Heat kernel expansion: user's manual

Abstract

The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients scattered in mathematical and physical literature. We present explicit expressions for these coefficients on manifolds with and without boundaries, subject to local and non-local boundary conditions, in the presence of various types of singularities (e.g., domain walls). In each case the heat kernel coefficients are given in terms of several geometric invariants. These invariants are derived for scalar and spinor theories with various interactions, Yang-Mills fields, gravity, and open bosonic strings. We discuss the relations between the heat kernel coefficients and quantum anomalies, corresponding anomalous actions, and covariant perturbation expansions of the effective action (both "low-" and "high-energy" ones).

113 pp, to be submitted to Phys.Repts, v2: added references and corrected typos

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• The heat kernel on symmetric spaces via integrating over the group of isometries
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• Heat kernel for antisymmetric tensor field on a disk
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Cited by in corpus (637)

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• Quantum Gravity from Causal Dynamical Triangulations: A Review
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• Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates
• A Tower Weak Gravity Conjecture from Infrared Consistency
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• Logarithmic Corrections to N=4 and N=8 Black Hole Entropy: A One Loop Test of Quantum Gravity
• Boundary Conformal Field Theory and a Boundary Central Charge
• Entanglement entropy for the n-sphere
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• Central Charges for BCFTs and Holography
• Geometry of the Scalar Sector
• Spectral geometry as a probe of quantum spacetime
• Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions
• Dimension and Dimensional Reduction in Quantum Gravity
• Quantum oscillations and black hole ringing
• Density perturbations in f(R) gravity theories in metric and Palatini formalisms
• Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions
• Black hole determinants and quasinormal modes
• Non-minimal coupling in Higgs-Yukawa model with asymptotically safe gravity
• Off-diagonal coefficients of the DeWitt-Schwinger and Hadamard representations of the Feynman propagator
• The Wave Function of Vasiliev's Universe - A Few Slices Thereof
• Constraining f(R) gravity in the Palatini formalism
• Some exact solutions of F(R) gravity with charged (a)dS black hole interpretation
• Induced Gauge Theory on a Noncommutative Space
• Casimir interaction of two plates inside a cylinder
• The Universal RG Machine
• Nut Charged Space-times and Closed Timelike Curves on the Boundary
• Unification of inflation and cosmic acceleration in the Palatini formalism
• Holographic Complexity Equals Which Action?
• Attractive and Repulsive Casimir Vacuum Energy with General Boundary Conditions
• Functional Determinants in Quantum Field Theory
• Thermal Casimir effect in ideal metal rectangular boxes
• A One-loop Test of Quantum Black Holes in Anti de Sitter Space
• Conformal Carroll Scalars with Boosts
• Graviton 1-loop partition function for 3-dimensional massive gravity
• Twist operators in higher dimensions
• Selected Topics in the Large Quantum Number Expansion
• Effects of eight-quark interactions on the hadronic vacuum and mass spectra of light mesons
• Entanglement Entropy in Critical Phenomena and Analogue Models of Quantum Gravity
• The spectral action for Moyal planes
• Kaluza-Klein models as pistons
• The 1/N correction in the D3-brane description of circular Wilson loop at strong coupling
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• Large charge at large N
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• Anomalous Breaking of Anisotropic Scaling Symmetry in the Quantum Lifshitz Model
• Observations on entanglement entropy in massive QFT's
• Krylov complexity in quantum field theory, and beyond
• Casimir Energy, Holographic Dark Energy and Electromagnetic Metamaterial Mimicking de Sitter
• On the non-local heat kernel expansion
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• Asymptotic Implied Volatility at the Second Order with Application to the SABR Model
• Anomalous gauge couplings from composite Higgs and warped extra dimensions
• Exact Results and Holography of Wilson Loops in N=2 Superconformal (Quiver) Gauge Theories
• Lorentz symmetry is relevant
• Manifestations of topological effects in graphene
• Aspects of Galileon Non-Renormalization
• An Exact Construction of Codimension two Holography
• Universality of squashed-sphere partition functions
• On the vacuum energy of a spherical plasma shell
• Rotating Black Hole Entropy from M5-branes
• Anomalies, entropy and boundaries
• Surface Defect, Anomalies and $b$-Extremization
• Defect CFT in the 6d (2,0) theory from M2 brane dynamics in AdS${}_7\times$S${}^4$
• Vacuum Expectation Value of the Spinor Massive field in the Cosmic String Space-Time
• Aspects of Nonlocality in Quantum Field Theory, Quantum Gravity and Cosmology
• Grand Symmetry, Spectral Action, and the Higgs mass
• Cosmological perturbations in Palatini modified gravity
• The metric-affine formalism of f(R) gravity
• Logarithmic Corrections to $N\ge 2$ Black Hole Entropy
• Ultraviolet Sensitivity in Higher Dimensions
