Worldline approach for spinor fields in manifolds with boundaries
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914844362407936 |
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| author | Manzo, Lucas |
| author_facet | Manzo, Lucas |
| contents | The worldline formalism is a useful scheme in Quantum Field Theory which has also become a powerful tool for numerical computations. It is based on the first quantisation of a 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 theory in a bounded manifold one needs to restrict the path integration domain of the point-particle to a specific subset of worldlines enclosed by those boundaries. In the present article it is shown how to implement this restriction for the case of a spinor field in a two-dimensional curved half-plane under MIT bag boundary conditions, and compute the first few heat-kernel coefficients as a verification of the proposed construction. This construction admits several generalisations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00218 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Worldline approach for spinor fields in manifolds with boundaries Manzo, Lucas High Energy Physics - Theory The worldline formalism is a useful scheme in Quantum Field Theory which has also become a powerful tool for numerical computations. It is based on the first quantisation of a 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 theory in a bounded manifold one needs to restrict the path integration domain of the point-particle to a specific subset of worldlines enclosed by those boundaries. In the present article it is shown how to implement this restriction for the case of a spinor field in a two-dimensional curved half-plane under MIT bag boundary conditions, and compute the first few heat-kernel coefficients as a verification of the proposed construction. This construction admits several generalisations. |
| title | Worldline approach for spinor fields in manifolds with boundaries |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2403.00218 |