CONSTRUCTION OF THE PERTURBATION SERIES FOR TRANSITION AMPLITUDES FROM THEIR ANALYTICITY AND UNITARITY PROPERTIES

Journal Article · Tue Sep 15 04:00:00 EDT 1959 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.115.1752· OSTI ID:4224748

Mandelstam, S

The analyticity properties of transition amplitudes are used in conjunction with the unitarity requirements to generate successive terms in the perturbation series, without referring to a specific Lagrangian. In the sixth and higher orders, production is neglected in the unitarity condition, subject to this approximation, it is found that the series can be so constructed. No analyticity properties which have not been rigorously proved need be employed, and the terms are found to satisfy the double dispersion representation. By examining the connection between this method and the conventional calculation oi the perturbation series, the types of spectral function corresponding to different Feynman diagrams can be found. Formulas are given for the regions in which the spectral functions are nonzero. (auth)

• Research Organization: Univ. of California, Berkeley
• NSA Number: NSA-14-004082
• OSTI ID: 4224748
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 115; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

DISPERSION RELATIONS
ELEMENTARY PARTICLES
FEYNMAN DIAGRAM
FIELD THEORY
INTERACTIONS
MANDELSTAM REPRESENTATION
MATRICES
PERTURBATION THEORY
PHYSICS
S- MATRIX
SCATTERING
UNITARITY