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Teoreticheskaya i Matematicheskaya Fizika, 1970, Volume 5, Number 3, Pages 343–355 (Mi tmf4213)  

Physical symmetries in field theory

Ya. Lopushanski
References:
Abstract: Results obtained previously by the author [1] [Commun. Math. Phys., 12, 80 (1969); 14, 158 (1969)] are extended to the more general case of several fields with an arbitrary transformation law under the Poincare group with several nonvanishing masses. Bound states are also taken into account. A number of locally conserved tensor currents corresponding to physical symmetries are considered. The main result is the proof of the assertion that the free fields obtained by a symmetry transformation from the asymptotic fields and the asymptotic fields are connected by a linear transformation. This assertion can be interpreted as a proof that nonlinear $n$-dimensional realizations of a symmetry group for which there do not exist linear $n$-dimensional representations of the group cannot be realized if there is a mass gap in a theory with interaction. This result indicates that nonlinear realizations are intimately connected with the presence of particles of vanishing mass subject to the condition that the fields and currents remain local and the charges are translationally invariant.
Received: 16.03.1970
English version:
Theoretical and Mathematical Physics, 1970, Volume 5, Issue 3, Pages 1193–1202
DOI: https://doi.org/10.1007/BF01035250
Language: Russian
Citation: Ya. Lopushanski, “Physical symmetries in field theory”, TMF, 5:3 (1970), 343–355; Theoret. and Math. Phys., 5:3 (1970), 1193–1202
Citation in format AMSBIB
\Bibitem{Lop70}
\by Ya.~Lopushanski
\paper Physical symmetries in field theory
\jour TMF
\yr 1970
\vol 5
\issue 3
\pages 343--355
\mathnet{http://mi.mathnet.ru/tmf4213}
\transl
\jour Theoret. and Math. Phys.
\yr 1970
\vol 5
\issue 3
\pages 1193--1202
\crossref{https://doi.org/10.1007/BF01035250}
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