Contact interactions between particle worldlines

Abstract

We construct contact interactions for bosonic and fermionic point particles. We first relate the resulting theories to classical electrostatics by taking functional averages over worldlines whose endpoints are fixed to charged particles. Counting those paths which pass through a space-time point $x^{\mu }$ gives the static electric field at that point, provided we take the limit where the length measured along the worldlines is large. We also investigate corrections to the classical field that arise beyond leading order in this limit before constructing a theory of point particles that interact when their worldlines intersect. We quantise this theory and show that the partition function contains propagator couplings between the endpoints of the particles before discussing how this is related to the worldline formalism of quantum field theory and general action at a distance theories.

48 pages. 4 figures. Version accepted to JHEP

References in corpus (6)

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• Scalar heat kernel with boundary in the worldline formalism
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Cited by in corpus (7)

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• Non-perturbative Quantum Propagators in Bounded Spaces
• Worldline formalism for a confined scalar field
• Intersection of world-lines on curved surfaces and path-ordering of the Wilson loop
• Steps Towards Generalization of Tensionless String Theory with Contact Interactions as Wilson loop of Non-Abelian Yang-Mills Theory