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arXiv · 1905.00945

Worldline formalism for a confined scalar field

Olindo Corradini·James P. Edwards·Idrish Huet·Lucas Manzo·Pablo Pisani
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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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Olindo Corradini, James P. Edwards, Idrish Huet, Lucas Manzo, Pablo Pisani. 2019-05-02. Worldline formalism for a confined scalar field. https://doi.org/10.1007/jhep08(2019)037

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