A covariant technique for the calculation of the one-loop effective action

Avramidi, Ivan G.

doi:10.1016/0550-3213(91)90492-g

Cited by 226 publications

(287 citation statements)

References 29 publications

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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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“…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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“…For manifolds without boundary the most complete calculation is done in [71] and in [72], see also [73]. There is even a computer program provided for that in [74].…”

Section: The Heat Kernel Expansionmentioning

confidence: 99%

New developments in the Casimir effect

2001

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We provide a review of both new experimental and theoretical developments in the Casimir effect. The Casimir effect results from the alteration by the boundaries of the zero-point electromagnetic energy. Unique to the Casimir force is its strong dependence on shape, switching from attractive to repulsive as function of the size, geometry and topology of the boundary. Thus the Casimir force is a direct manifestation of the boundary dependence of quantum vacuum. We discuss in depth the general structure of the infinities in the field theory which are removed by a combination of zeta-functional regularization and heat kernel expansion. Different representations for the regularized vacuum energy are given. The Casimir energies and forces in a number of configurations of interest to applications are calculated. We stress the development of the Casimir force for real media including effects of nonzero temperature, finite conductivity of the boundary metal and surface roughness. Also the combined effect of these important factors is investigated in detail on the basis of condensed matter physics and quantum field theory at nonzero temperature. The experiments on measuring the Casimir force are also reviewed, starting first with the older measurements and finishing with a detailed presentation of modern precision experiments. The latter are accurately compared with the theoretical results for real media. At the end of the review we provide the most recent constraints on the corrections to Newtonian gravitational law and other hypothetical long-range interactions at submillimeter range obtained from the Casimir force measurements.

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“…First, we present the heat kernel diagonal in the form 16) where ξx = ξ µ x µ , which can be transformed to 17) where H is the leading symbol of the operator L 18) and K is a first-order self-adjoint operator defined by 19) where the operator X µ is defined by (3.62). Here the operators in the exponent act on the unity matrix I from the left.…”

Section: Calculation Of the Invariantsmentioning

confidence: 99%

“…where A k are so-called heat invariants [26,20,16,19,18]. The coefficients A k are spectral invariants determined by the integrals over the manifold of some local invariants [26,16,20] (for a review, see [19,21]) constructed from the coefficients of the operator L and their derivatives so that they are polynomial in the derivatives of the coefficients of the operator L. The heat invariants A k determine further the large mass asymptotic expansion of the effective action as m → ∞ [16,19,20,21] …”

Section: Spectral Asymptoticsmentioning

confidence: 99%

Gauged Gravity via Spectral Asymptotics of non-Laplace type Operators

Avramidi

2004

J. High Energy Phys.

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We construct invariant differential operators acting on sections of vector bundles of densities over a smooth manifold without using a Riemannian metric. The spectral invariants of such operators are invariant under both the diffeomorphisms and the gauge transformations and can be used to induce a new theory of gravitation. It can be viewed as a matrix generalization of Einstein general relativity that reproduces the standard Einstein theory in the weak deformation limit. Relations with various mathematical constructions such as Finsler geometry and Hodge-de Rham theory are discussed.

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A covariant technique for the calculation of the one-loop effective action

Cited by 226 publications

References 29 publications

Stability Theorems for Chiral Bag Boundary Conditions

Stability Theorems for Chiral Bag Boundary Conditions

New developments in the Casimir effect

Gauged Gravity via Spectral Asymptotics of non-Laplace type Operators

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