WIGHTMAN FUNCTIONS, RETARDED FUNCTIONS AND THEIR ANALYTIC CONTINUATIONS

Journal Article · Sun Jan 01 04:00:00 EST 1961 · Progr. Theoret. Phys. (Kyoto)

DOI:https://doi.org/10.1143/PTPS.18.83· OSTI ID:4070237

Araki, H

Recent studies on the analyticity of the general n-point Wightman functions and the retarded functions in quantum field theory are reviewed. According to Wightman, the conventional axiom of quantum field theory is transcribed into an eqivalent set of properties of the Wightman functions. It is then shown that the Wightman functions are boundary values of analytic functions in complex ccordinate spaces and the linear propenties of the Wightman functions are transcribed into an equivalent requirement on domains of analyticity of these analytic functions. For the study of retarded functions, the contributions of vacuu intermediate states are systematically subtracted from th Wightman functions. The truncated Wightman functions thus obtained have the same linear propenties as those of the Wightman functions except for a smaller support in th momentum space. A generalization of theta -function (the step function of Heaviside) to the characteristic function of a convex polyhedral cone in an n- dimensional vector space is defined and is used to define the generalized retarded functions. The properties of the latter that are equivalent to the linear propenties of the Wightman functions are stated. It is then shown that the generalized retarded func tions are boundary values of analytic functions in complex momentum spaces, and a part of the properties of the former are transcribed into an equivalent requirement on domains of analyticity of the latter. The whole discussion is carried out regardless of the choice between local commutativity and anticommutativity. The problem of obtainin the envelope of holomorphic remains unsolved. (auth)

• Research Organization: Kyoto Univ.
• Sponsoring Organization: USDOE
• NSA Number: NSA-18-015000
• OSTI ID: 4070237
• Journal Information: Progr. Theoret. Phys. (Kyoto), Journal Name: Progr. Theoret. Phys. (Kyoto) Vol. Vol: Suppl., No. 18
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ANALYTIC FUNCTIONS
FIELD THEORY
MATHEMATICS
MOMENTUM
PHYSICS
QUANTUM MECHANICS
VACUUM
VECTORS
WIGHTMAN FUNCTIONS