Quadratic fock space calculus (I): some results on quadratic creation and preservation operators

This paper is a fundamental exploration of quantum theory within the quadratic Fock space in consistency with the quadratic quantization program, with a particular focus on two sets of operators that hold immense significance: the quadratic creation and preservation operators. In this paper, we high...

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Bibliographic Details
Published in:Quantum information processing Vol. 23; no. 3
Main Authors: Alzeley, Omar, Rebei, Habib, Rguigui, Hafedh
Format: Journal Article
Language:English
Published: New York Springer US 20.02.2024
Subjects:
Data Structures and Information Theory
Mathematical Physics
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum Physics
Spintronics
Quadratic Fock space
Quadratic exponential vector
Preservation operator
Mathematical operators
Creation operator
Quantum theory
ISSN:1573-1332, 1573-1332
Online Access:Get full text
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Summary:This paper is a fundamental exploration of quantum theory within the quadratic Fock space in consistency with the quadratic quantization program, with a particular focus on two sets of operators that hold immense significance: the quadratic creation and preservation operators. In this paper, we highlight a critical contribution to the quadratic quantization program. In which we prove that when the argument f is a real valued function, the quadratic preservation operator is symmetric and even essentially self-adjoint. This mathematical confirmation not only solidifies the foundations of quantum theory but also amplifies its practical applicability in real-world scenarios. In consistency with previous result, we give the exponential action of the creation operator on the domain of quadratic exponential vectors. This is an expansion of what obtained in Accardi, Ouerdiane, Rebei (Infin Dimens Anal Quantum Probab Relat Top 13(4):551–587, 2010) for the one-mode case.
ISSN:1573-1332
1573-1332
DOI:10.1007/s11128-024-04280-6