Theoretical analysis demonstrates counting rules and dispersion relations in non-Lorentz-invariant systems, highlighting the formation of canonically conjugate pairs.
Using the effective Lagrangian approach, we clarify general issues about Nambu-Goldstone bosons without Lorentz invariance. We show how to count their number and study their dispersion relations. Their number is less than the number of broken generators when some of them form canonically conjugate pairs. The pairing occurs when the generators have a nonzero expectation value of their commutator. For non-semi-simple algebras, central extensions are possible. The underlying geometry of the coset space in general is partially symplectic.
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Watanabe et al. (2012) studied this question.
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