Worldline approach for spinor fields in manifolds with boundaries

• Published in: The journal of high energy physics Vol. 2024; no. 6; pp. 144 - 33
• Main Author: Manzo, Lucas
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 21.06.2024; Springer Nature B.V; SpringerOpen
• Subjects: Anomalies in Field and String Theories; Boundary conditions; Classical and Quantum Gravitation; Differential and Algebraic Geometry; Elementary Particles; Half planes; Operators (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quantum theory; Regular Article - Theoretical Physics; Relativity Theory; Sigma Models; Spacetime Singularities; String Theory; Differential and Algebraic Geometry; Sigma Models; Anomalies in Field and String Theories; Spacetime Singularities
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP06(2024)144

A bstract 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.