Worldline Green Functions for Arbitrary Feynman Diagrams

Abstract

We propose a general method to obtain the scalar worldline Green function on an arbitrary 1D topological space, with which the first-quantized method of evaluating 1-loop Feynman diagrams can be generalized to calculate arbitrary ones. The electric analog of the worldline Green function problem is found and a compact expression for the worldline Green function is given, which has similar structure to the 2D bosonic Green function of the closed bosonic string.

20 pages, 6 figures; v2: typos corrected, references added

References in corpus (7)

• Field Theory Without Feynman Diagrams: One-Loop Effective Actions
• Worldline Green Functions for Multiloop Diagrams
• String techniques for the calculation of renormalization constants in field theory
• Multiloop World-Line Green Functions from String Theory
• Gauge theory renormalizations from the open bosonic string
• World-line approach to the Bern-Kosower formalism in two-loop Yang-Mills theory
• Two-loop Yang-Mills theory in the world-line formalism and an Euler-Heisenberg type action

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• Quantum mechanical path integrals in the first quantised approach to quantum field theory
• Worldline master formulas for the dressed electron propagator, part 1: Off-shell amplitudes
• Einstein gravity from the $\mathbb{N}=4$ spinning particle
• Loop amplitudes monodromy relations and color-kinematics duality
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• String-inspired representations of photon/gluon amplitudes
• The D^6 R^4 term from three loop maximal supergravity
• Asymptotics of the $D^8{R}^4$ genus-two string invariant
• Contact interactions between particle worldlines
• Dressed Dirac Propagator from a Locally Supersymmetric $\mathcal{N}=1$ Spinning Particle
• Worldline theories with towers of internal states
• Supergravity limit of genus two modular graph functions in the worldline formalism
• HS in flat spacetime. The effective action method
• Two-loop superstring five-point amplitudes I: Construction via chiral splitting and pure spinors
• HS in flat spacetime. YM-like models
• Worldline quantization of field theory, effective actions and $L_{\infty }$ structure
• Schwinger-type parametrization of open string worldsheets
• Pinching parameters for open (super) strings
• Dimensional Regularization for the Particle Transition Amplitude in Curved Space
• Some finite terms from ladder diagrams in three and four loop maximal supergravity
• Two-loop Yang-Mills diagrams from superstring amplitudes