Casimir Effects in Renormalizable Quantum Field Theories

Abstract

We review the framework we and our collaborators have developed for the study of one-loop quantum corrections to extended field configurations in renormalizable quantum field theories. We work in the continuum, transforming the standard Casimir sum over modes into a sum over bound states and an integral over scattering states weighted by the density of states. We express the density of states in terms of phase shifts, allowing us to extract divergences by identifying Born approximations to the phase shifts with low order Feynman diagrams. Once isolated in Feynman diagrams, the divergences are canceled against standard counterterms. Thus regulated, the Casimir sum is highly convergent and amenable to numerical computation. Our methods have numerous applications to the theory of solitons, membranes, and quantum field theories in strong external fields or subject to boundary conditions.

27 pp., 11 EPS figures, LaTeX using ijmpa1.sty; email correspondence to R.L. Jaffe <[email protected]> ; based on talks presented by the authors at the 5th workshop `QFTEX', Leipzig, September 2001

References in corpus (2)

• Quantum Energies of Interfaces
• Quantum Corrections to Q-Balls

Cited by in corpus (53)

• Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir Problem
• The Dirichlet Casimir Problem
• Casimir Energies in Light of Quantum Field Theory
• Systematics of the Relationship between Vacuum Energy Calculations and Heat Kernel Coefficients
• Wightman function and Casimir densities on AdS bulk with application to the Randall-Sundrum braneworld
• Casimir Energies and Pressures for $\delta$-function Potentials
• Nonsmooth backgrounds in quantum field theory
• Finite temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on zeta function technique
• Wightman function and vacuum fluctuations in higher dimensional brane models
• Casimir energy-momentum tensor for a brane in de Sitter spacetime
• The Casimir Effect for Fermions in One Dimension
• Calculating Casimir Energies in Renormalizable Quantum Field Theory
• Fermion-induced quantum action of vortex systems
• Fermionic Vacuum Energy from a Nielsen-Olesen Vortex
• A new renormalization approach to the Dirichlet Casimir effect for ϕ^4 theory in (1+1) dimensions
• The Dirichlet Casimir effect for ${\varphi }^4$ theory in (3+1) dimensions: A new renormalization approach
• Casimir densities for a spherical boundary in de Sitter spacetime
• Quantum QED Flux Tubes in 2+1 and 3+1 Dimensions
• On the Vacuum energy of a Color Magnetic Vortex
• Physically Sound Hamiltonian Formulation of the Dynamical Casimir Effect
• Radiative Correction to the Dirichlet Casimir Energy for $\lambda {\varphi }^4$ Theory in Two Spatial Dimensions
• On the issue of imposing boundary conditions on quantum fields
• Electromagnetic Casimir densities for a wedge with a coaxial cylindrical shell
• Casimir dynamics: Interactions of Surfaces with codimension >1 due to Quantum Fluctuations
• Casimir effect for scalar current densities in topologically nontrivial spaces
• Quantum Energies of Strings in a 2+1 Dimensional Gauge Theory
• Field of homogeneous Plane in Quantum Electrodynamics
• Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity
• Self-consistent bounces in two dimensions
• Weyl problem and Casimir effects in spherical shell geometry
• Whightman function and scalar Casimir densities for a wedge with a cylindrical boundary
• False vacuum decay by self-consistent bounces in four dimensions
• Scalar Casimir densities for cylindrically symmetric Robin boundaries
• Quantum stabilization of Z-strings, a status report on D=3+1 dimensions
• Lorentz violating scalar Casimir effect for a $D$-dimensional sphere
• The Dirichlet Casimir Energy for ${\varphi }^4$ Theory in a Rectangle
• Parity violating cylindrical shell in the framework of QED
• Casimir effect due to a single boundary as a manifestation of the Weyl problem
• Finite Temperature Induced Fermion Number In The Nonlinear sigma Model In (2+1) Dimensions
• Wightman function and scalar Casimir densities for a wedge with two cylindrical boundaries
• Casimir buoyancy
• The Casimir Energy For Scalar Field With Mixed Boundary Condition
• Heavy Fermion Quantum Effects in SU(2)_L Gauge Theory
• Radiative Correction to the Casimir Energy for Lorentz-violating Scalar Field in d+1 Dimensions
• Scarf for Lifshitz
• Riemann zeta zeros and zero-point energy
• Quantum stabilization of Z-strings in the electroweak model
• Energies of Quantum QED Flux Tubes
• One-loop corrections to the Nielsen-Olesen vortex: collective oscillations
• Quantization of Noncommutative Scalar Solitons at finite $\theta$
• One-Loop Correction to the Casimir Energy in Lorentz-Violating ${\varphi }^4$ Theory with Rough Membrane Boundaries
• Scalar Casimir effect for a conducting cylinder in a Lorentz violating background
• Casimir Energy for Lorentz-Violating Scalar Field with Helical Boundary Condition in d Spatial Dimensions