Spacetime locality of the antifield formalism : a "mise au point"

Some general techniques and theorems on the spacetime locality of the antifield formalism are illustrated in the familiar cases of the free scalar field, electromagnetism and Yang-Mills theory. The analysis explicitly shows that recent criticisms of the usual approach to dealing with locality are ill-founded.Comment: 15 pages in LaTeX, ULB-PMIF-93/0

Symmetry-deforming interactions of chiral p-forms

No-go theorems on gauge-symmetry-deforming interactions of chiral p-forms are reviewed. We consider the explicit case of p=4, D=10 and show that the only symmetry-deforming consistent vertex for a system of one chiral 4-form and two 2-forms is the one that occurs in the type II B supergravity Lagrangian.Comment: 7 pages, tiny typo corrections, based on a talk given by M. H. at the conference "Constrained Dynamics and Quantum Gravity " held in Villasimius (Sardinia), September 13-17 1999, to appear in the proceedings of the meeting (Nucl. Phys. B Proc. Suppl.

Hamiltonian Analysis of the Conformal Decomposition of the Gravitational Field

This short note is devoted to the Hamiltonian formulation of the conformal decomposition of the gravitational field that was performed in [gr-qc/0501092]. We also analyze the gauge fixed form of the theory when we fix the conformal symmetry by imposing the condition det g=1.Comment: 12 page

A dynamical inconsistency of Horava gravity

The dynamical consistency of the non-projectable version of Horava gravity is investigated by focusing on the asymptotically flat case. It is argued that for generic solutions of the constraint equations the lapse must vanish asymptotically. We then consider particular values of the coupling constants for which the equations are tractable and in that case we prove that the lapse must vanish everywhere -- and not only at infinity. Put differently, the Hamiltonian constraints are generically all second-class. We then argue that the same feature holds for generic values of the couplings, thus revealing a physical inconsistency of the theory. In order to cure this pathology, one might want to introduce further constraints but the resulting theory would then lose much of the appeal of the original proposal by Horava. We also show that there is no contradiction with the time reparametrization invariance of the action, as this invariance is shown to be a so-called "trivial gauge symmetry" in Horava gravity, hence with no associated first-class constraints.Comment: 28 pages, 2 references adde

Hamiltonian Analysis of Non-Relativistic Covariant RFDiff Horava-Lifshitz Gravity

We perform the Hamiltonian analysis of non-relativistic covariant Horava-Lifshitz gravity in the formulation presented recently in arXiv:1009.4885. We argue that the resulting Hamiltonian structure is in agreement with the original construction of non-relativistic covariant Ho\v{r}ava-Lifshitz gravity presented in arXiv:1007.2410. Then we extend this construction to the case of RFDiff invariant Ho\v{r}ava-Lifshitz theory. We find well behaved Hamiltonian system with the number of the first and the second class constraints that ensure the correct number of physical degrees of freedom of gravity.Comment: 15 pages, v2. Title changed, major corrections in section 3. performed, corrected typos and references added,v3: additional typos corrected, references added,v4.additional comments added, version published in PR

Consistent couplings between fields with a gauge freedom and deformations of the master equation

The antibracket in BRST theory is known to define a map $\rm{H^p \times H^q \longrightarrow H^{p+q+1}}$ associating with two equivalence classes of BRST invariant observables of respective ghost number p and q an equivalence class of BRST invariant observables of ghost number p+q+1. It is shown that this map is trivial in the space of all functionals, i.e., that its image contains only the zeroth class. However it is generically non trivial in the space of local functionals. Implications of this result for the problem of consistent interactions among fields with a gauge freedom are then drawn. It is shown that the obstructions to constructing such interactions lie precisely in the image of the antibracket map and are accordingly inexistent if one does not insist on locality. However consistent local interactions are severely constrained. The example of the Chern-Simons theory is considered. It is proved that the only consistent, local, Lorentz covariant interactions for the abelian models are exhausted by the non-abelian Chern-Simons extensions.Comment: 14 pages LaTeX file, ULB-PMIF-93/0

Gauge Properties of Conserved Currents in Abelian Versus Nonabelian Theories

We clarify the physical origin of the difference between gauge properties of conserved currents in abelian and nonabelian theories. In the latter, but not in the former, such currents can always be written on shell as gauge invariants modulo identically conserved, superpotential, terms. For the ``isotopic" vector and the stress tensor currents of spins 1 and 2 respectively, we explain this difference by the fact that the non-abelian theories are just the self-coupled versions of the abelian ones using these currents as sources. More precisely, we indicate how the self-coupling turns the non-invariantizable abelian conserved currents into (on-shell) superpotentials. The fate of other conserved currents is also discussed.Comment: latex, 9 page

Path Integral and Solutions of the Constraint Equations: The Case of Reducible Gauge Theories

It is shown that the BRST path integral for reducible gauge theories, with appropriate boundary conditions on the ghosts, is a solution of the constraint equations. This is done by relating the BRST path integral to the kernel of the evolution operator projected on the physical subspace.Comment: 10 pages Tex file, ULB-TH-94/0

On the Quantization of Reducible Gauge Systems

Reducible gauge theories with constraints linear in the momenta are quantized. The equivalence of the reduced phase space quantization, Dirac quantization and BRST quantization is established. The ghosts of ghosts are found to play a crucial role in the equivalence proof.Comment: 41 pages, Plain Tex file, ULB-PMIF\92-07, GTCRG/92-0