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Invariant Forms of the Lorentz Group
Author(s) -
LazoTueve D.,
Rühl W.
Publication year - 1980
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.19800280203
Subject(s) - multilinear map , invariant (physics) , mathematics , covariant transformation , pure mathematics , lorentz group , harmonic function , mathematical physics , lorentz transformation , lorentz covariance , mathematical analysis , physics , quantum mechanics
We study trilinear and multilinear invariant forms for the homogeneous Lorentz group. The residues of these trilinear forms generate particular trilinear forms themselves. They appear also if we sum Taylor expansions partially into a series of expressions each of which is covariant under infinitesimal Lorentz transformations. Multilinear invariant forms are submitted to harmonic analysis in different channels. They are thus expressed by invariant functions. Invariant functions for different channels are related by integral equations involving 6χ‐symbols, 9χ‐symbols etc. as “crossing kernels”. It is shown by construction that all invariant functions and n χ‐symbols can be represented as finite sums of Barnes type integrals. As example we analyze explicitly the four‐point Schwinger function of the massless Euclidean Thirring field with arbitrary spin and dimension.