• Toward Microstate Counting Beyond Large N in Localization and the Dual One-loop Quantum Supergravity
• Self-Dual Gravity
• Effective field equation on m-brane embedded in n-dimensional bulk of Einstein and f(R) gravity
• Heat Kernel Expansion and Extremal Kerr-Newmann Black Hole Entropy in Einstein-Maxwell Theory
• Physical renormalization schemes and asymptotic safety in quantum gravity
• Particle Physics from Almost Commutative Spacetimes
• Perturbative computation of string one-loop corrections to Wilson loop minimal surfaces in $Ad{S}_5\times S^5$
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• The number of eigenstates: counting function and heat kernel
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• Green's function method for handling radiative effects on false vacuum decay
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• One-loop Structure of Higher Rank Wilson Loops in AdS/CFT
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• Scalar-Tensor theories within Asymptotic Safety
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• On the resolvent and spectral functions of a second order differential operator with a regular singularity
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• Spectral dimension of quantum geometries
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• Monodromy Defects in Free Field Theories
• Precision Microstate Counting for the Entropy of Wrapped M5-branes
• On the trace anomaly of a Weyl fermion
• Consistent boundary conditions for supergravity
• One-loop Renormalization of Resonance Chiral Theory: Scalar and Pseudoscalar Resonances
• Exact RG Flow Equations and Quantum Gravity
• UV Sensitivity in Supersymmetric Large Extra Dimensions: The Ricci-flat Case
• Casimir effect in rugby-ball type flux compactifications
• Casimir energy in the Fulling--Rindler vacuum
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• Higgs inflation and quantum gravity: An exact renormalisation group approach
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• Interacting Fermions, Boundaries, and Finite Size Effects
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• Casimir interaction: pistons and cavity
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• Logarithmic Corrections to Black Hole Entropy: the Non-BPS Branch
• Bosonic Spectral Action Induced from Anomaly Cancelation
• Black Hole Spectroscopy and AdS${}_2$ Holography
• Multi-Loop Zeta Function Regularization and Spectral Cutoff in Curved Spacetime
• Self-force of a point charge in the space-time of a symmetric wormhole
• Scattering state and bound state of scalar field in Schwarzschild spacetime: Exact solution
• Worldline Formalism in Snyder Spaces
• Classical and quantum aspects of electric-magnetic duality rotations in curved spacetimes
• Universal Logarithmic Behavior in Microstate Counting and the Dual One-loop Entropy of AdS${}_4$ Black Holes
• Renormalization of the asymptotically expanded Yang-Mills spectral action
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• Proving the absence of large one-loop corrections to the power spectrum of curvature perturbations in transient ultra-slow-roll inflation within the path-integral approach
• Species scale, worldsheet CFTs and emergent geometry
• Lessons from conformally reduced quantum gravity
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• Renormalization of generalized vector field models in curved spacetime
• Spectral dimensions from the spectral action
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• Noncommutative QFT and Renormalization
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• Free energy and entropy for thin sheets
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• Quantum vacuum interaction between two cosmic strings revisited
• Asymptotics of physical solutions to the Lorentz-Dirac equation for a planar motion in constant electromagnetic fields
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• Entanglement and RG in the $O(N)$ vector model
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• The Massive Flat Space Limit of Cosmological Correlators
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• Spectral Noncommutative Geometry, Standard Model and all that
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• Scalar-Mediated Quantum Forces Between Macroscopic Bodies and Interferometry
• dS${}_2$ as excitation of AdS${}_2$
• $(\mathcal{F},\mathcal{G})$-summed form of the QED effective action
• New Covariant Feynman Rules for Effective Field Theories
• Logarithmic correction to the entropy of extremal black holes in $\mathcal{N}=1$ Einstein-Maxwell supergravity
• Kink fluctuation asymptotics and zero modes
• On Two-Loop Effective Action of 2D Sigma Model
• Conformal anomalies in 6d 4-derivative theories: a heat-kernel analysis
• Bootstrapped Newtonian quantum gravity
• Gravity-Induced Photon Interactions and Infrared Consistency in any Dimensions
• An approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions
• The Schwinger-DeWitt technique for quantum effective action in brane induced gravity models
• Approximate Solutions to Second Order Parabolic Equations I: analytic estimates
• One-loop effective potential of the Higgs field on the Schwarzschild background
• Free energy and entropy in Rindler and de Sitter space-times
• A Non-Singular One-Loop Wave Function of the Universe From a New Eigenvalue Asymptotics in Quantum Gravity
• Two-loop corrections to false vacuum decay in scalar field theory
• What spatial geometry does the (2+1)-dimensional QFT vacuum prefer?
