Journal of High Energy Physics (Aug 2019)

Worldline formalism for a confined scalar field

  • Olindo Corradini,
  • James P. Edwards,
  • Idrish Huet,
  • Lucas Manzo,
  • Pablo Pisani

DOI
https://doi.org/10.1007/JHEP08(2019)037
Journal volume & issue
Vol. 2019, no. 8
pp. 1 – 21

Abstract

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Abstract The worldline formalism is a useful scheme in quantum field theory which has also become a powerful tool for numerical computations. The key ingredient in this formalism is the first quantization of an auxiliary point-particle whose transition amplitudes correspond to the heat-kernel of the operator of quantum fluctuations of the field theory. However, to study a quantum field which is confined within some boundaries one needs to restrict the path integration domain of the auxiliary point-particle to a specific subset of worldlines enclosed by those boundaries. We show how to implement this restriction for the case of a scalar field confined to the D-dimensional ball under Dirichlet and Neumann boundary conditions, and compute the first few heat-kernel coefficients as a verification of our construction. We argue that this approach could admit different generalizations.

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