078 CIT0111 CIT0077 CIT0110 Schwinger J. (CIT0067) 2001 CIT0113 CIT0079 CIT0112 CIT0115 CIT0114 CIT0117 CIT0116 CIT0119 CIT0118 CIT0083 CIT0082 CIT0085 CIT0084 CIT0087 CIT0001 CIT0089 CIT0122 CIT0088 CIT0121 CIT0081 CIT0080 Ortiz G. (CIT0063) 2012 Sewell G. (CIT0039) 2002 Maldacena J. M. (CIT0008) 1998; 2 CIT0003 Nahin P. J. (CIT0026) 2002 CIT0123 CIT0005 CIT0126 CIT0004 CIT0125 CIT0007 CIT0128 CIT0006 CIT0127 CIT0009 CIT0129 CIT0094 CIT0093 CIT0096 CIT0095 CIT0098 CIT0131 CIT0130 CIT0012 CIT0133 CIT0011 CIT0132 Bredon G. E. (CIT0028) 1993 CIT0090 CIT0092 CIT0091 CIT0014 CIT0135 CIT0013 CIT0016 CIT0137 CIT0015 CIT0136 CIT0018 CIT0139 CIT0017 CIT0138 CIT0019 Suzuki M. (CIT0120) 1993 CIT0140 CIT0021 CIT0142 CIT0020 Wen X.-G. (CIT0134) 2004 CIT0141 CIT0023 CIT0144 CIT0022 CIT0143 Henkel M. (CIT0070) 1999 CIT0025 CIT0146 CIT0024 CIT0027 CIT0148 CIT0147 CIT0149 CIT0030 CIT0151 Rotman J. J. (CIT0071) 1999 CIT0150 CIT0032 CIT0031 CIT0034 CIT0033 Sunder V. S. (CIT0044) 1997 Schulman L. S. (CIT0058) 2005 Takahashi Y. (CIT0097) 1969 CIT0036 David Mermin N. (CIT0086) 2007 CIT0035 CIT0037 Dirac P. A.M. (CIT0002) 1982 CIT0043 CIT0042 CIT0045 Martin P. (CIT0072) 1991 von Neumann J. (CIT0038) 1938; 6 Barton G. (CIT0040) 1963 Kadanoff L. P. (CIT0041) 1966; 44 CIT0047 CIT0046 CIT0049 CIT0048 CIT0050 CIT0052 CIT0051 CIT0054 CIT0053 CIT0056 CIT0055 CIT0057 CIT0061 CIT0060 CIT0062 CIT0065 CIT0100 CIT0066 Fradkin E. (CIT0099) 1991 Baxter R. J. (CIT0029) 2007 Terras A. (CIT0145) 1999 Berezinskii V. L. (CIT0064) 1971; 32 CIT0109 Witten E. (CIT0010) 1998; 2 Rivers R. J. (CIT0059) 1988 CIT0069 CIT0102 CIT0068 CIT0101 CIT0104 CIT0103 CIT0106 CIT0105 CIT0108 CIT0107 |
| References_xml | – ident: CIT0118 doi: 10.1088/0022-3719/5/11/004 – volume-title: Fourier Analysis on Finite Groups and Applications year: 1999 ident: CIT0145 doi: 10.1017/CBO9780511626265 – ident: CIT0102 doi: 10.1103/PhysRev.131.2766 – volume-title: Functional Analysis, Spectral Theory year: 1997 ident: CIT0044 doi: 10.1007/978-93-80250-90-8 – ident: CIT0019 doi: 10.1103/PhysRevB.72.045137 – ident: CIT0004 doi: 10.1103/PhysRev.60.252 – ident: CIT0078 doi: 10.1016/0375-9601(84)90816-8 – volume-title: Quantum Monte Carlo Methods in Condensed Matter Physics year: 1993 ident: CIT0120 doi: 10.1142/2262 – ident: CIT0036 doi: 10.1103/PhysRevLett.46.379 – ident: CIT0065 doi: 10.1088/0022-3719/6/7/010 – ident: CIT0138 – ident: CIT0006 doi: 10.1103/RevModPhys.52.453 – ident: CIT0023 doi: 10.1103/PhysRevLett.86.1082 – ident: CIT0017 doi: 10.1209/0295-5075/84/36005 – ident: CIT0030 doi: 10.1017/S0305004100027419 – volume: 2 start-page: 253 year: 1998 ident: CIT0010 publication-title: Adv. Theor. Math. Phys. doi: 10.4310/ATMP.1998.v2.n2.a2 – ident: CIT0109 doi: 10.1016/0003-4916(62)90232-4 – ident: CIT0141 doi: 10.1073/pnas.0803726105 – ident: CIT0031 doi: 10.1016/0031-8914(73)90381-9 – ident: CIT0081 doi: 10.1103/PhysRevB.71.195120 – ident: CIT0132 doi: 10.1103/PhysRevD.25.1587 – volume-title: Topology and Geometry year: 1993 ident: CIT0028 doi: 10.1007/978-1-4757-6848-0 – ident: CIT0003 doi: 10.1088/0305-4470/30/18/005 – ident: CIT0056 doi: 10.1016/0550-3213(80)90403-4 – ident: CIT0148 doi: 10.1088/0034-4885/70/6/R03 – ident: CIT0011 doi: 10.1016/S0370-1573(99)00083-6 – volume-title: Introduction to Advanced Field Theory year: 1963 ident: CIT0040 – ident: CIT0114 doi: 10.1103/RevModPhys.36.856 – volume-title: Techniques and Applications of Path Integration year: 2005 ident: CIT0058 – ident: CIT0094 doi: 10.1016/0550-3213(94)90230-5 – ident: CIT0088 doi: 10.1103/PhysRevB.77.064302 – ident: CIT0137 doi: 10.1103/PhysRevLett.96.110405 – ident: CIT0108 doi: 10.1103/PhysRev.115.485 – ident: CIT0005 doi: 10.1103/PhysRev.65.117 – volume: 2 start-page: 231 year: 1998 ident: CIT0008 publication-title: Adv. Theor. Math. Phys. doi: 10.4310/ATMP.1998.v2.n2.a1 – ident: CIT0009 doi: 10.1016/S0370-2693(98)00377-3 – ident: CIT0119 doi: 10.1063/1.523343 – ident: CIT0016 doi: 10.1103/PhysRevB.79.214440 – ident: CIT0080 doi: 10.1126/science.288.5465.462 – ident: CIT0151 doi: 10.1017/CBO9780511470783 – volume-title: Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age year: 2002 ident: CIT0026 doi: 10.56021/9780801869099 – ident: CIT0047 doi: 10.1063/1.1665530 – ident: CIT0027 doi: 10.1103/RevModPhys.17.50 – ident: CIT0073 doi: 10.1103/PhysRevB.24.218 – ident: CIT0091 doi: 10.1016/0550-3213(79)90595-9 – ident: CIT0144 – ident: CIT0066 doi: 10.1007/BF01208273 – ident: CIT0135 doi: 10.1103/RevModPhys.80.1083 – ident: CIT0142 doi: 10.1103/PhysRevLett.94.040402 – ident: CIT0149 doi: 10.1007/978-1-4613-0097-7 – ident: CIT0096 doi: 10.1103/PhysRevLett.3.296 – ident: CIT0130 doi: 10.1103/PhysRevB.75.144401 – ident: CIT0046 doi: 10.1103/RevModPhys.63.1 – ident: CIT0129 doi: 10.1088/1742-5468/2005/09/P09012 – ident: CIT0014 doi: 10.1103/PhysRevLett.94.111601 – ident: CIT0082 doi: 10.1103/PhysRevB.80.081104 – ident: CIT0052 doi: 10.1007/978-1-4612-0869-3 – ident: CIT0037 doi: 10.1016/0003-4916(70)90270-8 – ident: CIT0021 doi: 10.1093/acprof:oso/9780199577224.001.0001 – ident: CIT0133 doi: 10.1016/j.nuclphysb.2004.12.016 – ident: CIT0150 doi: 10.1016/0370-1573(74)90023-4 – ident: CIT0077 doi: 10.1016/j.nuclphysb.2005.04.003 – ident: CIT0127 doi: 10.1016/0370-2693(92)90168-4 – ident: CIT0024 doi: 10.1103/PhysRevB.3.3918 – ident: CIT0007 doi: 10.1007/BF01089192 – volume: 6 start-page: 1 year: 1938 ident: CIT0038 publication-title: Compos. Math. – ident: CIT0121 doi: 10.1103/PhysRevB.24.5229 – ident: CIT0055 doi: 10.1103/PhysRevB.80.104413 – ident: CIT0020 doi: 10.1016/j.aop.2008.11.002 – volume-title: Quantum Field Theory of Many-Body Systems year: 2004 ident: CIT0134 – ident: CIT0013 doi: 10.1201/b10273 – ident: CIT0049 