open access

https://hdl.handle.net/2115/65804

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

英語

Weyl representation

2016-05

World Scientific

Reviews in Mathematical Physics

28(4)

1650007

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.

学術雑誌論文

Accepted Manuscript

Electronic version of an article published as Rev. Math. Phys., 28, 1650007 (2016) DOI:10.1142/S0129055X16500070 Copyright© 2016 World Scientific Publishing Co. http://www.worldscientific.com/worldscinet/rmp

0129-055X

1793-6659