Heat kernel expansion: user's manual

Vassilevich, D. V.

doi:10.1016/j.physrep.2003.09.002

Cited by 999 publications

(1,527 citation statements)

References 435 publications

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“…In particular, a 0 (x, y) does not depend on ξ. It is reassuring to note that our (diagonal) a 2 (y) coincides 5 with the one quoted in [18]. In turn, this also provides an indirect check for the (non-diagonal) coefficient a 1 (x, y).…”

Section: Solution To the Recursion Relations Of The Heat Equation In supporting

confidence: 79%

“…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%

“…If we choose c > d/2 − Re s, (3.18) is then valid for any x and y, including at x = y. The heat kernel K(t, x, y) is a well-known standard tool in quantum field theory on curved manifolds [14,16,18]. It has a very useful small t asymptotic expansion of the form…”

Section: Heat Kernel and Zeta Functionsmentioning

confidence: 99%

“…17) It follows that the geodesic distance in the Weyl transformed geometry is given by 18) or, in terms of the Weyl variation δ ω of 2 (x, 0) =…”

Section: Laplace Operatormentioning

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: Solution To the Recursion Relations Of The Heat Equation In supporting

confidence: 79%

Section: The Area Dependencementioning

confidence: 99%

Section: Heat Kernel and Zeta Functionsmentioning

confidence: 99%

“…17) It follows that the geodesic distance in the Weyl transformed geometry is given by 18) or, in terms of the Weyl variation δ ω of 2 (x, 0) =…”

Section: Laplace Operatormentioning

confidence: 99%

See 2 more Smart Citations

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

Bilal

Ferrari

2013

Nuclear Physics B

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“…K (2) ρ=0 = 1.45 and K (2) ρ=1 = 1.83. 13 In presence of both UV an IR BKTs, ΩI = log(kz)+r I 0 V +r I 0 +r I 1 for ++ gauge fields. 14 Deviations from UV localization lead to non-oblique operators for heavy fermions, such as anomalous Zbb couplings that we do not discuss in this paper.…”

Section: Jhep03(2014)102mentioning

confidence: 99%

Anomalous gauge couplings from composite Higgs and warped extra dimensions

Fichet

Gersdorff

2014

J. High Energ. Phys.

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We examine trilinear and quartic anomalous gauge couplings (AGCs) generated in composite Higgs models and models with warped extra dimensions. We first revisit the SU(2) L × U(1) Y effective Lagrangian and derive the charged and two-photon neutral AGCs. We derive the general perturbative contributions to the pure field-strength operators from spin 0, 1 2 , 1 resonances by means of the heat kernel method. In the composite Higgs framework, we derive the pattern of expected deviations from typical SO(N ) embeddings of the light composite top partner. We then study a generic warped extra dimension framework with AdS 5 background, recasting in few parameters the features of models relevant for AGCs. We also present a detailed study of the latest bounds from electroweak and Higgs precision observables, with and without brane kinetic terms. For vanishing brane kinetic terms, we find that the S and T parameters exclude KK gauge modes of the RS custodial [non-custodial] scenario below 7.7 [14.7] TeV, for a brane Higgs and below 6.6 [8.1] TeV for a Pseudo Nambu-Goldstone Higgs, at 95% CL. These constraints can be relaxed in presence of brane kinetic terms. The leading AGCs are probing the KK gravitons and the KK modes of bulk gauge fields in parts of the parameter space. In these scenarios, the future CMS and ATLAS forward proton detectors could be sensitive to the effect of KK gravitons in the multi-TeV mass range.

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Induced gauge theory on a noncommutative space

Wohlgenannt¹

2008

Fortschritte der Physik

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We consider a scalar φ 4 theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner to the scalar field. We extract the dynamics for the gauge field from the divergent terms of the 1-loop effective action using a matrix basis and propose an action for the noncommutative gauge theory, which is a candidate for a renormalisable model.

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Heat kernel expansion: user's manual

Cited by 999 publications

References 435 publications

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

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

Anomalous gauge couplings from composite Higgs and warped extra dimensions

Induced gauge theory on a noncommutative space

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