Gauge Invariance and Second Class Constraints in 3-D Linearized Gravity

In this paper we continue the study of the Hamiltonian formalism of the healthy extended Horava-Lifshitz gravity. We find the constraint structure of given theory and argue that this is the theory with the second class constraints. Then we discuss physical consequence of this result. We also apply the Batalin-Tyutin formalism of the conversion of the system with the second class constraints to the system with the first class constraints to the case of the healthy extended Hor...

The quantum gravity is formulated based on principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry and gravitational field is represented by gauge field. In leading order approximation, it gives out classical Newton's theory of gravity. It can also give out Einstein's field equation with cosmological constant. For classical tests, it gives out the same theoretical predictions as those of general relativity. This quantum ga...

In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or Hamiltonian formulation of general relativity allows for classical states that do not satisfy the full set of Einstein's equations. This amounts to loosening the Hamiltonian and momentum constraints that are imposed on the initial state. Never...

We present a new point of view on the quantization of the massive gravitational field, namely we use exclusively the quantum framework of the second quantization. The Hilbert space of the many-gravitons system is a Fock space ${\cal F}^{+}({\sf H}_{\rm graviton})$ where the one-particle Hilbert space ${\sf H}_{graviton}$ carries the direct sum of two unitary irreducible representations of the Poincar\'e group corresponding to two particles of mass $m > 0$ and spins 2 and 0, r...

In this paper, we discuss a gravitational theory based on the generalized gauge field. Our Lagrangian is invariant not only under local Lorentz transformation and the ordinary gauge transformation but also under a new gauge transformation. We show that the gauge field associated with this new transformation is a second-rank tensor field and that the Einstein-Hilbert term can be derived from our Lagrangian when the gauge field has a vacuum expectation value. We also show that ...

We analyze the issue of anomaly-free representations of the constraint algebra in Loop Quantum Gravity (LQG) in the context of a diffeomorphism-invariant gauge theory in three spacetime dimensions. We construct a Hamiltonian constraint operator whose commutator matches with a quantization of the classical Poisson bracket involving structure functions. Our quantization scheme is based on a geometric interpretation of the Hamiltonian constraint as a generator of phase space-dep...

We complete the Hamiltonian analysis of specific model of non-linear massive gravity that was started in arXiv:1112.5267. We identify the primary constraint and corresponding secondary constraint. We show that they are the second class constraints and hence they lead to the elimination of the additional scalar mode. We also find that the remaining constraints are the first class constraints with the structure that corresponds to the manifestly diffeomorphism invariant theory....

We perform a brief review on Dirac's procedure applied to the well known Einstein's linearized gravity in $N > 2$ dimensions. Considering it as a gauge theory and therefore the manifestation of second class constraints in analogy with the electromagnetic case, focussing our interest in the Coulomb's gauge. We also check the consistency with the Maskawa-Nakajima reduction procedure and end with some remarks on both procedures.

Performing Hamiltonian analysis of the massive gravity [9] in full phase space, we see that the theory is ghost free. We also see in a more clear way that this result is intrinsic of the interaction term and does not depend on the variables involved. Since no first class constraint emerges, the theory seems to lack gauge symmetry. We show that this is due to the presence of an auxiliary field, and the symmetry may be manifest in the Stuckelberg formulation. We give the genera...

We argue that the field-parametrization dependence of Dirac's procedure, for Hamiltonians with first-class constraints not only preserves covariance in covariant theories, but in non-covariant gauge theories it allows one to find the natural field parametrization in which the Hamiltonian formulation automatically leads to the simplest gauge symmetry.