PROOF OF DISPERSION RELATIONS FOR THE PRODUCTION OF PIONS BY REAL AND VIRTUAL PHOTONS AND FOR RELATED PROCESSES

Journal Article · Thu Jan 01 04:00:00 EST 1959 · Physical Review (U.S.) Superseded in part by Phys.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.113.371· OSTI ID:4270913

Oehme, R; Taylor, J G

It is shown that the amplitudes for the production of pions by photons and electrons (virtual photons) as well as for elastic photon-proton and photon- deuteron scattering, have certain analytic properties is functions of energy and momentum transfer. These properties are proven on the basis of the axioms of field theory, especically local commutativity and the spectral conditions. They guarantee the validity of the usual dispersion relations for restricted values of the invartiant momentum transfer. In the construction of these dispersion formulas the electromagnetic intcruction is treated in lowest order. The residua of the poles arising from the single-particle intermediate states are related to the corresponding vertex functions. For fixed values of the total energy the absorptive parts of the amplitudes are analytic functions of momentum transfer; they are regular inside certain ellipses. These properties make it possible to continue the absorptive parts into the "unphysical region" appearing in the nonforward dispersion relations by means of partialwave expansions. A brief survey is given of the limitiations in momentum transfer or the unphysical mass restrictions, which one encounters in the proof of dispersion relations for some elastic scattering processes. (auth)

• Research Organization: Univ. of Chicago; Univ. of Maryland, College Park
• NSA Number: NSA-13-010336
• OSTI ID: 4270913
• Journal Information: Physical Review (U.S.) Superseded in part by Phys.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 D, Journal Name: Physical Review (U.S.) Superseded in part by Phys.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: 113; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ABSORPTION
DEUTERONS
DISPERSION RELATIONS
ELECTROMAGNETISM
ELECTRONS
ENERGY
FIELD THEORY
INTERACTIONS
MOMENTUM
PERTURBATION THEORY
PHOTONS
PHYSICS AND MATHEMATICS
PIONS
PRODUCTION
PROTONS
QUANTUM MECHANICS
SCATTERING
SCATTERING AMPLITUDE