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TMF, 1973, Volume 15, Number 3, Pages 320–331 (Mi tmf3672)  

Consequences of the convexity of Legendre transformations (generalized Goldstone theorem)

A. N. Vasil'ev

Leningrad State University

Abstract: Some consequences of the already proven convexity of Legendre transformations are analyzed. Different possible behaviors of a system are considered; in particular, degeneracy and a phase transition. A generalization of Goldstone's theorem [1, 2] is proved: in every theory with continuous degeneracy of the solution, zero-mass particles are present. Spontaneous breaking of continuous symmetry automatically leads to Continuous degeneracy, which explains why zero-mass particles arise in theories with broken symmetry.

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English version:
Theoretical and Mathematical Physics, 1973, 15:3, 550–558

Received: 10.03.1972

Citation: A. N. Vasil'ev, “Consequences of the convexity of Legendre transformations (generalized Goldstone theorem)”, TMF, 15:3 (1973), 320–331; Theoret. and Math. Phys., 15:3 (1973), 550–558

Citation in format AMSBIB
\Bibitem{Vas73}
\by A.~N.~Vasil'ev
\paper Consequences of the convexity of Legendre transformations (generalized Goldstone theorem)
\jour TMF
\yr 1973
\vol 15
\issue 3
\pages 320--331
\mathnet{http://mi.mathnet.ru/tmf3672}
\transl
\jour Theoret. and Math. Phys.
\yr 1973
\vol 15
\issue 3
\pages 550--558
\crossref{https://doi.org/10.1007/BF01094561}


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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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