Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2011-09-28
Phys.Rev.D84:125013,2011
Physics
High Energy Physics
High Energy Physics - Phenomenology
9 pages, REVTeX 4.1; v2: Appendix D completely rewritten, numerous other minor modifications throughout the text
Scientific paper
10.1103/PhysRevD.84.125013
The low-energy physics of systems with spontaneous symmetry breaking is governed by the associated Nambu-Goldstone (NG) bosons. While NG bosons in Lorentz-invariant systems are well understood, the precise characterization of their number and dispersion relations in a general quantum many-body system is still an open problem. An inequality relating the number of NG bosons and their dispersion relations to the number of broken symmetry generators was found by Nielsen and Chadha. In this paper, we give a presumably first example of a system in which the Nielsen-Chadha inequality is actually not saturated. We suggest that the number of NG bosons is exactly equal to the number of broken generators minus the number of pairs of broken generators whose commutator has a nonzero vacuum expectation value. This naturally leads us to a proposal for a different classification of NG bosons.
Brauner Tomáš
Watanabe Haruki
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