Derives the elastic two-body unitarity relation for anisotropic scalar fields with different sound speeds, verifies it at one loop in a quartic model, and shows anisotropy modifies the radiatively generated scalon mass while leaving the Gildener-Weinberg flat direction unchanged.
Dimensional Reduction of a Lorentz and CPT-violating Maxwell-Chern-Simons Model
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abstract
Taking as starting point a Lorentz and CPT non-invariant Chern-Simons-like model defined in 1+3 dimensions, we proceed realizing its dimensional reduction to D=1+2. One then obtains a new planar model, composed by the Maxwell-Chern-Simons (MCS) sector, a Klein-Gordon massless scalar field, and a coupling term that mixes the gauge field to the external vector, $v^{\mu}$. In spite of breaking Lorentz invariance in the particle frame, this model may preserve the CPT symmetry for a single particular choice of $v^{\mu}$. Analyzing the dispersion relations, one verifies that the reduced model exhibits stability, but the causality can be jeopardized by some modes. The unitarity of the gauge sector is assured without any restriction, while the scalar sector is unitary only in the space-like case. PACS numbers: 11.10.Kk; 11.30.Cp; 11.30.Er; 12.60.-i
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Disparity in sound speeds: implications for elastic unitarity and the effective potential in quantum field theory theory
Derives the elastic two-body unitarity relation for anisotropic scalar fields with different sound speeds, verifies it at one loop in a quartic model, and shows anisotropy modifies the radiatively generated scalon mass while leaving the Gildener-Weinberg flat direction unchanged.