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.
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
\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}
Linking options:
https://www.mathnet.ru/eng/tmf3672
https://www.mathnet.ru/eng/tmf/v15/i3/p320
This publication is cited in the following 1 articles:
Peter Millington, Paul M Saffin, “Vertex functions and their flow equations from the 2PI effective action”, J. Phys. A: Math. Theor., 55:43 (2022), 435402
Citation in format AMSBIB
Contact us: