# Are Goldstone bosons necessarily spin-0 particles?

EDIT: Bosonic fields with spin $s>0$ transform non-trivially under Lorentz transformation. Hence, if any of them acquires a VEV, that would violate Lorentz invariance as I learnt from the posts 1 , 2 , and 3. Does it mean that Goldstone bosons, obtained after spontaneous symmetry breaking, are necessarily spin-0 particles in a theory which respects Lorentz invariance? If yes, does it mean that one can have $s>0$ bosonic Goldstone particles in non-relativistic field theories such as condensed matter systems?

• Jan 17, 2017 at 17:40
• @AccidentalFourierTransform Can Goldstone bosons be anything other than spin-0 bosons?
– SRS
Jan 17, 2017 at 17:46
• Ordinary continuous symmetry breaking leads to spin-0 Goldstone bosons. Supersymmetry breaking leads to spin-1/2 Goldstone fermions ("Goldstinos"). More generally, $p$-form symmetry breaking leads to $p$-form Goldstones (arxiv.org/abs/1412.5148v2). For example, U(1) gauge theory has a spontaneously broken 1-form global symmetry, whose Goldstone is the photon itself. Jan 17, 2017 at 19:27
• @SRS. It does not mean anything of the sort! You appear stymied by a a misconception that the field with the nontrivial v.e.v. is the Goldstone particle. Studying the SSB mechanism reminds you that this simply is not so. The goldstons of the σ-model are the πs, not the σ. Likewise in Susy-breaking models, you recall the vev particle is a scalar, but the goldstons are its former super partner fermions. Jan 17, 2017 at 22:12
• To have a vector goldston, however, you'd have to work harder, as you cannot transfer a scalar v.e.v. to the transform of a vector. So, you'd have to break spacetime symmetries, as is well-known. Jan 17, 2017 at 22:21

No. Magnons are spin-1 Goldstone bosons.

• But magnons only appear in a non-relativistic context, and OP is asking about "a theory which respects Lorentz invariance". This might seem to be a trivial requirement, but symmetry breaking and Lorentz symmetry are interrelated. (I'm not saying that the answer is bad; after all, OP chose to include the tag condensed-matter for some reason; I just think that it is important to emphasise the role of the Lorentz symmetry). Jan 21, 2017 at 10:05