• Divergences in QED on a Graph
• Nonrelativistic trace and diffeomorphism anomalies in particle number background
• High-temperature expansion of the one-loop free energy of a scalar field on a curved background
• Zeta Determinant for Laplace Operators on Riemann Caps
• Zero modes of various graphene configurations from the index theorem
• Renormalizability conditions for almost-commutative geometries
• The universe is accelerating. Do we need a new mass scale?
• Quantum magnetic flux lines, BPS vortex zero modes, and one-loop string tension shifts
• Casimir effect due to a single boundary as a manifestation of the Weyl problem
• Vacuum energy from noncommutative models
• Calculating eigenvalues of many-body systems from partition functions
• Pure connection gravity at one loop: Instanton background
• The Conformal Anomaly in bCFT from Momentum Space Perspective
• Half-integer anomalous currents in 2D materials from a QFT viewpoint
• Spectral Functions for Regular Sturm-Liouville Problems
• Numerical Analysis of some Generalized Casimir Pistons
• Renormalization on noncommutative torus
• Logarithmic corrections to the entropy of non-extremal black holes in $\mathcal{N}=1$ Einstein-Maxwell supergravity
• Partition Functions with spin in AdS_2 via Quasinormal Mode Methods
• Gravitational mass-shift effect in the Standard Model
• A rederivation of the conformal anomaly for spin-1/2
• New Heat Kernel Method in Lifshitz Theories
• Zeta Function on Surfaces of Revolution
• Clifford Structures in Noncommutative Geometry and the Extended Scalar Sector
• A statistical mechanical approach to restricted integer partition functions
• Sakharov's induced gravity on the AdS background: SM scale as inverse mass parameter of the Schwinger-DeWitt expansion
• On the renormalization of the Gibbons-Hawking boundary term
• One-Loop Correction to the AdS/BCFT Partition Function in the Three Dimensional Pure Gravity
• Normal modes in thermal AdS via the Selberg zeta function
• Heat kernel for flat generalized Laplacians with anisotropic scaling
• Notes on peculiarities of Schwinger--DeWitt technique: one-loop double poles, total-derivative terms and determinant anomalies
• CFT(4) Partition Functions and the Heat Kernel on AdS(5)
• BRST-invariant boundary conditions and strong ellipticity
• Conformal Anomaly and Off-Shell Extensions of Gravity
• Heat kernel expansion and induced action for the matrix model Dirac operator
• Heat kernel coefficients for massive gravity
• Computing black hole partition functions from quasinormal modes
• Functional determinants, index theorems, and exact quantum black hole entropy
• Cosmological bounds on TeV-scale physics and beyond
• Quantum corrections to vacuum energy sequestering (with monodromy)
• Quantum entropy couples matter with geometry
• Low-Energy Effective Action in Non-Perturbative Electrodynamics in Curved Spacetime
• Casimir Effect and Holographic Dual of Wedges
• Covariant spin-parity decomposition of the Torsion and Path Integrals
• Noncommutative SU(N) theories, the axial anomaly, Fujikawa's method and the Atiyah-Singer index
• Semiclassical $p$-branes in hyperbolic space
• Special Galileon at one loop
• Non-perturbative Quantum Propagators in Bounded Spaces
• Heat Kernel, Spectral Functions and Anomalies in Weyl Semimetals
• Vacuum polarization energy of the Shifman-Voloshin soliton
• Domain walls in a non-linear ${\mathbb{S}}^2$-sigma model with homogeneous quartic polynomial potential
• R-summed form of adiabatic expansions in curved spacetime
• Regularization versus renormalization: Why are Casimir energy differences so often finite?
