On the Representation of the Canonical Commutation Relation of Bose Fields

1 June 1960

journal article
Published by Oxford University Press (OUP) in Progress of Theoretical Physics

Vol. 23 (6) , 989-1002
https://doi.org/10.1143/ptp.23.989

Abstract

A presentation of the canonical commutation relation of Bose fields is given in a way which is independent of the choice of the bases of the test functions and covariant with respect to the Euclidean transformation of the coordinate system. It is shown that the representation is characterized by an integral on the conjugate space L^* of the space L of the test functions and a real function on Σ⊗L^* where Σ is the group of the transformations f→u^-1f+φ; fεL^*, φεL and u is a Euclidean transformation of L^*. The conditions for the irreducibility of a representation and the unitary equivalence of the representations and the existence of unique vacuum state are given. An example of the inequivalent Euclidean covariant irreducible representations containing unique vacuum state is given.

Keywords

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