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Zeta Regularization Techniques with Applications

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Casimir Free Energy for Massive Scalars: A Comparative Study of Various Approaches
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Borel transform and integral identities involving λ‐Bessel and λ‐Tricomi matrix functions
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Complete Zeta-Function Approach to the Electromagnetic Casimir Effect for Spheres and Circles
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Aspects of Quasi-Phase-Structure of the Schwinger Model on a Cylinder with Broken Chiral Symmetry
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Symbolic Computations
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Quiver Diagram
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Regularization, zeta function method
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Two Examples of Zeta-Regularization
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Integrating Gauge Fields in the ζ-Formulation of Feynman’s Path Integral
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Bosonic Strings
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Superstrings
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Quantum Superfield Supersymmetry
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Scalar Fields at Zero and Finite Temperature
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Quantum Fields and Particles, Gauge Theories and Strings
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Abelian Gauge Theories
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Introduction to String Theory
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On How the Cyberspace Arose to Fulfill Theoretical Physicists’ Needs and Eventually Changed the World: Personal Recallings and a Practitioner’s Perspective
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Relative-Zeta and Casimir Energy for a Semitransparent Hyperplane Selecting Transverse Modes
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Introduction
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The Dwelling of the Spectral Action
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Emili Elizalde. Perspectives on his Life and Work
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Colliding Hadrons as Cosmic Membranes and Possible Signatures of Lost Momentum
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Pistons Modelled by Potentials
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Local ζ -functions, stress-energy tensor, field fluctuations, and all that, in curved static spacetime
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Zeta-regularization and exact WKB method for a general 1D Schrödinger equation
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Black Hole Thermodynamics and Perturbative Quantum Gravity
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Black Hole Thermodynamics and Perturbative Quantum Gravity
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Zeta function determinant of the Laplace operator on theD-dimensional ball
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Schwinger-Dyson equations and dynamic symmetry violation in two-dimensional quantum quadratic gravitation
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Vacuum energy induced by a singular magnetic vortex
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Quantum-induced interactions in the moduli space of degenerate BPS domain walls
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Gravitational corrections to Higgs potentials
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Cosmic string and brane induced effects on the fermionic vacuum in AdS spacetime
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Functional Determinants for Radial Operators in AdS2
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Functional determinants of radial operators in AdS2
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Sine-dilaton gravity vs double-scaled SYK: exploring one-loop quantum corrections
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Magnetic susceptibility of QCD matter and its decomposition from the lattice
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Leptonic CP violating effective action for Dirac and Majorana neutrinos
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Critical dimensions and small cycle dominance from all-orders asymptotics of d-matrix theory
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Perils of towers in the swamp: dark dimensions and the robustness of EFTs
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Modular properties of massive scalar partition functions
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Finite temperature Casimir effect for a spinor field in cosmic dispiration spacetime
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Modular invariance in finite temperature Casimir effect
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Mass-deformed super Yang-Mills theory on $$ {\mathbbm{T}}^4 $$: sum over twisted sectors, θ-angle, and CP violation
