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Why fields carrying spin cannot obtain non-zero vacuum expectation value in a Lorentz invariant theory?

Qmechanic
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joginder goswami
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1 Answers1

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A field that carries spin indices is not invariant with respect to Lorentz transforms. Therefore, if such a field has a vacuum expectation value, then the vacuum would carry spin indices. With every continuous symmetry, there is an associated conserved quantity, according to Noether's theorem. If the vacuum carries spin indices then the conserved quantities associated with Lorentz invariance can flow into the vacuum. As a result, these quantities would not be conserved. Therefore, the symmetries would be spontaneously broken. Does that make sense?

flippiefanus
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