ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract Recent results on the structure of theS matrix at them-particle threshold (m≧2) in a simplifiedm→m scattering theory with no subchannel interaction are extended to the Green functionF on the basis of off-shell unitarity, through an adequate mathematical extension of some results of Fredholm theory: local two-sheeted or infinite-sheeted structure ofF arounds=(mμ)2 depending on the parity of (m−1)(ν−1) (where μ〉0 is the mass and ν is the dimension of space-time), off-shell definition of the irreducible kernelU which is the analogue of theK matrix in the two different parity cases (m−1)(ν−1) odd or even, and related local expansion ofF, for (m−1)(ν−1) even, in powers of σβ ln σ(σ=(mμ)2−s). It is shown that each term in this expansion is the dominant contribution to a Feynman-type integral in which each vertex is a kernelU. The links between the kernelU and Bethe-Salpeter type kernelsG of the theory are exhibited in both parity cases, as also the links between the above expansion ofF and local expansions, in the Bethe-Salpeter type framework, ofF λ in terms of Feynman-type integrals in which each vertex is a kernelG and which include both dominant and subdominant contributions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01209478
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