Spontaneous Lorentz violation and nonpolynomial interactions
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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, B. & Kostelecký, V.A. (2005). Spontaneous Lorentz violation and nonpolynomial interactions. Physics Letters B, 628(1–2), 106–112. http://dx.doi.org/10.1016/j.physletb.2005.09.018