doi: 10.1088/1751-8113/41/7/075001 – ident: CIT0100 doi: 10.1017/CBO9780511622625 – ident: CIT0107 doi: 10.1016/0550-3213(78)90153-0 – ident: CIT0025 doi: 10.1103/PhysRevD.19.3682 – volume-title: 40 Years of the Berezinskii–Kosterlitz–Thouless Theory year: 2012 ident: CIT0063 – ident: CIT0050 doi: 10.1016/j.aop.2006.05.007 – ident: CIT0068 doi: 10.1103/PhysRevD.19.3698 – ident: CIT0061 doi: 10.1088/0305-4470/13/4/037 – ident: CIT0001 doi: 10.1063/1.881616 – ident: CIT0035 doi: 10.1103/RevModPhys.51.659 – ident: CIT0051 doi: 10.1088/0305-4470/27/4/008 – ident: CIT0087 doi: 10.1016/S0003-4916(02)00018-0 – ident: CIT0101 doi: 10.1063/1.1704281 – ident: CIT0111 doi: 10.1088/0305-4470/20/9/043 – volume-title: Exactly Solved Models in Statistical Mechanics year: 2007 ident: CIT0029 – ident: CIT0093 doi: 10.1016/0550-3213(92)90269-H – ident: CIT0131 doi: 10.1103/PhysRevB.82.060411 – ident: CIT0089 – volume: 32 start-page: 493 year: 1971 ident: CIT0064 publication-title: Sov. Phys. JETP – ident: CIT0105 doi: 10.1016/0550-3213(78)90502-3 – volume: 44 start-page: 276 year: 1966 ident: CIT0041 publication-title: Nuovo Cimento doi: 10.1007/BF02710808 – ident: CIT0043 – ident: CIT0076 doi: 10.1103/PhysRevLett.93.047003 – ident: CIT0123 doi: 10.1103/PhysRevD.72.054509 – ident: CIT0079 doi: 10.1070/PU1982v025n04ABEH004537 – volume-title: Potts Models and Related Problems in Statistical Mechanics year: 1991 ident: CIT0072 doi: 10.1142/0983 – ident: CIT0092 doi: 10.1016/0550-3213(94)90093-0 – ident: CIT0116 doi: 10.1103/PhysRevB.2.723 – ident: CIT0147 doi: 10.1016/S0550-3213(00)00770-7 – volume-title: Path Integral Methods in Quantum Field Theory year: 1988 ident: CIT0059 – ident: CIT0106 doi: 10.1016/0550-3213(78)90382-6 – ident: CIT0115 doi: 10.1063/1.1665111 – ident: CIT0117 doi: 10.1088/0305-4470/16/12/004 – ident: CIT0033 doi: 10.1016/0370-2693(79)91269-3 – ident: CIT0126 doi: 10.1103/PhysRevLett.63.322 – ident: CIT0015 doi: 10.1103/PhysRevLett.104.020402 – ident: CIT0139 – ident: CIT0122 doi: 10.1016/j.physletb.2004.10.042 – ident: CIT0146 doi: 10.1017/CBO9780511600722 – volume-title: Quantum Mechanics and Its Emergent Macrophysics year: 2002 ident: CIT0039 doi: 10.1515/9780691221274 – ident: CIT0057 doi: 10.1142/9789812799838 – ident: CIT0083 doi: 10.1016/0003-4916(78)90252-X – ident: CIT0140 doi: 10.1103/PhysRevLett.92.107902 – ident: CIT0032 doi: 10.1063/1.522914 – ident: CIT0054 doi: 10.1103/PhysRevLett.61.2376 – ident: CIT0048 doi: 10.1016/j.aop.2005.10.005 – volume-title: The Principles of Quantum Mechanics year: 1982 ident: CIT0002 – ident: CIT0090 doi: 10.1016/0370-2693(77)90076-4 – ident: CIT0042 doi: 10.2307/1968693 – ident: CIT0112 doi: 10.1103/PhysRevD.21.2316 – volume-title: Conformal Invariance and Critical Phenomena year: 1999 ident: CIT0070 doi: 10.1007/978-3-662-03937-3 – ident: CIT0095 doi: 10.1016/0370-2693(95)00777-I – ident: CIT0136 doi: 10.1103/PhysRevLett.96.110404 – ident: CIT0045 doi: 10.1103/PhysRevD.25.1103 – ident: CIT0143 doi: 10.1016/j.aop.2010.11.002 – volume-title: Quantum Mechanics: Symbolism of Atomic Measurements year: 2001 ident: CIT0067 doi: 10.1007/978-3-662-04589-3 – volume-title: Introduction to Field Quantization year: 1969 ident: CIT0097 – volume-title: Field Theories of Condensed Matter Systems year: 1991 ident: CIT0099 – ident: CIT0110 doi: 10.1142/9789812832870 – ident: CIT0069 doi: 10.1088/1751-8113/40/49/006 – ident: CIT0074 doi: 10.1016/0550-3213(85)90350-5 – ident: CIT0128 doi: 10.1103/PhysRevE.51.1004 – ident: CIT0012 doi: 10.1103/PhysRevD.75.085020 – ident: CIT0062 doi: 10.1088/0953-8984/20/27/275233 – ident: CIT0018 – ident: CIT0060 doi: 10.1143/PTP.56.1454 – ident: CIT0034 doi: 10.1103/PhysRevD.19.3715 – volume-title: Quantum Theory of Solids year: 1987 ident: CIT0075 – ident: CIT0084 doi: 10.1103/PhysRevD.10.2445 – ident: CIT0098 doi: 10.1016/0370-1573(76)90052-1 – ident: CIT0022 doi: 10.1103/PhysRevD.17.2637 – ident: CIT0125 doi: 10.1088/0305-4470/38/21/001 – volume-title: Quantum Computer Science: An Introduction year: 2007 ident: CIT0086 doi: 10.1017/CBO9780511813870 – ident: CIT0113 doi: 10.1143/PTP.6.907 – ident: CIT0085 doi: 10.1103/PhysRevD.11.395 – ident: CIT0103 doi: 10.1088/1126-6708/2005/05/066 – ident: CIT0053 doi: 10.1103/PhysRevB.35.8865 – volume-title: An Introduction to the Theory of Groups year: 1999 ident: CIT0071 – ident: CIT0104 doi: 10.1007/BF01213610 |
| SSID | ssj0005713 |
| Score | 2.4207425 |
| SecondaryResourceType | review_article |
| Snippet | An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion... |
| SourceID | proquest pascalfrancis crossref informaworld |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 679 |
| SubjectTerms | 03.65.Fd Algebraic methods 05.30.-d Quantum statistical mechanics 05.50.+q Lattice theory and statistics 64.60.Cn Order-disorder transformations Algebra Algorithms bond algebras, operator algebras Bonding Classical and quantum physics: mechanics and fields dimensional reduction Exact sciences and technology fermionization field theory Gages gauge theories Gauges High temperature Lattice theory Logic, set theory, and algebra Low temperature Mapping Mathematical methods in physics Mathematical models Other topics in mathematical methods in physics Phase boundaries phase transitions Physics quantum and classical dualities Quantum mechanics Quantum physics statistical mechanics Transformations |
| Title | The bond-algebraic approach to dualities |
| URI | https://www.tandfonline.com/doi/abs/10.1080/00018732.2011.619814 https://www.proquest.com/docview/900916895 https://www.proquest.com/docview/963856726 |
| Volume | 60 |
