Nonrelativistic Theorem Analogous to the Goldstone Theorem

Publisher Website
Google Scholar
Abstract
The Goldstone theorem states that a relativistic theory with a broken symmetry must have a zero-mass particle. In this context, broken symmetry means that the vacuum state is not invariant under the continuous group of transformations generated by the total charge operator referring to some microscopically conserved current. We prove that if the ground state in a nonrelativistic theory lacks such invariance, there will exist an excitation with zero energy in the long-wavelength limit, so long as the interactions in the theory have finite range. For purposes of demonstration the Heisenberg model of ferromagnetism is employed, but the theorem holds for other nonrelativistic broken-symmetry theories as well. Special care is given the limiting procedures involved in the proof so that ambiguities found in previous work on this question are avoided.

This publication has 10 references indexed in Scilit: