Abstract
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.
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Notes
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.
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.
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© 2000 Springer Science+Business Media New York
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Stone, M. (2000). Functional Methods. In: The Physics of Quantum Fields. Graduate Texts in Contemporary Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0507-4_13
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DOI: https://doi.org/10.1007/978-1-4612-0507-4_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6794-2
Online ISBN: 978-1-4612-0507-4
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