| WOSCitedRecordID | wos000295451600001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAWR databaseName: Taylor and Francis Online Journals customDbUrl: eissn: 1460-6976 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0005713 issn: 0001-8732 databaseCode: TFW dateStart: 19520101 isFulltext: true titleUrlDefault: https://www.tandfonline.com providerName: Taylor & Francis |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8QwEA6yKHjxLa6rSw8evAQ2TZsmRxEXT4uHFfcW8oQFaWXb9fc76ctdRAW9FZq0zUwmmS-d-Qahm5Q7EROrcUK1CUc3DnPqKVxp8J9poiaW18UmstmMLxbiaSOLP4RVBgztG6KIeq0Oxq102UXEheQDwjMaNwScgAB4Xckadv5gmfPpy2eMR0baUmoEhx5d7tw3D9nam7aYS0PIpCpBar4pd_Fl5a63o-nh_wdyhA5aVzS6a-bOMdpx-Qnaq0NCTXmKbmEGRbrILQ6lQABUL03UMZBHVRHZOh0TgPYZep4-zO8fcVtXARsqWIVN7JknE8U0-FcAL4zxFl4dG-WVc8Q5T6nwxPM4IypVnDvrEkA2xCWUM03oORrkRe4uUGRTwYTixiobkA2BpqkRibFGZIbodIhoJ1FpWtLxUPviVZKem7SRgQwykI0Mhgj3vd4a0o1f2vNNZcmqPuxoVSXpz13HW4rt3xd49njC2RCNOk3L1rxLKcAzJYwLGF_U3wW7DD9bVO6KNTSBhS1lWcwu__5xI7QfdyGH5AoNqtXaXaNd814ty9W4nuofFPP3fQ |
| linkProvider | Taylor & Francis |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1bS8MwFA4yFX3xLs7p7IMPvhSWpk2TRxHHxDl8mLi3kOYCA2ll7fz9nvSmQ1QQ3wpN2uacXM6XfvkOQpcRMzzAOvFDkii3dWN8RiyBqwTiZxLKgWZlsol4MmGzGX-s2YR5Tat0GNpWQhHlXO0Gt9uMbihx7vQBZjEJKgVOgADMpbJej2CpdfL50-HzB8sjxnUyNey7Ks3puW-esrI6rWiXOtKkzMFutkp48WXuLhek4e4_NGUP7dTRqHdddZ99tGbSA7RZskJVfoiuoBN5SZZq32UDAVw9V14jQu4VmafLE5mAtY_Q0_B2ejPy69QKviKcFr4KLLV4IGkCIRYgDKWshlcHSlppDDbGEsIttiyIsYwkY0abEMANNiFhNMHkGHXSLDUnyNMRp1wypaV24AZD0UjxUGnFY4WTqItIY1Khat1xl_7iReBWnrSygXA2EJUNushva71Wuhu_lGefvSWKcr-j9pUgP1ftr3i2fZ-T2mMho13Ua1wt6hGeCw7BKaaMQ_u89i4MTfe_RaYmW0IRmNsiGgf09O8fd4G2RtOHsRjfTe57aDtoGIj4DHWKxdKcow31VszzRb_s9-_N7_un |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8QwEA6yPvDiW1xX1x48eClsmjZNjqIuirLsYcW9hTQPWJB22Xb9_U760kVU0FuhSdPMTNL50plvELqMmOEB1okfkkS5oxvjM2IJXCXgP5NQDjQri03EoxGbTvn4Uxa_C6t0GNpWRBHlXu0W91zbJiLOJR9gFpOgIuAEBMBcJet18Jyps_HJ8OUjyCPGdS017LsuTfLcN09Z-TitUJe6mEmZg9hsVe_iy9Zdfo-Gu_-fyR7aqX1R77oynn20ZtIDtFnGhKr8EF2BCXlJlmrf1QIBVD1TXkNB7hWZp8t8TEDaR-h5eDe5uffrwgq-IpwWvgostXggaQIOFuALpayGoQMlrTQGG2MJ4RZbFsRYRpIxo00I0AabkDCaYHKMOmmWmhPk6YhTLpnSUjtog6FppHiotOKxwknURaSRqFA167grfvEqcEtOWslAOBmISgZd5Le95hXrxi_t2WdliaI87ahVJcjPXfsrim3Hc0R7LGS0i3qNpkW9vnPBwTXFlHGYn9fehYXp_rbI1GRLaAI7W0TjgJ7-_eUu0Nb4diieHkaPPbQdNOGH-Ax1isXSnKMN9VbM8kW_tPp30KL6WQ |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=The+bond-algebraic+approach+to+dualities&rft.jtitle=Advances+in+physics&rft.au=Cobanera%2C+Emilio&rft.au=Ortiz%2C+Gerardo&rft.au=Nussinov%2C+Zohar&rft.date=2011-10-01&rft.pub=Taylor+%26+Francis&rft.issn=0001-8732&rft.eissn=1460-6976&rft.volume=60&rft.issue=5&rft.spage=679&rft.epage=798&rft_id=info:doi/10.1080%2F00018732.2011.619814&rft.externalDocID=619814 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0001-8732&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0001-8732&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0001-8732&client=summon |