Constrained field theories on spherically symmetric spacetimes with horizons

Fernandes, Karan; Lahiri, Amitabha; Ghosh, Suman

doi:10.1103/physrevd.95.045012

Cited by 3 publications

(10 citation statements)

References 73 publications

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“…Finally, we note that the BRST formalism provides an interesting and powerful means to investigate quantized fields in the Hamiltonian framework. Following our analysis in this paper and in [41], it can be argued that the BRST charge operator will involve the additional surface terms contained in the constraints. Thus the physical states defined by the cohomology of the BRST charge will have to satisfy non-trivial conditions on the horizon.…”

Section: Discussionmentioning

confidence: 73%

Constrained field theories on Kerr backgrounds

Fernandes

Lahiri

2019

Eur. Phys. J. C

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We analyze the constraints of gauge theories on Kerr and Kerr-de Sitter spacetimes, which contain one or more horizons. We find that the constraints are modified on such backgrounds through the presence of additional surface terms at the horizons. As a concrete example, we consider the Maxwell field and find that the Gauss law constraint involves surface corrections at the horizons. These surface contributions correspond to induced surface charges and currents on the horizons, which agree with those found within the membrane paradigm. The modification of the Gauss law constraint also influences the gauge fixing and Dirac brackets of the theory. *

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Section: Discussionmentioning

confidence: 73%

Constrained field theories on Kerr backgrounds

Fernandes

Lahiri

2019

Eur. Phys. J. C

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“…As promised earlier, we will find that the Gauss law constraint receives a contribution from the horizons of the background. For a similar result in the case of the free Maxwell field, we refer the reader to [35] for spherically symmetric backgrounds and [36] for a certain class of axisymmetric backgrounds.…”

Section: Scalar Electrodynamicsmentioning

confidence: 95%

“…(3.18) and have non-vanishing brackets with them. The construction of Dirac brackets on spherically symmetric backgrounds with horizons, following gauge fixing choices which involve surface terms at the horizons, has been described in further detail in [35]. Eq.…”

Section: Scalar Electrodynamicsmentioning

confidence: 99%

“…The finiteness of gauge-invariant scalars and the arbitrariness of gauge parameters at the horizons served as the basis of our recent work on the constrained dynamics of field theories on curved backgrounds with Killing horizons [35,36]. Using the Dirac-Bergmann formalism, it was shown there that the Gauss law constraint of gauge theories gets additional surface contributions from the horizons of the background.…”

Section: Introductionmentioning

confidence: 99%

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Hamiltonian BRST formalism for gauge fields on black hole spacetimes

Fernandes

Lahiri

2019

Phys. Rev. D

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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 ≥ 0). 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 involves null components of the electromagnetic field at the horizons.We find that the presence of the surface terms in the constraint forces the ghost and gauge fixing actions to include additional terms at the horizons. The null combination of the gauge fields at the horizons is shown to modify the ghost number charge of the theory through additional terms at the horizons. We also demonstrate how one can construct a gauge-fixing fermion which generates its own nilpotent symmetry transformations, called co-BRST transformations, that leave the theory invariant. The BRST and co-BRST transformations are further used to identify dressed (gauge invariant) fields of theory, whose dressings are affected by the presence of Killing horizons. We conclude with a discussion of potential applications of our results in soft limits and thermal field theories on black hole backgrounds. *

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“…Let us now briefly discuss the role of the Green function in that problem; for more details we refer the reader to [36].…”

Section: Inverse Spatial Laplacian Of the De Sitter Backgroundmentioning

confidence: 99%

The inverse spatial Laplacian of spherically symmetric spacetimes

Fernandes¹,

Lahiri²

2017

Class. Quantum Grav.

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We derive the inverse spatial Laplacian for static, spherically symmetric backgrounds by solving Poisson's equation for a point source. This is different from the electrostatic Green function, which is defined on the four dimensional static spacetime, while the equation we consider is defined on the spatial hypersurface of such spacetimes. This Green function is relevant in the Hamiltonian dynamics of theories defined on spherically symmetric backgrounds, and closed form expressions for the solutions we find are absent in the literature. We derive an expression in terms of elementary functions for the Schwarzschild spacetime, and comment on the relation of this solution with the known Green function of the spacetime Laplacian operator. We also find an expression for the Green function on the static pure de Sitter space in terms of hypergeometric functions. We conclude with a discussion of the constraints of the electromagnetic field.

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Constrained field theories on spherically symmetric spacetimes with horizons

Cited by 3 publications

References 73 publications

Constrained field theories on Kerr backgrounds

Constrained field theories on Kerr backgrounds

Hamiltonian BRST formalism for gauge fields on black hole spacetimes

The inverse spatial Laplacian of spherically symmetric spacetimes

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