Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCovariant Approach to the No-ghost Theorem in Massive Gravity
161
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We discuss the no-ghost theorem in the massive gravity in a covariant manner. Using the BRST formalism and St{u}ckelberg fields, we first clarify how the Boulware-Deser ghost decouples in the massive gravity theory with Fierz-Pauli mass term. Here we find that the crucial point in the proof is that there is no higher (time) derivative for the St{u}ckelberg `scalar field. We then analyze the nonlinear massive gravity proposed by de Rham, Gabadadze and Tolley, and show that there is no ghost for general admissible backgrounds. In this process, we find a very nontrivial decoupling limit for general backgrounds. We end the paper by demonstrating the general results explicitly in a nontrivial example where there apparently appear higher time derivatives for St{u}ckelberg scalar field, but show that this does not introduce the ghost into the theory.
rate research
Read More
It is possible to couple Dirac-Born-Infeld (DBI) scalars possessing generalized Galilean internal shift symmetries (Galileons) to nonlinear massive gravity in four dimensions, in such a manner that the interactions maintain the Galilean symmetry. Such a construction is of interest because it is not possible to couple such fields to massless General Relativity in the same way. We show that this theory has the primary constraint necessary to eliminate the Boulware-Deser ghost, thus preserving the attractive properties of both the Galileons and ghost-free massive gravity.
Recently, a practical approach to holographic renormalization has been developed based on the Hamilton-Jacobi formulation. Using a simple Einstein-scalar theory, we clarify that this approach does not conflict with the Hamiltonian constraint as it seems. Then we apply it to the holographic renormalization of massive gravity. We assume that the shift vector is falling off fast enough asymptotically. We derive the counterterms up to the boundary dimension d=4. Interestingly, we find that the conformal anomaly can even occur in odd dimensions, which is different from the Einstein gravity. We check that the counterterms cancel the divergent part of the on-shell action at the background level. At the perturbation level, they are also applicable in several time-dependent cases.
We review the covariant canonical formalism initiated by DAdda, Nelson and Regge in 1985, and extend it to include a definition of form-Poisson brackets (FPB) for geometric theories coupled to $p$-forms, gauging free differential algebras. The form-Legendre transformation and the form-Hamilton equations are derived from a $d$-form Lagrangian with $p$-form dynamical fields $phi$. Momenta are defined as derivatives of the Lagrangian with respect to the velocities $dphi$ and no preferred time direction is used. Action invariance under infinitesimal form-canonical transformations can be studied in this framework, and a generalized Noether theorem is derived, both for global and local symmetries. We apply the formalism to vielbein gravity in $d=3$ and $d=4$. In the $d=3$ theory we can define form-Dirac brackets, and use an algorithmic procedure to construct the canonical generators for local Lorentz rotations and diffeomorphisms. In $d=4$ the canonical analysis is carried out using FPB, since the definition of form-Dirac brackets is problematic. Lorentz generators are constructed, while diffeomorphisms are generated by the Lie derivative. A doubly covariant hamiltonian formalism is presented, allowing to maintain manifest Lorentz covariance at every stage of the Legendre transformation. The idea is to take curvatures as velocities in the definition of momenta.
We study ghosts in multimetric gravity by combining the mini-superspace and the Hamiltonian constraint analysis. We first revisit bimetric gravity and explain why it is ghost-free. Then, we apply our method to trimetric gravity and clarify when the model contains a ghost. More precisely, we prove trimetric gravity generically contains a ghost. However, if we cut the interaction of a pair of metrics, trimetric gravity becomes ghost-free. We further extend the Hamiltonian analysis to general multimetric gravity and calculate the number of ghosts in various models. Thus, we find multimetric gravity with loop type interactions never becomes ghost-free.
We analyze conformal gravity in translationally invariant approximation, where the metric is taken to depend on time but not on spatial coordinates. We find that the field mode which in perturbation theory has a ghostlike kinetic term, turns into a tachyon when nonlinear interaction is accounted for. The kinetic term and potential for this mode have opposite signs. Solutions of nonlinear classical equations of motion develop a singularity in finite time determined by the initial conditions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
