Worldline formalism for a confined scalar field

• Autores: Corradini, Olindo; Edwards, James P.; Huet, Idrish; Manzo, Lucas; González Pisani, Pablo Andrés
• Año de publicación: 2019
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Ciencias Exactas; Física; Field Theories in Higher Dimensions; Spacetime Singularities; Differential and Algebraic Geometry
• Institución: Universidad Nacional de La Plata

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.
Facultad de Ciencias Exactas
Instituto de Física La Plata