Generalized spherically symmetric gravitational model: Hamiltonian dynamics in extended phase space and BRST charge
T. P. Shestakova
备注：
18 pages. A revised version. The introduction is expanded and included some additional comments. Section 3 of the old version and Appendix C are omitted. Some new references are added
We construct Hamiltonian dynamics of the generalized spherically symmetric gravitational model in extended phase space. We start from the Faddeev - Popov effective action with gauge-fixing and ghost terms, making use of gauge conditions in differential form. It enables us to introduce missing velocities into the Lagrangian and then construct a Hamiltonian function according a usual rule which is applied for systems without constraints. The main feature of Hamiltonian dynamics in extended phase space is that it can be proved to be completely equivalent to Lagrangian dynamics derived from the effective action. We find a BRST invariant form of the effective action by adding terms not affecting Lagrangian equations. After all, we construct the BRST charge according to the Noether theorem. Our algorithm differs from that by Batalin, Fradkin and Vilkovisky, but the resulting BRST charge generates correct transformations for all gravitational degrees of freedom including gauge ones. Generalized spherically symmetric model imitates the full gravitational theory much better then models with finite number of degrees of freedom, so that one can expect appropriate results in the case of the full theory.
Hamiltonian dynamics in extended phase space for gravity and its consistency with Lagrangian formalism: a generalized spherically symmetric model as an example
In the Batalin - Fradkin - Vilkovisky approach to quantization of gauge theories a principal role is given to the BRST charge which can be constructed as a series in Grassmannian (ghost) variables with coefficients given by generalized structure functions of constraints algebra. Alternatively, the BRST charge can be derived making use of the Noether theorem and global BRST invariance of the effective action. In the case of Yang - Mills fields the both methods lead to the same expression for the BRST charge, but it is not valid in the case of General Relativity. It is illustrated by examples of…
We investigate the Becchi-Rouet-Stora-Tyutin (BRST) formalism for gauge theories on spherically symmetric black hole spacetimes, with or without a cosmological constant ($Λ\geq0$). This is illustrated through the example of scalar electrodynamics. We first demonstrate that the horizons contribute additional surface terms to the Gauss law constraint of the theory when gauge transformations are not required to vanish on the horizons. We then consider the BRST invariant path integral including these surface terms following the Hamiltonian BRST formalism. We fix a radiation-like gauge which involv…
We work out the description of the gauge symmetry of unimodular gravity in the constrained Hamiltonian formalism. In particular, we demonstrate how the transversality conditions restricting the diffeomorphism parameters emerge from the algebra of the Hamiltonian constraints. The alternative form is long known as parametrizing the volume preserving diffeomorphisms by unrestricted two-forms instead of the transverse vector fields. This gauge symmetry is reducible. We work out the Hamiltonian description of this form of unimodular gravity (UG) gauge symmetry. Becchi-Rouet-Stora-Tyutin--Batalin-Fr…
BRST quantization is an elegant and powerful method to quantize theories with local symmetries. In this article we study the Hamiltonian BRST quantization of cosmological perturbations in a universe dominated by a scalar field, along with the closely related quantization method of Dirac. We describe how both formalisms apply to the perturbations in a time-dependent background, and how expectation values of gauge-invariant operators can be calculated in the in-in formalism. Our analysis focuses mostly on the free theory. By appropriate canonical transformations we simplify and diagonalize the f…
Anomaly freedom has been one of the most important issues in canonical quantization of gravity. In a physically meaningful (anomaly free) theory, the constraint operators must be first class, and their commutator algebra is expected to resemble the corresponding classical Poisson-bracket algebra. In this paper, we review the "constructive" approach to obtaining a consistent set of constraints: start with a Hamiltonian constraint and generate the corresponding diffeomorphism constraint as a commutator of two Hamiltonians. Closure of the constraint operator algebra then requires that the diffeom…
Max-Planck-Institut für Physik, Werner–Heisenberg–Institut（马克斯·普朗克物理研究所，维尔纳·海森堡研究所）；Arnold Sommerfeld Center, Ludwig-Maximilians-Universität（阿诺德·索末菲中心，慕尼黑路德维希-马克西米利安大学）
Hamiltonian Formulation of Relativistic Magnetohydrodynamic Accretion on a General Spherically Symmetric and Static Black Hole: Quantum effects on Shock States
Consistent Canonical Quantization of Gravity: Recovery of Classical GR from BRST-invariant Coherent States
Max-Planck-Institut für Physik（马克斯·普朗克物理研究所）；Arnold Sommerfeld Center, Ludwig-Maximilians-Universität（慕尼黑大学阿诺德·索末菲中心）；Sydney Consortium for Particle Physics and Cosmology, School of Physics, The University of Sydney（悉尼大学物理学院粒子物理与宇宙学联盟）
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