Abstract
We consider two theories undergoing the same spontaneous symmetry breaking pattern but with different representations of an order parameter under the Lorentz group. The effective description of the first theory includes a massive Nambu-Goldstone field, while in the second example it is absent. Based on this, we clarify the physical meaning of massive Nambu-Goldstone fields as non-radial modes needed to describe the fluctuations of an order parameter. The connection with the inverse Higgs phenomenon is also discussed.
Highlights
It is known that in the case of spontaneous breakdown of spacetime symmetries some of the Nambu-Goldstone (NG) fields1 can be redundant or massive [1,2,3,4,5]
We consider two theories undergoing the same spontaneous symmetry breaking (SSB) pattern but with order parameters belonging to different representations of the spacetime symmetry group
The effective description of the first theory includes massive Nambu-Goldstone modes, while in the second example they are absent. Generalizing this observation, we conclude that mNG fields are present in an effective theory when they are needed to provide the full set of independent fluctuations of the vacuum
Summary
It is known that in the case of spontaneous breakdown of spacetime symmetries some of the Nambu-Goldstone (NG) fields can be redundant or massive [1,2,3,4,5]. We demonstrate that these two observations are closely related to each other For this purpose, we consider two theories undergoing the same spontaneous symmetry breaking (SSB) pattern but with order parameters belonging to different representations of the spacetime symmetry group. The effective description of the first theory includes massive Nambu-Goldstone (mNG) modes, while in the second example they are absent. Generalizing this observation, we conclude that mNG fields are present in an effective theory when they are needed to provide the full set of independent fluctuations of the vacuum.
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