• Functional Determinants of Radial Operators in $Ad{S}_2$
• Non-perturbative corrections to the one-loop free energy induced by a massive scalar field on a stationary slowly varying in space gravitational background
• Unification of Coupling Constants, Dimension six Operators and the Spectral Action
• A Note on Quantum Compactons
• Collapse of the wavefunction, the information paradox and backreaction
• Spacetime and Planck mass generation from scale-invariant degenerate gravity
• Small-time asymptotics for a general local-stochastic volatility model with a jump-to-default: curvature and the heat kernel expansion
• Geometry of the Shannon mutual information in continuum QFT
• Nilpotent noncommutativity and renormalization
• Small Mass Expansion of Functional Determinants on the Generalized Cone
• Divergences in the vacuum energy for frequency-dependent interactions
• On the Expected Production of Gravitational Waves During Preheating
• One-loop omega-potential of quantum fields with ellipsoid constant-energy surface dispersion law
• Effective action and heat kernel in a toy model of brane-induced gravity
• Hearing the shape of inequivalent spin structures and exotic Dirac operators
• Non-Perturbative One-Loop Effective Action for Electrodynamics in Curved Spacetime
• Conformal Enhancement of Holographic Scaling in Black Hole Thermodynamics: A Near-Horizon Heat-Kernel Framework
• Heat kernel of non-minimal gauge field kinetic operators on Moyal plane
• Volume stabilization in a warped flux compactification model
• Bose-Einstein Condensation on Product Manifolds
• First-order correction to the Casimir force within an inhomogeneous medium
• High-temperature expansion of the one-loop effective action induced by scalar and Dirac particles
• Bose-Einstein condensation temperature of finite systems
• Schwinger--DeWitt expansion for the heat kernel of nonminimal operators in causal theories
• Lectures in Quantum Gravity
• Dynamical Edge Modes in $p$-form Gauge Theories
• Logarithmic correction to the entropy of a Kerr-Newman family of black holes in $U(1{)}^2$-charged STU supergravity models
• Worldline approach for spinor fields in manifolds with boundaries
• Is the Euclidean path integral always equal to the thermal partition function?
• Cosmic bounce and phantom-like equation of state from tunnelling
• Microscopics of de Sitter Entropy from Precision Holography
• Chiral current induced by torsional Weyl anomaly
• Spectral interaction between universes
• Vacuum expectation values in non-trivial background space from three types of UV improved Green's functions
• Worldline formalism for a confined scalar field
• Asymptotic Expansion of the Heat Kernel Trace of Laplacians with Polynomial Potentials
• Nonlocal Quantum Effective Actions in Weyl-Flat Spacetimes
• Self-consistent radiative corrections to false vacuum decay
• One loop partition function of six dimensional conformal gravity using heat kernel on AdS
• Conformal gravity 1-loop partition function
• Heat kernel expansions, ambient metrics and conformal invariants
• One-loop correction to the energy of a wavy line string in AdS_5
• Fermions and noncommutative emergent gravity II: Curved branes in extra dimensions
• Quantum aspects of a noncommutative supersymmetric kink
• Intrinsic time gravity, heat kernel regularization, and emergence of Einstein's theory
• Axion anomalies
• Free energy dependence on spatial geometry for (2+1)-dimensional QFTs
• The two-sphere partition function in two-dimensional quantum gravity at fixed area
• Energy spectrum of interacting gas: cluster expansion method
• UV completion of extradimensional Yang-Mills theory for Gauge-Higgs unification
• Radiative corrections to false vacuum decay in quantum mechanics
• A topological state sum model for fermions on the circle
• One-loop partition function of gravity with leaky boundary conditions
• Spectral dimension of bosonic string theory
• Can one hear the density of a drum? Weyl's law for inhomogeneous media
