ON THE ASYMPTOTIC CONDITIONS IN QUANTUM FIELD THEORY

Journal Article · Sat Jun 01 04:00:00 EDT 1957 · Progr. Theoret. Phys. (Japan)

DOI:https://doi.org/10.1143/PTP.17.765· OSTI ID:4344360

Nishijima, K

In this paper the so-called asymptotic conditions are introduced ln a different way than usually done, thereby making use of Helsenberg operators alone. These conditions are regarded as the defining equations for a complete set of state vectors, either incomimg or outgoing wave states. By closely examining the self-consistency of these defining equations, a set of integral equations for the vac uum expectation values of retarded products of operator is found. The unitarity condition of the S matrix is one o the inevitable consequences of these equations. These integral equations are essentially equivalent to those given by Chew and Low, and also independently by Lehmann, Symanzik, and Zimmermann. The advantage of the new integral equations over the older ones of the above men tioned authors consists in that the new ones are manife covariant in form and also in that all quantities appeari in the equations are related only to connected Feynman diagrams in contrast to the T products. The possibility extend the present formalism so as to include the bound states is also discussed. Finally it is shown ln the perturbation theory that these integral equations are satisfied only by the renormalized solutions of the renormalizable field theories provided that the microscopic causality condition is imposed as the boundary condition. (auth)

• Research Organization: Originating Research Org. not identified
• Sponsoring Organization: USDOE
• NSA Number: NSA-12-004008
• OSTI ID: 4344360
• Journal Information: Progr. Theoret. Phys. (Japan), Journal Name: Progr. Theoret. Phys. (Japan) Vol. Vol: 17
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BINDING ENERGY
BOUND STATE
EQUATIONS
EXPECTATION VALUE
FEYNMAN DIAGRAM
FIELD THEORY
INTERACTIONS
MATHEMATICS
MATRICES
PERTURBATION THEORY
PHYSICS
QUANTUM MECHANICS
S-MATRIX
SCATTERING
STATISTICS
VECTORS