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Gauge-noninvariant vector field theories with superficially nonrenormalizable nonpolynomial interactions are studied. We show that nontrivial relevant and stable theories have spontaneous Lorentz violation, and we present a large class of asymptotically free theories. The Nambu–Goldstone modes of these theories can be identified with the photon, with potential experimental implications.
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Altschul et al. (2005) studied this question.
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