• Unveiling horizons in quantum critical collapse
• On a possible method of Casimir pressure renormalization in a ball
• One-loop beta-function for an infinite-parameter family of gauge theories
• Heat Determinant on Manifolds
• Small-time expansion of the Fokker-Planck kernel for space and time dependent diffusion and drift coefficients
• Spectral asymmetry on the ball and asymptotics of the asymmetry kernel
• Dynamical edge modes in Maxwell theory from a BRST perspective, with an application to the Casimir energy
• Dimensional Deception from Noncommutative Tori: An alternative to Horava-Lifschitz
• Statistical ensembles and logarithmic corrections to black hole entropy
• On the Hurwitz Zeta Function of Imaginary Second Argument
• Renormalization of vector fields with mass-like coupling in curved spacetime
• Abelian M5-brane on $S^6$
• Non-topological fractional fermion number in the Jackiw-Rossi model
• The ultrarelativistic limit of 2D dilaton gravity and its energy momentum tensor
• Induced Chern-Simons action on noncommutative torus
• Scarf for Lifshitz
• Vacuum polarization of a massive scalar field in a wormhole spacetime
• Clifford-based spectral action and renormalization group analysis of the gauge couplings
• Heat coefficient $a_4$ for nonminimal Laplace type operators
• Thermal Casimir Effect for Rectangular Cavities inside D+1-dimensional Minkowski Spacetime Revisited
• Does the Round Sphere Maximize the Free Energy of (2+1)-Dimensional QFTs?
• Radiative corrections to the $R$ and $R^2$ invariants from torsion fluctuations on maximally symmetric spaces
• Fundamental Membranes and the String Dilaton
• The two-sphere partition function in two-dimensional quantum gravity
• Commutator technique for the heat kernel of minimal higher derivative operators
• Path integral calculation of heat kernel traces with first order operator insertions
• Discrete time heat kernel and UV modified propagators with Dimensional Deconstruction
• Casimir self-energy of a δ-δ' sphere
• Mathematical Tools for Calculation of the Effective Action in Quantum Gravity
• Fermionic spectral action and the origin of nonzero neutrino masses
• Self-action in Gravity
• The ubiquitous $\zeta$-function and some of its "usual" and "unusual" meromorphic properties
• Ordered Exponential and Its Features in Yang-Mills Effective Action
• Discrete heat kernel, UV modified Green's function, and higher derivative theories
• Vacuum expectation value of twist fields
• Spectral Action and Gravitational effects at the Planck scale
• A note on one-loop soliton quantum mass corrections
• Sakharov's induced gravity and the Poincaré gauge theory
• Bounding the Heat Trace of a Calabi-Yau Manifold
• Emergent gravity from off-shell energy fixing
• Casimir Effect for Quantum Field theory in Networks
• On the resilience of the gravitational variational principle under renormalization
• Bulk-boundary entanglement correspondence and the Ryu-Takayanagi conjecture in an $Ad{S}_2/CF{T}_1$ setup
• Irreducible Scalar Many-Body Casimir Energies: Theorems and Numerical Studies
• Geometry-Information Duality: Quantum Entanglement Contributions to Gravitational Dynamics
• Observed Cosmological Reexpansion in Minimal QFT with Bose and Fermi Fields
• Some Developments of the Casimir Effect in $p$-Cavity of $(D+1)$-Dimensional Spacetime
• Constraints, gauge symmetries, and noncommutative gravity in two dimensions
• Bose and Fermi Statistics and the Regularization of the Nonrelativistic Jacobian for the Scale Anomaly
• A note on the heat kernel coefficients for nonminimal operators
• A New Example of the Effects of a Singular Background on the Zeta Function
• Technically Natural Vacuum Energy at the Tip of a Supersymmetric Teardrop
• Some new results for the one-loop mass correction to the compactified $\lambda {\varphi }^4$ theory
• A Surprising Similarity Between Holographic CFTs and a Free Fermion in $(2+1)$ Dimensions
• Strings in Bimetric Spacetimes
• Supersymmetry breaking, brane dynamics and Swampland conjectures
