One-loop Amplitudes in the Worldline Formalism
arXiv:2201.12457 · doi:10.1088/1402-4896/ac6a1e
Abstract
We summarize recent progress in applying the worldline formalism to the analytic calculation of one-loop N-point amplitudes. This string-inspired approach is well-adapted to avoiding some of the calculational inefficiencies of the standard Feynman diagram approach, most notably by providing master formulas that sum over diagrams differing only by the position of external legs and/or internal propagators. We illustrate the mathematical challenge involved with the low-energy limit of the N-photon amplitudes in scalar and spinor QED, and then present an algorithm that, in principle, solves this problem for the much more difficult case of the N-point amplitudes at full momentum in phi^3 theory. The method is based on the algebra of inverse derivatives in the Hilbert space of periodic functions orthogonal to the constant ones, in which the Bernoulli numbers and polynomials play a central role.
arXiv comment12 pages, 4 figures, talk given by C. Moctezuma Mata at ICNFP 2021, 23. 8. - 7. 10. 2021, submitted to the conference proceedings
References in corpus (8)
- Perturbative Quantum Field Theory in the String-Inspired Formalism
- Field Theory Without Feynman Diagrams: One-Loop Effective Actions
- On the Calculation of Effective Actions by String Methods
- Multiloop Calculations in the String-Inspired Formalism: The Single Spinor-Loop in QED
- Two-loop self-dual Euler-Heisenberg Lagrangians (I): Real part and helicity amplitudes
- On the low-energy limit of the QED N-photon amplitudes
- Quantum mechanical path integrals in the first quantised approach to quantum field theory
- New Techniques for Worldline Integration