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Author Zwanziger, D.
Source United States Department of Energy Office of Scientific and Technical Information
Content type Text
Language English
Subject Keyword PHYSICS ♦ ELEMENTARY PARTICLES ♦ FIELD THEORY ♦ GAUGE INVARIANCE ♦ GROUP THEORY ♦ INVARIANCE PRINCIPLE ♦ LORENTZ GROUP ♦ LORENTZ TRANSFORMATIONS ♦ MATRICES ♦ MOMENTUM ♦ PHOTONS ♦ POLARIZATION ♦ QUANTUM MECHANICS ♦ RELATIVITY THEORY ♦ S- MATRIX ♦ SCATTERING ♦ SPIN ♦ VECTORS
Abstract The fundamental statement of relativistic invariance for scattering amplitudes is that the amplitude remains invariant when the momentum and spin variables of each particle are transformed according to the corresponding irreducible, unitary representation of the inhomogeneous Lorentz group. To construct an amplitude'' is to find the most general function that has the required transformation properties. This construction, which had been previously effected for any number of massive particles of arbitrary spin, is extended to include massless particles of arbitrary spin as well. In the case of photons, the resulting formalisni is compared with the usual one that makes use of transverse polarization vectors and a gauge-invariance condition. The two formalisms are proven to be equivalent. It is concluded that the gauge condition is superfluous as an independent physical principle for the purpose of constructing amplitudes. Its use in the conventional formalism is simply a way of imposing the Lorentz-transformation properties appropriate to massless particles. The known analogous construction for massive spin-one particles is shown to be equivalent to the usual formalism, and the requirement of Lorentz invariance is shown to be equivalent to the usual prescription for virtual photons as well. (auth)
ISSN 0031899X
Educational Use Research
Learning Resource Type Article
Publisher Date 1964-02-24
Publisher Department Istituto Nazionale di Fisica Nucleare, Rome and Universita, Rome
Journal Physical Review
Volume Number 133
Organization Istituto Nazionale di Fisica Nucleare, Rome and Universita, Rome


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