Bern-Kosower Rule for Scalar QED

Abstract

We derive a full Bern-Kosower-type rule for scalar QED starting from quantum field theory: we derive a set of rules for calculating $S$-matrix elements for any processes at any order of the coupling constant. Gauge-invariant set of diagrams in general is first written in the worldline path-integral expression. Then we integrate over $x(\tau )$, and the resulting expression is given in terms of correlation function on the worldline $⟨x(\tau )x({\tau }^{\prime })⟩$. Simple rules to decompose the correlation function into basic elements are obtained. Gauge transformation known as integration by parts technique can be used to reduce the number of independent terms before integration over proper-time variables. The surface terms can be omitted provided the external scalars are on-shell. Also, we clarify correspondence to the conventional Feynman rule, which enabled us to avoid any ambiguity coming from the infinite dimensionality of the path-integral approach.

38pages, 18 Postscript figures, uses epsf.sty

References in corpus (4)

• Multi-Parton Amplitudes in Gauge Theories
• Field Theory Without Feynman Diagrams: One-Loop Effective Actions
• Worldline Green Functions for Multiloop Diagrams
• Multiloop String-Like Formulas for QED

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• The Two-Loop Euler-Heisenberg Lagrangian in Dimensional Renormalization
• Exact Combinatorics of Bern-Kosower-type Amplitudes for Two-Loop ${\Phi }^3$ Theory
• Multiloop World-Line Green Functions from String Theory
• Light bending from eikonal in worldline quantum field theory
• Quantum mechanical path integrals in the first quantised approach to quantum field theory
• Multiphoton amplitudes and generalized LKF transformation in Scalar QED
• Dressed scalar propagator in a non-abelian background from the worldline formalism
• Worldline master formulas for the dressed electron propagator, part 1: Off-shell amplitudes
• World-line approach to the Bern-Kosower formalism in two-loop Yang-Mills theory
• Master formulas for the dressed scalar propagator in a constant field
• Worldline master formulas for the dressed electron propagator, part 2: On-shell amplitudes
• Classical off-shell currents
• Multiloop ${\Phi }^3$ Amplitudes from Bosonic String Theory
• The QED four -- photon amplitudes off-shell: part 1
• The QED four-photon amplitudes off-shell: part 2
• Compton-like scattering of a scalar particle with N photons and one graviton
• The worldline formalism in strong-field QED
• The Generalised LKF Transformations for Arbitrary $N$-point Fermion Correlators
• Pinched Gluon Vertex Operator in Super-Worldline Formalism
• Dressed Dirac Propagator from a Locally Supersymmetric $\mathcal{N}=1$ Spinning Particle
• New Perspective On The Unruh Effect
• Everything is a "matter" of perspective: the Unruh effect
• Dimensional Regularization for the Particle Transition Amplitude in Curved Space
• Photon emission in a constant magnetic field in 2+1 dimensional space-time