• Resummed heat-kernel for surface contributions: Dirichlet semitransparent boundary conditions
• Anomaly inflow for local boundary conditions
• Casimir energy for spinor fields with $\delta$-shell potentials
• Brane Stabilization and Regionality of Extra Dimensions
• Weyl invariance, non-compact duality and conformal higher-derivative sigma models
• Edge states and the $\eta$ invariant
• Black hole one-loop determinants in the large dimension limit
• Archimedes Force on Casimir Apparatus
• Free Energy on a Cycle Graph and Trigonometric Deformation of Heat Kernel Traces on Odd Spheres
• Electromagnetic vacuum densities induced by a cosmic string
• Probability Thermodynamics and Probability Quantum Field
• Super Heat Kernel of General Second Order Operators in $N=1$ Superspace and One-Loop Divergence of Dilaton-coupled SYM Theory
• Heat Trace and Functional Determinant in One Dimension
• Spectral Analysis of Causal Dynamical Triangulations via Finite Element Method
• Central charges, elliptic genera, and Bekenstein-Hawking entropy in $\mathcal{N}=(2,2)$ AdS${}_3$/CFT${}_2$
• Entanglement Entropy of $(2+1)$D Quantum Critical Points with Quenched Disorder: Dimensional Reduction Approach
• Moduli Stabilization in a de Sitter Compactification Model
• Graphene shapes from quantum elasticity
• The spectral $\zeta$-function for quasi-regular Sturm--Liouville operators
• Theoretical Radio Signals from Radio-Band Gravitational Waves Converted from the Neutron Star Magnetic Field
• Heat kernel of non-minimal second-order operators
• Geometric realization of stress-tensor deformed field theory
• On the Invariant and Geometric Structure of the Holomorphic Unified Field Theory
• One-loop effective potential in M4 x T2 with and without 't Hooft flux
• Casimir type effects for scalar fields interacting with material slabs
• Bose-Einstein condensation in two-dimensional traps
• Quantum Corrections in Classicalon Theories
• Covariant perturbation expansion of off-diagonal heat kernel
• Can Spectral Action be a Window to Very High Energies?
• Scattering approach for calculating one-loop effective action and vacuum energy
• Krein's Formula And Heat-Kernel Expansion For Some Differential Operators With A Regular Singularity
• Induced Gauge Theory on a Noncommutative Space
• Gravitons on Nariai Edges
• Effects of Curvature-Scalar Coupling on Vacuum Energy in Flat (3+1)-Dimensional Space-Time
• Casimir energy for acoustic phonons in graphene
• Boundary gauge and gravitational anomalies from Ward identities
• Fundamental solutions of heat equation on unitary groups establish an improved relation between $\epsilon$-nets and approximate unitary $t$-designs
• Holographic Anomalous Current at a Finite Temperature
• Superspace worldline formalism approach to Quantum Gravity: dimensional reduction and Holography
• Supersymmetric localization: $\mathcal{N}=(2,2)$ theories on S${}^2$ and AdS${}_2$
• The Casimir Effect for Thick Pistons
• Undecidability in Spacetime Geometry via the AdS/CFT Correspondence
• Spectral geometry of symplectic spinors
• Casimir energy of smooth compact surfaces
• Relational de Sitter State Counting with an SU(3) Clock
• Boundary Shape and Casimir Energy
• Proper time method in de Sitter space
• In-in worldline formalism in pair creating fields
• Quantizing non-projectable Hořava gravity with Lagrangian path integral
• Spectral interactions between strings in the Higgs background
• Non-relativistic Limit of Thermodynamics of Bose Field in a Static Space-time and Bose-Einstein Condensation
• Implications of the complex Singlet field for Noncommutative Geometry model
• Thermal Casimir effect for a Dirac field on flat space with a nontrivial circular boundary condition
• Partition functions on squashed seven-spheres and holography
• Yang-Mills action from minimally coupled bosons on R^4 and on the 4D Moyal plane
• Graph-theory induced gravity and strongly-degenerate fermions in a self-consistent Einstein universe