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Vacuum currents in braneworlds on AdS bulk with compact dimensions
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Quantum flux operators for Carrollian diffeomorphism in general dimensions
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Modularity in d > 2 free conformal field theory
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Classification of compactified su(Nc) gauge theories with fermions in all representations
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Classification of compactified su(Nc) gauge theories with fermions in all representations
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Notes on massless scalar field partition functions, modular invariance and Eisenstein series
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Zeta determinants on cones and products
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The Exotic Structure of the Spectral $$\zeta $$-function for the Schrödinger Operator with Pöschl–Teller Potential
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Spectral Analysis and Zeta Determinant on the Deformed Spheres
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Regularized Determinants of the Laplacian for cofinite kleinian groups with Finite-Dimensional Unitary Representations
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The Product Over All Primes is 4π2
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The Spectral Zeta Function for Laplace Operators on Warped Product Manifolds of the type I × f N
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Zeta-Function Regularization, the Multiplicative Anomaly and the Wodzicki Residue
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Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone
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Multiple ΛCDM cosmology with string landscape features and future singularities
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Brane cosmology from observational surveys and its comparison with standard FRW cosmology
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Surface vacuum energy and stresses on a brane in AdS space with an application to the brane-world model
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Induced Cosmological Constant in Brane Models with a Compact Dimension
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Fermionic Vacuum Stresses in Models with Toroidal Compact Dimensions
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Topological Casimir Effect in Models with Helical Compact Dimensions
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Self-Normalizing Path Integrals
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Casimir energy–momentum tensor for curved boundaries in de Sitter space-time
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Observational assessment of the viability of de Sitter Gödel de Sitter phase transition
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Casimir Forces for Robin Scalar Field on Cylindrical Shell in de Sitter Space
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Casimir Effect for Moving Branes in Static dS4+1 Bulk
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The Casimir Effect for Parallel Plates in the Spacetime with a Fractal Extra Compactified Dimension
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Casimir Effect in Hemisphere Capped Tubes
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The Casimir Effect at Finite Temperature in a Six-Dimensional Vortex Scenario
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Casimir Effect for Two Parallel Plates Through a Gupta-Bleuler Type Quantization on the Static Domain Wall Background
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QFT Over the Finite Line. Heat Kernel Coefficients, Spectral Zeta Functions and Selfadjoint Extensions
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Regularized Laplacian determinants of self-similar fractals
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The spectral $$\zeta $$-function for quasi-regular Sturm–Liouville operators
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Casimir effect for a collection of parallel conducting surfaces
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Functional determinants for the second variation
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Functional determinant of Laplacian on Cayley projective plane $${\mathbf {P}}^\mathbf{2 }$$($${\mathbf {Cay}}$$)
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Minakshisundaram–Pleijel coefficients for non-compact higher rank symmetric spaces
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Casimir pistons with generalized boundary conditions: a step forward
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Partition function of massless scalar field in Schwarzschild background
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Spectral $$\varvec{\zeta }$$-functions and $$\varvec{\zeta }$$-regularized functional determinants for regular Sturm–Liouville operators
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Explicit descriptions of spectral properties of Laplacians on spheres $${\mathbb {S}}^{N}\,(N\ge 1)$$: a review
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Maclaurin spectral results on rank one symmetric spaces of noncompact type
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Generation of off-critical zeros for hypercubic Epstein zeta functions
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Instanton constraints and renormalization
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On the Casimir energy for a massive quantum scalar field and the cosmological constant
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Schwinger–Dyson equation and NJL approximation in massive gauge theory with fermions
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Exciton in matrix formulation of quantum Hall effect
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Partition functions for quantum gravity, black holes, elliptic genera and Lie algebra homologies
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One-loop kink mass shifts: A computational approach
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Casimir pistons with general boundary conditions
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Low-dimensional Heisenberg magnets: Riemann zeta function regularization
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Casimir energy–momentum tensor for a brane in de Sitter spacetime
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Repulsive Casimir force from fractional Neumann boundary conditions
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Casimir densities for a boundary in Robertson–Walker spacetime
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Quantum spring from the Casimir effect
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Electromagnetic two-point functions and Casimir densities for a conducting plate in de Sitter spacetime
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Vacuum polarization energy for general backgrounds in one space dimension
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Resolution of challenging problems in quantum cosmology with electromagnetic radiation
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Confined Maxwell field and temperature inversion symmetry
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String fluctuations, AdS/CFT and the soft pomeron intercept
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Instability of effective potential for non-abelian toroidal D-brane
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Energy of the vacuum with a perfectly conducting and infinite cylindrical surface
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Quantum effects for extrinsic geometry of strings via the generalized Weierstrass representation
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Multiplicative anomaly and finite charge density
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On the dimensional reduction procedure
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Dimensional regularization of a compact dimension
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Parity breaking in 2 + 1 dimensions and finite temperature
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Semiclassical and Stochastic Gravity
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Preface
inferred← citeshttps://doi.org/10.1017/9780511667497.002openalex-snapshot
Overview: Main Themes. Key Issues. Reader’s Guide
inferred← citeshttps://doi.org/10.1017/9780511667497.004openalex-snapshot
‘In-Out’ Effective Action. Dimensional Regularization
inferred← citeshttps://doi.org/10.1017/9780511667497.005openalex-snapshot
‘In-In’ Effective Action. Stress Tensor. Thermal Fields
inferred← citeshttps://doi.org/10.1017/9780511667497.006openalex-snapshot
Stress-Energy Tensor and Correlators: Zeta-Function Method
inferred← citeshttps://doi.org/10.1017/9780511667497.007openalex-snapshot
Stress-Energy Tensor and Correlation. Point Separation
inferred← citeshttps://doi.org/10.1017/9780511667497.009openalex-snapshot
Infrared Behavior of Interacting Quantum Field
inferred← citeshttps://doi.org/10.1017/9780511667497.010openalex-snapshot
Advanced Field Theory Topics
inferred← citeshttps://doi.org/10.1017/9780511667497.011openalex-snapshot
Backreaction of Early Universe Quantum Processes
inferred← citeshttps://doi.org/10.1017/9780511667497.013openalex-snapshot
Metric Correlations at One-Loop: In-In and Large N
inferred← citeshttps://doi.org/10.1017/9780511667497.014openalex-snapshot
The Einstein–Langevin Equation
inferred← citeshttps://doi.org/10.1017/9780511667497.015openalex-snapshot
Metric Fluctuations in Minkowski Spacetime
inferred← citeshttps://doi.org/10.1017/9780511667497.017openalex-snapshot
Cosmological Backreaction with Fluctuations
inferred← citeshttps://doi.org/10.1017/9780511667497.018openalex-snapshot
Structure Formation in the Early Universe
inferred← citeshttps://doi.org/10.1017/9780511667497.019openalex-snapshot
Black Hole Backreaction and Fluctuations
inferred← citeshttps://doi.org/10.1017/9780511667497.021openalex-snapshot
Stress-Energy Tensor Fluctuations in de Sitter Space
inferred← citeshttps://doi.org/10.1017/9780511667497.022openalex-snapshot
Two-Point Metric Perturbations in de Sitter
