A family of inequivalent Weyl representations of canonical commutation relations with applications to quantum field theory

作者：Arai Asao^*

来源：Reviews in Mathematical Physics, 2016, 28(4): 1650007.

DOI：10.1142/S0129055X16500070

• Boson Fock space
• canonical commutation relations
• inequivalent representation
• quantum field
• time-zero field
• Weyl representation

We consider a family of irreducible Weyl representations of canonical commutation relations with infinite degrees of freedom on the abstract boson Fock space over a complex Hilbert space. Theorems on equivalence or inequivalence of the representations are established. As a simple application of one of these theorems, the well-known inequivalence of the time-zero field and conjugate momentum for different masses in a quantum scalar field theory is rederived with space dimension d >= 1 arbitrary. Also a generalization of representations of the time-zero field and conjugate momentum is presented. Comparison is made with a quantum scalar field in a bounded region in R-d. It is shown that, in the case of a bounded space region with d = 1, 2, 3, the representations for different masses turn out to be mutually equivalent.

• 出版日期2016-5