Inequivalent Representations of Canonical Commutation and Anti-Commutation Relations

• Mathematical Preliminaries.- Representations of Canonical Commutation Relations with Finite.- Aharonov–Bohm Effect and Inequivalent Representations of CCR.- Time Operators.- Representations of Canonical Anti-commutation Relations with Finite Degrees of Freedom.- Elements of the Theory of Boson Fock Spaces.- Elements of the Theory of Fermion Fock Spaces.- Representations of CCR with Infinite Degrees of Freedom.- Representations of CAR with Infinite Degrees of Freedom.- Physical Correspondences in Quantum Field Theory.

“The monograph under review gives a perspective on the various realizations of the canonical commutation/anti-commutation relations with finitely or infinitely many degrees of freedom. This is a welcome addition to the literature in this research area, which emphasizes the applications to quantum physics.” (Daniel Beltiţă, Mathematical Reviews, October, 2022)