Alternative Frenkel liquid Lagrangian

Abstract

Based on the Caldirola-Kanai approach, we endeavor to investigate a dissipative Lorentz Breaking scalar field theory in Minkowski space–time. We present its free-particle solutions for complex ${\omega }^{\mu }$ components. We find three profiles of dispersion relations, two of them support gapped-momentum states. We also present an alternative view of this model, where dissipation acts as a geometric effect, and an effective negative scalar curvature space–time emerges. Finally, we also illustrate how the present model could be adapted to describe shear waves in Frenkel liquids and and its quantization process in order to compare with Trachenko’s original field theory.