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Heat kernel expansion: user's manual (Q1412192)

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Language	Label	Description	Also known as
English	Heat kernel expansion: user's manual	scientific article

Statements

scholarly article

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Heat kernel expansion: user's manual (English)

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zbMATH Open document ID

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10.1016/j.physrep.2003.09.002

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Physics Reports

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publication date

9 November 2003

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full work available at URL

https://arxiv.org/abs/hep-th/0306138

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Mathematics Subject Classification ID

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zbMATH DE Number

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zbMATH Keywords

geometric invariants

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covariant perturbation expansions

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quantum anomalies

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Dmitri V. Vassilevich

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MaRDI profile type

MaRDI publication profile

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On Gauge Invariance and Vacuum Polarization

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Quantum Theory of Gravity. I. The Canonical Theory

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A Generalization of Epstein Zeta Functions

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Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds

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Can One Hear the Shape of a Drum?

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The index of elliptic operators on compact manifolds

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Curvature and the eigenvalues of the Laplacian for elliptic complexes

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Quantum Fields in Curved Space

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New developments in the Casimir effect

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Curvature phase transition in \(\mathbb{R}^ 2\) quantum gravity and induction of Einstein gravity

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Euclidean quantum gravity on manifolds with boundary

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A new algebraic approach for calculating the heat kernel in quantum gravity

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Ten Physical Applications of Spectral Zeta Functions

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Zeta-function regularization is uniquely defined and well

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Functional calculus of pseudodifferential boundary problems.

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Singular Integrals and Boundary Value Problems

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The Resolvent of an Elliptic Boundary Problem

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An asymptotic expansion for the heat equation

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Zeta function regularization of path integrals in curved spacetime

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Residues of the eta function for an operator of Dirac type

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Residues of the eta function for an operator of Dirac type with local boundary conditions

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A NOTE ON THE HEAT KERNEL METHOD APPLIED TO FERMIONS

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Mixed boundary conditions in quantum field theory

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ONE-LOOP QUANTUM GRAVITY ON DE SITTER SPACE

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The path integral measure, conformal factor problem and stability of the ground state of quantum gravity

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Quantizing gravity with a cosmological constant

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Functional integration over geometries

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Black hole pair creation in de Sitter space: A complete one-loop analysis

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A diffeomorphism-invariant eigenvalue problem for metric perturbations in a bounded region

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Boundary operators in Euclidean quantum gravity

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Gauge theories on manifolds with boundary

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Lack of strong ellipticity in Euclidean quantum gravity

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Non-local boundary conditions in Euclidean quantum gravity

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The spectral geometry of a Riemannian manifold

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Evaluation of the heat kernel in Riemann - Cartan space

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Induced classical gravity

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Curvature and the eigenvalues of the Laplacian

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b <sub>8</sub> 'Hamidew' coefficient for a scalar field

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Index-free heat kernel coefficients

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New gravitational index theorems and super theorems

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A Characteristic Function in Riemannian Space and its Application to the Solution of Geodesic Triangles

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A DeWitt expansion of the heat kernel for manifolds with a boundary

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Heat kernel asymptotics for mixed boundary conditions

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Heat equation asymptotics of ‘‘nonminimal’’ operators on differential forms

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On gauge independence in quantum gravity

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HEAT KERNEL ASYMPTOTICS OF OPERATORS WITH NON-LAPLACE PRINCIPAL PART

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One-loop divergences in theories with an arbitrary nonminimal operator in curved space

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Boundary terms in the heat kernel expansion

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Heat kernel coefficients of the Laplace operator on the <i>D</i>-dimensional ball

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Further functional determinants

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Robin conditions on the Euclidean ball

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Spectral zeta functions for a cylinder and a circle

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Heat-kernel coefficients and functional determinants for higher-spin fields on the ball

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Casimir energy for a massive fermionic quantum field with a spherical boundary

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Vector fields on a disk with mixed boundary conditions

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1-loop effective action on the 4-ball

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Zeta function for the Laplace operator acting on forms in a ball with gauge boundary conditions

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One-loop quantum cosmology: \(\zeta\)-function technique for the Hartle-Hawking wave function of the universe

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The Asymptotics of The Laplacian on a Manifold with Boundary

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The asymptotics of the heat equation for a boundary value problem

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Conformal invariance and the regularised one-loop effective action

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Heat kernel coefficients for Chern-Simons boundary conditions in QED

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Casimir force between Chern-Simons surfaces

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The eta invariant for a class of elliptic boundary value problems

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Asymptotic expansion of the heat kernel for generalized boundary conditions

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Heat-kernel coefficients for oblique boundary conditions

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The <i>a</i> <sub>3/2</sub> heat kernel coefficient for oblique boundary conditions

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New invariants in the 1-loop divergences on manifolds with boundary

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Nonlinear electrodynamics from quantized strings

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Spectral asymmetry and Riemannian Geometry. I

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Are there irreducible spherically symmetric solutions in the SU(3) and SU(4) Yang-Mills theories?

