Worldline formalism for a confined scalar field
| Autor: | Corradini, Olindo, Edwards, James P., Huet, Idrish, Manzo, Lucas, Pisani, Pablo |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | JHEP 1908 (2019) 037 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/JHEP08(2019)037 |
| Popis: | 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. Comment: 24 pages, 1 figure. Published version |
| Databáze: | arXiv |
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