info:eu-repo/semantics/article
Worldline formalism for a confined scalar field
Fecha
2019-08-07Registro en:
Corradini, Olindo; Edwards, James P.; Huet, Idrish; Manzo, Lucas; González Pisani, Pablo Andrés; Worldline formalism for a confined scalar field; Springer; Journal of High Energy Physics; 8; 37; 7-8-2019; 1-21
1126-6708
CONICET Digital
CONICET
Autor
Corradini, Olindo
Edwards, James P.
Huet, Idrish
Manzo, Lucas
González Pisani, Pablo Andrés
Resumen
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.