Functional Methods

  • Michael Stone
Part of the Graduate Texts in Contemporary Physics book series (GTCP)


In this chapter we will introduce some useful functional that are analogous to thermodynamic potentials. We will use them to investigate spontaneous symmetry breaking and Goldstone’s theorem.


Ward Identity Goldstone Boson Functional Method Spontaneous Symmetry Breaking Free Energy Density 
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  1. 1.
    This latter effect will always occur in simple quantum-mechanical systems since the ground state is always nondegenerate. To illustrate this point consider a particle of mass M free to move on a circle. The eigenfunctions are corresponding to A state corresponding to the particle sitting at a definite angle can only be an eigenstate if. Similarly, tunneling will restore the symmetry in the discrete double-well case.Google Scholar
  2. 2.
    Note the difference between the relativistically invariant sytem we are considering here and the nonrelativistic Bose system we considered in chapter 12. The latter does not have distinct radial and tangential modes.Google Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Michael Stone
    • 1
  1. 1.Loomis Laboratory Department of PhysicsUniversity of IllinoisUrbanaUSA

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