inferred← citeshttps://doi.org/10.1017/9780511667497.023openalex-snapshot
Riemann Tensor Correlator in de Sitter
inferred← citeshttps://doi.org/10.1017/9780511667497.024openalex-snapshot
Epilogue: Linkage with Quantum Gravity
inferred← citeshttps://doi.org/10.1017/9780511667497.025openalex-snapshot
Index
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Gravity as a Source of Phase Transitions
inferred← citeshttps://doi.org/10.1023/a:1021189211783openalex-snapshot
Moduli Stabilization in Warped Compactifications at One Loop
inferred← citeshttps://doi.org/10.1023/a:1025770918832openalex-snapshot
Moduli Fields in Warped Compactifications
inferred← citeshttps://doi.org/10.1023/a:1027314126258openalex-snapshot
Letter: Trace Anomaly and Backreaction of the Dynamical Casimir Effect
inferred← citeshttps://doi.org/10.1023/b:acap.0000024207.37694.3bopenalex-snapshot
Zeta Regularizations
inferred← citeshttps://doi.org/10.1023/b:gerg.0000010479.98616.daopenalex-snapshot
Casimir Energy for Spherical Shell in Schwarzschild Black Hole Background
inferred← citeshttps://doi.org/10.1023/b:gerg.0000036054.14902.a6openalex-snapshot
Letter: Casimir Stress for Cylindrical Shell in de Sitter Space
inferred← citeshttps://doi.org/10.1023/b:tamp.0000015072.58252.19openalex-snapshot
Semiclassical Wormholes with a Smooth Throat
inferred← citeshttps://doi.org/10.1063/1.2174291openalex-snapshot
Casimir effect in a two-dimensional signature changing space-time
inferred← citeshttps://doi.org/10.1063/1.2760374openalex-snapshot
Finite temperature Casimir effect for a massless fractional Klein-Gordon field with fractional Neumann conditions
inferred← citeshttps://doi.org/10.1063/1.3427320openalex-snapshot
Erratum: “Functional determinants in higher derivative Lagrangian theories” [J. Math. Phys. 50, 103517 (2009)]
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The formal path integral and quantum mechanics
inferred← citeshttps://doi.org/10.1063/1.3656881openalex-snapshot
On the Hurwitz zeta function of imaginary second argument
inferred← citeshttps://doi.org/10.1063/1.4770050openalex-snapshot
Relation between primes and nontrivial zeros in the Riemann hypothesis; Legendre polynomials, modified zeta function and Schrödinger equation
inferred← citeshttps://doi.org/10.1063/1.4891148openalex-snapshot
Tunnel determinants from spectral zeta functions. Instanton effects in quantum mechanics
inferred← citeshttps://doi.org/10.1063/1.530469openalex-snapshot
The vacuum energy density for spherical and cylindrical universes
inferred← citeshttps://doi.org/10.1063/1.531215openalex-snapshot
The conformal anomaly in N-dimensional spaces having a hyperbolic spatial section
inferred← citeshttps://doi.org/10.1063/1.532929openalex-snapshot
One-loop stress-tensor renormalization in curved background: The relation between ζ-function and point-splitting approaches, and an improved point-splitting procedure
inferred← citeshttps://doi.org/10.1063/1.59656openalex-snapshot
Spectral functions in mathematics and physics
inferred← citeshttps://doi.org/10.1063/5.0071099openalex-snapshot
The zeta function for the triangular potential
inferred← citeshttps://doi.org/10.1080/10652469.2019.1684487openalex-snapshot
Operational, umbral methods, Borel transform and negative derivative operator techniques
inferred← citeshttps://doi.org/10.1080/1726037x.2006.10698500openalex-snapshot
Complex Topological Invariants of Three-Hyperbolic Manifolds
inferred← citeshttps://doi.org/10.1088/0004-637x/772/2/85openalex-snapshot
STATISTICS OF DARK MATTER HALOS FROM THE EXCURSION SET APPROACH
inferred← citeshttps://doi.org/10.1088/0031-8949/76/1/009openalex-snapshot
Evaluation of the Casimir force for a dielectric–diamagnetic cylinder with light velocity conservation condition and the analogue of Sellmeir's dispersion law
inferred← citeshttps://doi.org/10.1088/0031-8949/82/03/035101openalex-snapshot
Finite temperature Casimir effect and dispersion in the presence of compactified extra dimensions
inferred← citeshttps://doi.org/10.1088/0253-6102/53/6/27openalex-snapshot
Casimir Force on a Piston in Randall–Sundrum Models
inferred← citeshttps://doi.org/10.1088/0253-6102/54/6/21openalex-snapshot
Neumann Boundary Conditions Inhibiting SSB in Coleman—Weinberg Mechanism
inferred← citeshttps://doi.org/10.1088/0253-6102/55/1/20openalex-snapshot
Shape of Compact Toroidal Dimensions T θ d and Casimir Effect on M D × T θ d Spacetime
inferred← citeshttps://doi.org/10.1088/0253-6102/58/2/11openalex-snapshot
Casimir Effect at Finite Temperature in the Presence of One Fractal Extra Compactified Dimension
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Casimir Effect at Finite Temperature in the Presence of Compactified Universal Extra Dimensions
inferred← citeshttps://doi.org/10.1088/0256-307x/22/9/014openalex-snapshot
Casimir effect for a Cavity in the Spacetime with an Extra Dimension
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The Casimir Force between Parallel Plates in Randall–Sundrum I Model
inferred← citeshttps://doi.org/10.1088/0264-9381/11/12/010openalex-snapshot
Dynamical generation of spacetime signature by massive quantum fields on a topologically non-trivial background
