Feynman Amplitudes in Periodically Compactified Spaces -- Spin 0

Abstract

We propose an extension of the Schwinger parametric representation for Feynman amplitudes in $D$ euclidean dimensions to a scenario where $d$ dimensions are compactified ($d<D$) through the introduction of periodic boundary conditions in space. We obtain two valid representations, one useful near the bulk (large compactification length) and another useful near the dimensional reduction (small compactification length). Also, to illustrate, we exhibit some Feynman amplitudes up to three loops in a compactified scalar field theory.

arXiv comment16 pages, 4 figures. (Missing information added)

References in corpus (51)

• Large N Field Theories, String Theory and Gravity
• Eleven-Dimensional Supergravity on a Manifold with Boundary
• New Developments in the Casimir Effect
• The Casimir force between real materials: experiment and theory
• Chiral symmetry breaking from five dimensional spaces
• The Casimir effect: Recent controversies and progress
• Moving Multi-Channel Systems in a Finite Volume with Application to Proton-Proton Fusion
• Finite volume effects for meson masses and decay constants
• B-factory Signals for a Warped Extra Dimension
• Rare K and B Decays in a Warped Extra Dimension with Custodial Protection
• QED in finite volume and finite size scaling effect on electromagnetic properties of hadrons
• Scalar mesons in a finite volume
• Finite volume QCD at fixed topological charge
• $K\to \pi \pi$ Decays in a Finite Volume
• Chiral transition in a finite system and possible use of finite size scaling in relativistic heavy ion collisions
• Thermodynamic Properties of Strongly Interacting Matter in a Finite Volume using the Polyakov-Nambu-Jona-Lasinio model
• Effects of Universal Extra Dimensions on $B^0-{\bar{B}}^0$ Mixing
• Circle compactification and 't Hooft anomaly
• Twisted Circle Compactifications of 6d SCFTs
• A Model of Electroweak Symmetry Breaking from a Fifth Dimension
• Renormalization: an advanced overview
• Quantum field theory on toroidal topology: algebraic structure and applications
• Fluctuation of strongly interacting matter in Polyakov Nambu Jona-Lasinio model in finite volume
• Dimensional Reduction and Screening Masses in Pure Gauge Theories at Finite Temperature
• QCD on a small circle
• Non-Commutative Complete Mellin Representation for Feynman Amplitudes
• Finite-size effects on the chiral phase diagram of four-fermion models in four dimensions
• Electroweak Symmetry Breaking and Precision Tests with a Fifth Dimension
• Finite-size effects on the phase diagram of difermion condensates in two-dimensional four-fermion interaction models
• Glueball-Like Screening Masses in Pure SU(3) at Finite Temperatures
• Fractional instantons and bions in the principal chiral model on ${\mathbb{R}}^2\times S^1$ with twisted boundary conditions
• Finite volume effects on the chiral phase transition from Dyson-Schwinger equations of QCD
• Polyakov--Nambu--Jona-Lasinio model in finite volumes
• Critical behaviour of the compactified $\lambda {\varphi }^4$ theory
• Geometrically confined thermal field theory: Finite size corrections and phase transitions
• Phase transition in the massive Gross-Neveu model in toroidal topologies
• Volume independence for Yang-Mills fields on the twisted torus
• Vacuum polarization for compactified $QE{D}_{4+1}$ in a magnetic flux background
• First-order phase transitions in superconducting films: A Euclidean model
• Magnetic effects on spontaneous symmetry breaking/restoration in a toroidal topology
• Large-N transition temperature for superconducting films in a magnetic field
• Properties of size-dependent models having quasiperiodic boundary conditions
• Spontaneous symmetry restoration in a field theory at finite chemical potential in a toroidal topology
• Dimensional reduction of a finite-size scalar field model at finite temperature
• A note on the infrared behavior of the compactified Ginzburg--Landau model in a magnetic field
• Phases of circle-compactified QCD with adjoint fermions at finite density
• Fermion inter-particle potentials in 5D and a dimensional restriction prescription to 4D
• Influence of external magnetic field, finite-size effects and chemical potential on the phase transition of a complex scalar field
• The effect of boundary conditions on dimensionally reduced field-theoretical models at finite temperature
• Asymptotic Expansions of Feynman Amplitudes in a Generic Covariant Gauge
• Dimensional renormalizability in compactified spaces