Is It Physically Sound to Add a Topologically Massive Term to Three-Dimensional Massive Electromagnetic or Gravitational Models?

Abstract

The addition of a topologically massive term to an admittedly nonunitary three-dimensional massive model, be it an electromagnetic system or a gravitational one, does not cure its non-unitarity. What about the enlargement of avowedly unitary massive models by way of a topologically massive term? The electromagnetic models remain unitary after the topological augmentation but, surprisingly enough, the gravitational ones have their unitarity spoiled. Here we analyze these issues and present the explanation why unitary massive gravitational models, unlike unitary massive electromagnetic ones, cannot coexist from the viewpoint of unitarity with topologically massive terms. We also discuss the novel features of the three-term effective field models that are gauge-invariant.Topologically massive models; massive electromagnetic models; massive gravitational models; unitarity; effective field models.

Aspects of degrees of freedom in higher derivative massive electromagnetic theories

“…It has been proved [9,10] that only first term of the propagator, the -component ( 6 ) contributes to the current-current transition amplitude. Based on this result, we study the residues at each simple pole only of this component of the propagator, namely, we analyze the roots of the cubic equation.…”

“…In order to analyze whether the two models are plagued by tachyons and/or ghosts, we write the propagator associated with each theory and study the residues at each simple pole of the saturated propagator with external conserved currents [9,10].…”

A first-class approach of higher derivative Maxwell–Chern–Simons–Proca model

“…A generalization of the Proca action for a massive vector field with derivative self-interactions in D = 4 has been constructed in [35]. In [36][37][38][39][40] one finds higher derivative extensions that involve the Maxwell and/or Chern-Simons (CS) terms [28][29][30]. The Lagrangian of such model is the sum of Maxwell, CS, and higher derivative extensions of these terms.…”

“…The generalized MCS-Podolsky model [38,41] is a such theory and was introduced in order to smooth ultraviolet singularities. Starting from the observation that the study of Einstein-Chern-Simons-Proca massive gravity (ECSPMG) (the Lagrangian of ECSPMG is the sum of the Einstein, (third derivative order) CS and Procalike mass terms) [42] is often accompanied [39,40,43] by the analysis of the MCS-Proca model (a non-higher derivative model) [37,38,[43][44][45], we consider a model described by Lagrangian action containing the Maxwell term, a higher derivative extension of the CS topological invariant [36], and a Proca mass term…”

Boson-Boson Bound States in Higher-Derivative Electromagnetism Augmented by a Chern-Simons Term

“…Nonetheless, charged-scalar-boson -charged-scalar-boson bound states do exist in the framework of Mawell-Chern-Simons theory [2]. Interesting enough, numerical calculations show that there are also scalar Cooper pairs within the context of three-dimensional electromagnetism with a cutoff [3,4] (three-dimensional electromagnetism with higher derivatives) enlarged by a Chern-Simons term. The electromagnetic part of this model is defined by the Lagrangian…”