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Dirac operator on a disk with global boundary conditions

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Spectral boundary conditions and index theorem for two-dimensional compact manifold with boundary

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DIRAC FIELDS IN THE BACKGROUND OF A MAGNETIC FLUX STRING AND SPECTRAL BOUNDARY CONDITIONS

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Weakly parametric pseudodifferential operators and Atiyah-Patodi-Singer boundary problems

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Zeta and eta functions for Atiyah-Patodi-Singer operators

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Logarithmic terms in asymptotic expansions of heat operator traces

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Spectral boundary conditions for generalizations of Laplace and Dirac operators

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Covariant algebraic method for calculation of the low-energy heat kernel

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Topologically nontrivial supermembranes

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Classical and quantum scattering on a cone

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Generalized sums over histories for quantum gravity. I: Smooth conifolds

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Spectral geometry of singular Riemannian spaces

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Heat equation asymptotics for singular Sturm-Liouville problems

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The resolvent expansion for second order regular singular operators

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Heat kernel expansion on a generalized cone

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Functional determinants on spheres and sectors

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The trace of the heat kernel on a compact hyperbolic 3-orbifold

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Heat-kernels and functional determinants on the generalized cone

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The heat kernel for deformed spheres

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Smeared heat-kernel coefficients on the ball and generalized cone

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Ground state energy of massive scalar field inside a spherical region in the global monopole background

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The ground state energy of a massive scalar field in the background of a semi-transparent spherical shell

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Heat trace asymptotics with transmittal boundary conditions and quantum brane-world scenario

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Heat kernel expansions for distributional backgrounds

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Heat trace asymptotics defined by transfer boundary conditions

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The heat-kernel coefficient in the presence of boundary discontinuities

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On functional determinants of Laplacians in polygons and simplicial complexes

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Casimir energy of a semi-circular infinite cylinder

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Non-smoothness of the boundary and the relevant heat kernel coefficients

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Path-integral quantization of electrodynamics in dielectric media

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Divergencies in the Casimir energy for a medium with realistic ultraviolet behaviour

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Zeta-function regularization, the multiplicative anomaly and the Wodzicki residue

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Non-local conformal anomalies

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Twenty years of the Weyl anomaly

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Dilaton gravity in two dimensions

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One-loop effective action for spherical scalar field collapse

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Conformal anomaly in two-dimensional dilaton-scalar theory

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Comment on Chiral and Conformal Anomalies

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Diagrams for heat kernel expansions

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Inverse mass expansion of the one-loop effective action

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Derivative expansion and soliton masses

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Leading Terms in the Heat Invariants

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Explicit time-dependent Schrodinger propagators

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Algebraic approach to Kaluza-Klein models

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DeWitt-Schwinger expansion for projective and Grassmann spaces

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Antisymmetric tensor fields on spheres: Functional determinants and non-local counterterms

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Abelian gauge theories on homogeneous spaces

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QUANTUM GRAVITY ON CP<sup>2</sup>

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A nonlocal action for the trace anomaly

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Conformal transformations and the effective action in the presence of boundaries

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Conserved currents and the energy-momentum tensor in conformally invariant theories for general dimensions

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Vacuum polarization in Schwarzschild space-time by anomaly induced effective actions

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The partition function of a degenerate functional

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Discrete symmetries of functional determinants

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Bosonic M theory

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D-branes and dual gauge theories in type \(0\) strings

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Supersymmetry and Morse theory

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Generalized abelian \(S\)-duality and coset constructions

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Non-minimal coupling, boundary terms and renormalization of the Einstein-Hilbert action and black hole entropy

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Integrable Models

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ON PROPERTIES OF THE ASYMPTOTIC EXPANSION OF THE HEAT TRACE FOR THE N/D PROBLEM

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The spectral geometry of the higher order Laplacian

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Mathematics(1 entry)

mardi Publication:1412192

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