The quantization of a vector model presenting spontaneous breaking of Lorentz symmetry in flat Minkowski spacetime is discussed. The Stueckelberg trick of introducing an auxiliary field along with a local symmetry in the initial Lagrangian is used to convert the second-class constraints present in the initial Lagrangian to first-class ones. An additional deformation is employed in the resulting Lagrangian to handle properly the first-class constraints, and the equivalence with the initial model is demonstrated using the BRST invariance of the deformed Lagrangian. The framework for performing perturbation theory is constructed and the structure of the Fock space is discussed. Despite the presence of ghost and tachyon modes in the spectrum of the theory, it is shown that one can implement consistent conditions to define a unitary and stable reduced Fock space. Within the restricted Fock space, the free model turns out to be equivalent to the Maxwell electrodynamics in the temporal gauge.Comment: Improved exposition; typos corrected; to be published in Phys. Rev. D; 34 page

We investigate the effects of (Curvature) 2 -and (Torsion) 2 -terms in the Einstein-Hilbert-Chern-Simons Lagrangian. The purposes are two-fold: (i) to show the efficacy of an orthogonal basis of degree-of-freedom projection operators recently proposed and to ascertain its adequacy for obtaining propagators of general parity-breaking gravity models in three dimensions; (ii) to analyze the role of the topological Chern-Simons term for the unitarity and the particle spectrum of the model squared-curvature terms in connection with dynamical torsion. Our conclusion is that the Chern-Simons term does not influence the unitarity conditions imposed on the parameters of the Lagrangian, but significantly modifies the particle spectrum. * Electronic address: helayel@cbpf.br † Electronic address: carlos@cbpf.br ‡ Electronic address: bpdias@cbpf.br § Electronic address: alfredov@cbpf.br ¶ Electronic address: vjose@cbpf.br

We present two different versions of the consistent theory of massive gravitons in arbitrary space-times which are simple enough for practical applications. The theory is described by a non-symmetric rank-2 tensor whose equations of motion imply six algebraic and five differential constraints reducing the number of independent components to five. The theory reproduces the standard description of massive gravitons in Einstein spaces. In generic spacetimes it does not show the massless limit and always propagates five degrees of freedom, even for the vanishing mass parameter. We illustrate these features by an explicit calculation for a homogeneous and isotropic cosmological background. We find that the gravitons are stable if they are sufficiently massive, hence they may be a part of Dark Matter at present. We discuss also other possible applications.

The combined effects of the Lorentz-symmetry violating Chern-Simons and Ricci-Cotton actions are investigated for the Einstein-Hilbert gravity in the second-order formalism modified by higher derivative terms, and their consequences on the spectrum of excitations are analyzed. We follow the lines of previous works and build up an orthonormal basis of projector-like operators for the degrees of freedom, rather than for the spin modes of the fields. With this new basis, the attainment of the propagators is remarkably simplified and the identification of the physical and unphysical modes becomes more immediate. Our conclusion is that the only tachyon-and ghost-free model is the Einstein-Hilbert action added up by the Chern-Simons term with a timelike vector of the type v ¼ ð;0Þ. Spectral consistency imposes that the Ricci-Cotton term must be switched off. We then infer that gravity with Lorentz-symmetry violation imposes a drastically different constraint on the background if compared to ordinary gauge theories whenever conditions for the suppression of tachyons and ghosts are imposed.

We show the explicit connection between two distinct and complementary approaches to the fractional quantum Hall system (FQHS): the quantum wires formalism and the topological low-energy effective description given in terms of an Abelian Chern-Simons theory. The quantum wires approach provides a description of the FQHS directly in terms of fermions arranged in an array of one-dimensional coupled wires. In this sense it is usually referred to as a microscopic description. On the other hand, the effective theory has no connection with the microscopic modes, involving only the emergent topological degrees of freedom embodied in an Abelian Chern-Simons gauge field, which somehow encodes the collective dynamics of the strongly correlated electrons. The basic strategy pursued in this work is to bosonize the quantum wires system and then consider the continuum limit. By examining the algebra of the bosonic operators in the Hamiltonian, we are able to identify the bosonized microscopic fields with the components of the field strength (electric and magnetic fields) of the emergent gauge field. Thus our study provides a bridge between the microscopic physical degrees of freedom and the emergent topological ones without relying on the bulk-edge correspondence. * Electronic address: weslei@uel.br † Electronic address: pedrogomes@uel.br ‡ Electronic address: hernaski@uel.br

In this work, we analyze a gravity model with higher derivatives including a CPT-even Lorentzviolating term. In principle, the model could be a low-energy limit of a Lorentz-invariant theory presenting the violation of Lorentz symmetry as a consequence of a spontaneous symmetry-breaking mechanism if a decoupling between the metric and the Nambu-Goldstone modes is assumed. We have set up a convenient operator basis for the expansion of wave operators for symmetric secondrank tensors in the presence of a background vector. By using this set of operators, the particle content is obtained, and its consistency, regarding the conditions for stability and unitarity, is discussed. We conclude that this extra Lorentz noninvariant contribution is unable to address the problems of stability and unitarity of higher-derivative gravity models.

We propose a new basis of spin-operators, specific for the case of planar theories, which allows a Lagrangian decomposition into spin-parity components. The procedure enables us to discuss unitarity and spectral properties of gravity models with parity-breaking in a systematic way.

Spontaneous violation of Lorentz symmetry by the vacuum condensation of an antisymmetric 2-tensor is considered. The coset construction for nonlinear realization of spacetime symmetries is employed to build the most general low-energy effective action for the Goldstone modes interacting with photons. We analyze the model within the context of the Standard-Model Extension and noncommutative QED. Experimental bounds for some parameters of the model are discussed, and we readdress the subtle issues of stability and causality in Lorentz non-invariant scenarios. Besides the two photon polarizations, just one Goldstone mode must be dynamical to set a sensible low-energy effective model, and the enhancement of the stability by accounting interaction terms points to a protection against observational Lorentz violation. * Electronic address: carlos.hernaski@gmail.com