• Quantum Field Theory on Multifractal Spacetime: Varying Dimension and Ultraviolet Completeness
• Supersymmetric localisation of $\mathcal{N}=(2,2)$ theories on a spindle
• Toward Supergravity Spectral Action
• Vacuum configuration of winding superstrings from non-standard semiclassical quantization
• Two-loop dimension Six Effective Action: Integrating Out Heavy Scalar
• Stability of the de-Sitter universe: One-loop nonlocal $f(R)$ gravity
• Symmetry-Resolved Entanglement Entropy in Higher Dimensions
• Calculations in induced gravity from higher-derivative field theories
• The Polyakov loop dependence of bulk viscosity of QCD matter
• Renormalization group flow, Entropy and Eigenvalues
• Entanglement Entropy Evolution under Double-trace Deformation
• On space-time noncommutative U(1) model at high temperature
• Heat kernel approach for confined quantum gas
• Coarse-graining of the Einstein-Hilbert Action rewritten by the Fisher information metric
• Vacuum instability in Kaluza-Klein manifolds
• Electrically charged black hole solutions in semiclassical gravity and dynamics of linear perturbations
• Particle production rate for a dynamical system using the path integral approach
• Fermionic zero modes in the vortex field in arbitrary dimensions and index of Dirac operator with Majorana-like interaction
• Bounds on the heat kernel of the Schroedinger operator in a random electromagnetic field
• Proper-time evaluation of the effective action: unequal masses in the loop
• Torsional Hall Viscosity of Massive Chern Insulators: Magnetic Field and Momentum Deformations
• Vortex Fractional Fermion Number through Heat Kernel methods and Edge States
• Finite temperature Casimir effect for a spinor field in cosmic dispiration spacetime
• Casimir energy through transfer operators for sine-Gordon backgrounds
• Exact Green's function for fermions in an external Yang-Mills gauge field
• Impact of space-time curvature coupling on the vacuum energy induced by a magnetic topological defect in flat space-time of arbitrary dimension
• Temperatures of AdS${}_2$ black holes and holography revisited
• On the Imaginary Part of the Effective Action in de Sitter Spacetime with Different Regularization Schemes
• Bose-Fermi Equivalence in Three Dimensional Non-commutative Space-Time
• Conformal gauge theory of vector-spinors and spin-3/2 particles
• Pseudodifferential calculus in Schwinger--DeWitt formalism: UV and IR parts
• Geometry-Induced Vacuum Polarization and Mode Shifts in Maxwell-Klein-Gordon Theory
• Heat kernel approach to the one-loop effective action for nonlinear electrodynamics
• On equivalent methods for functional determinants
• Regularization from Superpositions of Time Evolutions
• De Sitter Cores from Nonlocal Quantum Field Theories
• Edge physics and the Casimir interaction in Maxwell-Chern-Simons theory on a strip
• Liouville theory on a horizon: point particle/scalar field duality and Page-like curve
• Possible large-N fixed-points and naturalness for O(N) scalar fields
• Spectral Asymptotics of Elliptic Operators on Manifolds
• Ward identities under the frame transformations in curved spacetime
• Effective gravitational action for 2D massive Majorana fermions on arbitrary genus Riemann surfaces
• The geodesic rule for higher codimensional global defects
• The thermodynamic limit of an ideal Bose gas by asymptotic expansions and spectral $\zeta$-functions
• Non-minimal non-Abelian quantum vector fields in curved spacetime
• Type-II two-Higgs-doublet model in noncommutative geometry
• Non-linear sigma models on constant curvature target manifolds: a functional renormalization group approach
• Remark on the synergy between the heat kernel techniques and the parity anomaly
• Vacuum energy of scalar fields on spherical shells with general matching conditions
• A new and gauge-invariant Littlest Higgs model with T-parity
• Enhancement of Anomalous Boundary Current by High Temperature
• Bulk entanglement and its shape dependence
• Virial coefficients expressed by heat kernel coefficients