Anomalous Jacobian Factor in the Polyakov Measure for Abelian Gauge Field in Curved Spacetimes

Hiroki Fukutaka

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Anomalous Jacobian Factor in the Polyakov Measure for Abelian Gauge Field in Curved Spacetimes

Hiroki Fukutaka

High Energy Physics - Theory · Submitted 13 Jan 1992

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It is shown that the two representations are different by an anomalous Jacobian factor from each other and also that the factor has a direct relationship to an uncancellation factor of the contributions from the Faddeev-Popov ghost and the unphysical part of the gauge field to the covariant one-loop partition function.

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arXiv IDhep-th/9201022 (version 1)

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CitationHiroki Fukutaka. "Anomalous Jacobian Factor in the Polyakov Measure for Abelian Gauge Field in Curved Spacetimes." arXiv:hep-th/9201022 (1992). https://pith.science/paper/BCY3IKSQ

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.64 · mentions code or data availability 0.02.

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The Polyakov measure for the Abelian gauge field is considered in the Robertson-Walker spacetimes. The measure is concretely represented by adopting two kind of decompositions of the gauge field degrees of freedom which are most familiarly used in the covariant and canonical path integrals respectively. It is shown that the two representations are different by an anomalous Jacobian factor from each other and also that the factor has a direct relationship to an uncancellation factor of the contributions from the Faddeev-Popov ghost and the unphysical part of the gauge field to the covariant one-loop partition function.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The Polyakov measure for the Abelian gauge field is considered in the Robertson-Walker spacetimes.	background 0.76	0.44	0.03	asserted 0.95
s1	The measure is concretely represented by adopting two kind of decompositions of the gauge field degrees of freedom which are most familiarly used in the covariant and canonical path integrals respectively.	method 0.98	0.80	0.04	asserted 1.00
s2	It is shown that the two representations are different by an anomalous Jacobian factor from each other and also that the factor has a direct relationship to an uncancellation factor of the contributions from the Faddeev-Popov ghost and the unphysical part of the gauge field to the covariant one-loop partition function.	result 1.00	0.92	0.90	asserted 1.00

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Original abstract

The Polyakov measure for the Abelian gauge field is considered in the Robertson-Walker spacetimes. The measure is concretely represented by adopting two kind of decompositions of the gauge field degrees of freedom which are most familiarly used in the covariant and canonical path integrals respectively. It is shown that the two representations are different by an anomalous Jacobian factor from each other and also that the factor has a direct relationship to an uncancellation factor of the contributions from the Faddeev-Popov ghost and the unphysical part of the gauge field to the covariant one-loop partition function.

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3 arXiv papers cite this in 3 sentences

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Cites it as background 2 papers

The compatibility of the manifestly covariant path integral formalism with the manifestly unitary canonical formalism has been a source of confusion [ref] , ultimately resolved in [ref] by arguing the form of the canonical partition function.

Generalised symmetries and state-operator correspondence for nonlocal operators · Current algebra and the spectrum · 0.92
Finally, it would be interesting to investigate whether our proposal for the physical states in gauge theory and perturbative gravity gives any insight into the discrepancy between the unitary and covariant formulations of these theories in de Sitter spacetime, or in curved spacetime in general [ref] .

Infrared problem in the Faddeev-Popov-ghost propagator in perturbative quantum gravity in de Sitter spacetime · Summary and Discussion · 0.89

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