Dimensional Regularization for the Particle Transition Amplitude in Curved Space
arXiv:2109.11804 · doi:10.1140/epjc/s10052-022-10026-4
Abstract
We compute the perturbative short-time expansion for the transition amplitude of a particle in curved space time, by employing Dimensional Regularization (DR) to treat the divergences which occur in some Feynman diagrams. The present work generalizes known results where DR was applied to the computation of one-loop effective actions, which in the worldline approach are linked to particle path integrals on the circle, i.e. with periodic boundary conditions. The main motivation of the present work comes from revived interest in particle transition amplitudes in curved space-times, due to their use in the recently proposed worldline quantum field theory (in curved space-time).
arXiv comment17 pages. Discussion improved, typos corrected. Matches the published version
References in corpus (37)
- Perturbative Quantum Field Theory in the String-Inspired Formalism
- Field Theory Without Feynman Diagrams: One-Loop Effective Actions
- Classical black hole scattering from a worldline quantum field theory
- Constant External Fields in Gauge Theory and the Spin 0, 1/2, 1 Path Integrals
- String-Based Methods in Perturbative Gravity
- Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
- The Duality Between Color and Kinematics and its Applications
- Worldline Green Functions for Multiloop Diagrams
- Photon Splitting in a Strong Magnetic Field: Recalculation and Comparison With Previous Calculations
- Worldline formalism in a gravitational background
- Worldline approach to vector and antisymmetric tensor fields
- The Path Integral for a Particle in Curved Spaces and Weyl Anomalies
- Spinning particles and higher spin fields on (A)dS backgrounds
- On the string-inspired approach to QED in external field
- Two-loop self-dual Euler-Heisenberg Lagrangians (I): Real part and helicity amplitudes
- Worldline approach to vector and antisymmetric tensor fields II
- Gravitational corrections to the Euler-Heisenberg Lagrangian
- Worldline Green Functions for Arbitrary Feynman Diagrams
- Reparametrization Invariance of Path Integrals
- Berends-Giele currents in Bern-Carrasco-Johansson gauge for - and -deformed Yang-Mills amplitudes
- Effective action for higher spin fields on (A)dS backgrounds
- Quantum mechanical path integrals in the first quantised approach to quantum field theory
- Bern-Kosower Rule for Scalar QED
- Worldline master formulas for the dressed electron propagator, part 1: Off-shell amplitudes
- Einstein gravity from the spinning particle
- Dimensional regularization of nonlinear sigma models on a finite time interval
- Dimensional regularization of the path integral in curved space on an infinite time interval
- On Mode Regularization of the Configuration Space Path Integral in Curved Space
- Thermal Green's Functions from Quantum Mechanical Path Integrals
- 6D trace anomalies from quantum mechanical path integrals
- Color-kinematics duality from the Bern-Kosower formalism
- Reparametrization Invariance of Perturbatively Defined Path Integrals. II. Integrating Products of Distributions
- Compton-like scattering of a scalar particle with N photons and one graviton
- Extension of worldline computational algorithms for QCD to open fermionic contours
- Hard Thermal Loops and Beyond in the Finite Temperature World-Line Formulation of QED
- World Graph Formalism for Feynman Amplitudes
- A Monte Carlo Approach to the Worldline Formalism in Curved Space