inferred← citeshttps://doi.org/10.1088/0264-9381/11/4/002openalex-snapshot
Dynamical determination of the metric signature in spacetime of non-trivial topology
inferred← citeshttps://doi.org/10.1088/0264-9381/14/3/008openalex-snapshot
Quantum fields in hyperbolic spacetimes with finite spatial volume
inferred← citeshttps://doi.org/10.1088/0264-9381/14/5/009openalex-snapshot
Geometric entropy and curvature coupling in conical spaces: -function approach
inferred← citeshttps://doi.org/10.1088/0264-9381/15/5/003openalex-snapshot
Vacuum energy for the supersymmetric twisted D -brane in a constant electromagnetic field
inferred← citeshttps://doi.org/10.1088/0264-9381/18/12/308openalex-snapshot
Casimir effect for a spherical shell in de Sitter space
inferred← citeshttps://doi.org/10.1088/0264-9381/18/14/304openalex-snapshot
Casimir stress on parallel plates in a de Sitter space
inferred← citeshttps://doi.org/10.1088/0264-9381/18/15/316openalex-snapshot
Quantum radiation of uniformly accelerated spherical mirrors
inferred← citeshttps://doi.org/10.1088/0264-9381/20/16/315openalex-snapshot
Casimir densities for a spherical shell in the global monopole background
inferred← citeshttps://doi.org/10.1088/0264-9381/23/14/008openalex-snapshot
Spinor Casimir effect for concentric spherical shells in the global monopole spacetime
inferred← citeshttps://doi.org/10.1088/0264-9381/23/18/004openalex-snapshot
Casimir energy density for spherical universes inn-dimensional spacetime
inferred← citeshttps://doi.org/10.1088/0264-9381/23/3/006openalex-snapshot
The Casimir effect in a wormhole spacetime
inferred← citeshttps://doi.org/10.1088/0264-9381/24/4/010openalex-snapshot
Casimir effect in E 3 closed spaces
inferred← citeshttps://doi.org/10.1088/0264-9381/24/6/016openalex-snapshot
The cosmological constant as an eigenvalue of f ( R )-gravity Hamiltonian constraint
inferred← citeshttps://doi.org/10.1088/0264-9381/26/19/195004openalex-snapshot
Casimir densities for a plate in de Sitter spacetime
inferred← citeshttps://doi.org/10.1088/0264-9381/26/7/075024openalex-snapshot
Time-reversal and parity conservation for gravitating quarks
inferred← citeshttps://doi.org/10.1088/0264-9381/27/22/225009openalex-snapshot
Casimir effect for curved boundaries in Robertson–Walker spacetime
inferred← citeshttps://doi.org/10.1088/0264-9381/30/1/015002openalex-snapshot
Fermionic vacuum polarization by a flat boundary in cosmic string spacetime
inferred← citeshttps://doi.org/10.1088/0264-9381/32/2/025009openalex-snapshot
Scalar Casimir densities induced by a cylindrical shell in de Sitter spacetime
inferred← citeshttps://doi.org/10.1088/0305-4470/27/9/010openalex-snapshot
Zeta-function regularization is uniquely defined and well
inferred← citeshttps://doi.org/10.1088/0305-4470/37/38/r01openalex-snapshot
The Casimir effect: recent controversies and progress
inferred← citeshttps://doi.org/10.1088/0305-4470/37/39/013openalex-snapshot
Finite-temperature properties of the Dirac operator under local boundary conditions
inferred← citeshttps://doi.org/10.1088/0305-4470/37/47/018openalex-snapshot
Zeta function regularization for a scalar field in a compact domain
inferred← citeshttps://doi.org/10.1088/0305-4470/38/29/003openalex-snapshot
One-loop integrals at finite temperature
inferred← citeshttps://doi.org/10.1088/0305-4470/38/37/011openalex-snapshot
Eta invariants with spectral boundary conditions
inferred← citeshttps://doi.org/10.1088/0305-4470/38/41/009openalex-snapshot
ζ-determinants of Laplacians with Neumann and Dirichlet boundary conditions
inferred← citeshttps://doi.org/10.1088/0305-4470/38/50/011openalex-snapshot
Spectral analysis of a flat plasma sheet model
inferred← citeshttps://doi.org/10.1088/0305-4470/39/21/s15openalex-snapshot
One-loopf(R) gravitational modified models
inferred← citeshttps://doi.org/10.1088/0305-4470/39/21/s21openalex-snapshot
Uses of zeta regularization in QFT with boundary conditions: a cosmo-topological Casimir effect
inferred← citeshttps://doi.org/10.1088/0305-4470/39/21/s25openalex-snapshot
Krein's formula and heat-kernel expansion for some differential operators with a regular singularity
inferred← citeshttps://doi.org/10.1088/0305-4470/39/21/s66openalex-snapshot
Spectral functions for the flat plasma sheet model
inferred← citeshttps://doi.org/10.1088/0305-4470/39/21/s73openalex-snapshot
Analytical regularization for confined quantum fields between parallel surfaces
inferred← citeshttps://doi.org/10.1088/0305-4470/39/21/s79openalex-snapshot
The Casimir free energy in high- and low-temperature limits
inferred← citeshttps://doi.org/10.1088/0305-4470/39/3/017openalex-snapshot
Multidimensional cut-off technique, odd-dimensional Epstein zeta functions and Casimir energy of massless scalar fields
inferred← citeshttps://doi.org/10.1088/0305-4470/39/38/017openalex-snapshot
Functional determinants for radial operators
inferred← citeshttps://doi.org/10.1088/0305-4470/39/42/011openalex-snapshot
Scalar Casimir densities for cylindrically symmetric Robin boundaries
inferred← citeshttps://doi.org/10.1088/1126-6708/1999/07/015openalex-snapshot
On the concept of determinant for the differential operators of quantum physics
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