R-Torsion and the Laplacian on Riemannian manifolds

Ray, Daniel; Singer, I. M.

doi:10.1016/0001-8708(71)90045-4

Cited by 846 publications

(885 citation statements)

References 11 publications

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“…Of course, heat kernel and zeta function methods have been used long before in many different ways in quantum field theory on curved spacetimes, see e.g. [3,14,15,16,17] and in particular the review [18], book [13] and references therein.…”

Section: The Area Dependencementioning

confidence: 99%

“…3 The hatted heat kernel To make a more general analysis, we start from the formula (4.28) which, together with (4.29), yields the integral representation…”

Section: Basic Propertiesmentioning

confidence: 99%

“…In principle, one may use dimensional regularization, but this scheme it is not very natural in curved spacetime because there is no canonical way to generalize a general d-dimensional spacetime manifold M d to arbitrary d + dimensions. A much preferred and powerful regularization method is the zeta function scheme [3]. This approach is very elegant and manifestly reparameterization invariant.…”

Section: Introductionmentioning

confidence: 99%

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Multi-loop zeta function regularization and spectral cutoff in curved spacetime

Bilal

Ferrari

2013

Nuclear Physics B

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We emphasize the close relationship between zeta function methods and arbitrary spectral cutoff regularizations in curved spacetime. This yields, on the one hand, a physically sound and mathematically rigorous justification of the standard zeta function regularization at one loop and, on the other hand, a natural generalization of this method to higher loops. In particular, to any Feynman diagram is associated a generalized meromorphic zeta function. For the one-loop vacuum diagram, it is directly related to the usual spectral zeta function. To any loop order, the renormalized amplitudes can be read off from the pole structure of the generalized zeta functions. We focus on scalar field theories and illustrate the general formalism by explicit calculations at one-loop and two-loop orders, including a two-loop evaluation of the conformal anomaly.

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Section: The Area Dependencementioning

confidence: 99%

“…3 The hatted heat kernel To make a more general analysis, we start from the formula (4.28) which, together with (4.29), yields the integral representation…”

Section: Basic Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multi-loop zeta function regularization and spectral cutoff in curved spacetime

Bilal

Ferrari

2013

Nuclear Physics B

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“…[4]. Our approach consists in calculating first the fourdimensional integrals using the dimensional regularization, and then evaluating the sum over the KK modes, using the ζ-function regularization [14]. The idea to calculte the sums over KK modes in multidimensional theories by means of the ζ-function regularization method is not new and was used in a number of papers (see for example [2,15,16,17]).…”

Section: Introductionmentioning

confidence: 99%

Effective potential and KK-renormalization scheme in a 5D supersymmetric theory

Clemente

Kubyshin

2002

Nuclear Physics B

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We calculate the 1-loop effective potential in a supersymmetric model in 5D with S 1 /(Z 2 × Z 2 ) orbifold compactification. The procedure of calculation consists of evaluating first the integrals over four-momenta using the dimensional regularization and then the sum over Kaluza-Klein modes using the zeta-regularization. We show that both fermionic and bosonic contributions are separately finite and argue that, supersymmetry is not necessary for the finiteness of the theory at 1-loop. Also, some general arguments on the finiteness of the theory with arbitrary number of extra dimensions are presented.

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“…In [11] the following complex valued analogue of the square of the Ray-Singer torsion [20] was introduced and studied: q det (Δ E,g,b,q ) (−1) q q ∈ C × := C \ {0}.…”

mentioning

confidence: 99%

Complex valued Ray–Singer torsion II

Burghelea

Haller

2010

Mathematische Nachrichten

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In this paper we extend Witten-Helffer-Sjöstrand theory from selfadjoint Laplacians based on fiber wise Hermitian metrics to nonselfadjoint Laplacians based on fiber wise non-degenerate symmetric bilinear forms. As an application we show that results about the asymptotics of the Ray-Singer torsion of self-adjoint Witten deformation, as well as the strategy proposed by Burghelea-Friedlander-Kappeler to derive the comparison of Ray-Singer and Reidemeister torsion, can be extended to nonself-adjoint Witten deformation. This is then used to conclude the equality of complex analytic and Milnor-Turaev torsion, at least for odd dimensional manifolds, up to sign.

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R-Torsion and the Laplacian on Riemannian manifolds

Cited by 846 publications

References 11 publications

Multi-loop zeta function regularization and spectral cutoff in curved spacetime

Multi-loop zeta function regularization and spectral cutoff in curved spacetime

Effective potential and KK-renormalization scheme in a 5D supersymmetric theory

Complex valued Ray–Singer torsion II

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