Path integral calculation of heat kernel traces with first order operator insertions

Bastianelli, Fiorenzo; Comberiati, Francesco

doi:10.1016/j.nuclphysb.2020.115183

Cited by 4 publications

(4 citation statements)

References 37 publications

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“…In particular, the SI method differs from the DBC method by total derivatives which are often beneficial, in that they deliver the final result in a very compact form, see for instance the Seeley-DeWitt coefficients calculated for abelian gauge theories in [41]. The extension of the SI method to curved space has been discussed in [42], while [43] carries an exemplification of both methods.…”

Section: The Scalar Particlementioning

confidence: 99%

Worldline path integrals for the graviton

Bastianelli,

Damia Paciarini

2024

Class. Quantum Grav.

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We present an extension to arbitrary dimensions of a worldline path integral approach to one-loop quantum gravity, which was previously formulated in four spacetime dimensions. By utilizing this method, we recalculate gauge invariant coeﬃcients related to the UV divergences of quantum gravity. These gauge invariant coeﬃcients were previously obtained in arbitrary dimensions through two alternative techniques: the quantization of the N = 4 spinning particle that propagates the graviton on Einstein spaces and the more conventional heat kernel approach. Our worldline path integrals are closer to the latter method and are employed to compute the trace of the heat kernel.

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Section: The Scalar Particlementioning

confidence: 99%

Worldline path integrals for the graviton

Bastianelli,

Damia Paciarini

2024

Class. Quantum Grav.

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“…The one for n = 3 is mass independent and corresponds to the usual logarithmic divergence seen in dimensional regularization. The specific calculation of the coefficients in (3.5) can be done as in [16,[39][40][41], and gives the answer…”

Section: Jhep12(2021)023mentioning

confidence: 99%

“…imposing q(0) = q(1) = 0) or using the "string-inspired" boundary conditions (that is requiring ´1 0 dτ q µ (τ ) = 0). They give equivalent results, see [41] for a recent application and comparison of the two methods. The integration of the zero modes factorizes, as perturbatively there is no action for them, and there remains the path integral over the quantum fluctuations q µ .…”

Section: The Color Variables Approachmentioning

confidence: 99%

Worldline description of a bi-adjoint scalar and the zeroth copy

Bastianelli

Comberiati

Cruz

2021

J. High Energ. Phys.

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Bi-adjoint scalars are helpful in studying properties of color/kinematics duality and the double copy, which relates scattering amplitudes of gauge and gravity theories. Here we study bi-adjoint scalars from a worldline perspective. We show how a global G × $$ \overset{\sim }{G} $$ G ~ symmetry group may be realized by worldline degrees of freedom. The worldline action gives rise to vertex operators, which are compared to similar ones describing the coupling to gauge fields and gravity, thus exposing the color/kinematics interplay in this framework. The action is quantized by path integrals to find a worldline representation of the one-loop QFT effective action of the bi-adjoint scalar cubic theory. As simple applications, we recover the one-loop beta function of the theory in six dimensions, verifying its vanishing, and compute the self-energy correction to the propagator. The model is easily extendable to that of a particle carrying an arbitrary representation of direct products of global symmetry groups, including the multi-adjoint particle, whose one-loop beta function we reproduce as well.

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“…There are two heat kernel expansions: the covariant perturbation theory [9][10][11][12][13][14][15] and the Schwinger-DeWitt technique [3,16]. Various methods are developed for heat kernel approaches, such as calculating heat kernel traces by the path integral [17], the Green function approach [18], the technique of labeled operators [19], and heat kernel diagrammatic equations [20]. The heat kernel of higher-order differential operators is considered [21].…”

Section: Introductionmentioning

confidence: 99%

Scattering approach for calculating one-loop effective action and vacuum energy

Li¹,

Chen²,

Li³

et al. 2022

Preprint

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An approach for calculating one-loop effective actions and vacuum energies is suggested. Spectral functions are functions of the eigenvalue spectrum of an operator. The starting point is to regard one-loop effective actions and vacuum energies in quantum field theory and scattering phase shifts and amplitudes in quantum mechanics as spectral functions of an operator. Different spectral functions of the same operator may belong to different fields of physics. Methods for calculating various spectral functions can be interconverted through transform relations among spectral functions. In this paper, we convert the method for calculating scattering phase shifts and amplitudes to a method for calculating one-loop effective actions and vacuum energies. In principle, all methods for the calculation of scattering phase shifts and amplitudes can be converted to methods for the calculation of the one-loop effective actions and vacuum energies. As an example, we convert the Born approximation in quantum-mechanical scattering theory to a method for calculating one-loop effective actions and vacuum energies. In appendices, we provide integral representations of the Bessel function for calculating the sum encountered.

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Path integral calculation of heat kernel traces with first order operator insertions

Cited by 4 publications

References 37 publications

Worldline path integrals for the graviton

Worldline path integrals for the graviton

Worldline description of a bi-adjoint scalar and the zeroth copy

Scattering approach for calculating one-loop effective action and vacuum energy

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