The covariant technique for the calculation of the heat kernel asymptotic expansion

Avramidi, Ivan G.

doi:10.1016/0370-2693(90)92105-r

Cited by 82 publications

(111 citation statements)

References 13 publications

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“…Using this method beyond the first few orders becomes increasingly cumbersome and other more efficient methods have been devised [61] and [62]. It is important to realize that at no point of our calculation did we choose a particular vacuum in which to define our propagator.…”

Section: Resultsmentioning

confidence: 99%

Quantum corrections to inflaton and curvaton dynamics

Markkanen

Tranberg²

2012

J. Cosmol. Astropart. Phys.

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We compute the fully renormalized one-loop effective action for two interacting and self-interacting scalar fields in FRW space-time. We then derive and solve the quantum corrected equations of motion both for fields that dominate the energy density (such as an inflaton) and fields that do not (such as a subdominant curvaton). In particular, we introduce quantum corrected Friedmann equations that determine the evolution of the scale factor. We find that in general, gravitational corrections are negligible for the field dynamics. For the curvaton-type fields this leaves only the effect of the flat-space Coleman-Weinberg-type effective potential, and we find that these can be significant. For the inflaton case, both the corrections to the potential and the Friedmann equations can lead to behaviour very different from the classical evolution. Even to the point that inflation, although present at tree level, can be absent at one-loop order.

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Section: Resultsmentioning

confidence: 99%

Quantum corrections to inflaton and curvaton dynamics

Markkanen

Tranberg²

2012

J. Cosmol. Astropart. Phys.

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“…The invariants e n (x, D) vanish for n odd and are known for n = 0, 2, 4, 6, 8, see for example [4,5,6]. The boundary invariants e n,ν (y, D, B) are considerably more subtle.…”

Section: Introductionmentioning

confidence: 99%

Stability Theorems for Chiral Bag Boundary Conditions

Gilkey

Kirsten

2005

Lett Math Phys

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Abstract. We study asymptotic expansions of the smeared L 2 -traces F e −tP 2 and F P e −tP 2 , where P is an operator of Dirac type and F is an auxiliary smooth endomorphism. We impose chiral bag boundary conditions depending on an angle θ. Studying the θ-dependence of the above trace invariants, θ-independent pieces are identified. The associated stability theorems allow one to show the regularity of the eta function for the problem and to determine the most important heat kernel coefficient on a four dimensional manifold.

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“…Due to De Witt [3], these methods became standard in quantum field theory. The De Witt iteration procedure proved to work quite well on manifolds without boundaries and (after certain improvements) allowed to calculate many terms in the asymptotic expansion of the heat kernel [4,5,6,7]. On manifolds with boundaries, the methods based on functorial properties of the heat kernel [8,9,10] appeared to be more appropriate.…”

Section: Introductionmentioning

confidence: 99%

Multiple reflection expansion and heat kernel coefficients

et al. 2001

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We propose the multiple reflection expansion as a tool for the calculation of heat kernel coefficients. As an example, we give the coefficients for a sphere as a finite sum over reflections, obtaining as a byproduct a relation between the coefficients for Dirichlet and Neumann boundary conditions. Further, we calculate the heat kernel coefficients for the most general matching conditions on the surface of a sphere, including those cases corresponding to the presence of delta and delta prime background potentials. In the latter case, the multiple reflection expansion is shown to be non-convergent.

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The covariant technique for the calculation of the heat kernel asymptotic expansion

Cited by 82 publications

References 13 publications

Quantum corrections to inflaton and curvaton dynamics

Quantum corrections to inflaton and curvaton dynamics

Stability Theorems for Chiral Bag Boundary Conditions

Multiple reflection expansion and heat kernel coefficients

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