Graphene billiards with fourfold symmetry

Zhang, Weihua; Dietz, Barbara

doi:10.1103/physrevresearch.5.043028

Cited by 2 publications

(1 citation statement)

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“…Another closely related, physically meaningful possibility are the chiral bag boundary conditions, first introduced in [53] to construct a chirally symmetric theory in Quantum Chromodynamics. Since then, they were applied in other areas such as fermionic monopoles [54], fermionic billiards [24], graphene devices [55] and Weyl semimetals [56]. These conditions can be written as Π − Ψ| ∂M = 0 using the non-Hermitian projector Π − = 1 2 1 − i/ nγ ch e r(x α )γ ch , where r(x α ) is a real-valued function of the tangential coordinates.…”

Section: Discussionmentioning

confidence: 99%

Worldline approach for spinor fields in manifolds with boundaries

Manzo

2024

J. High Energ. Phys.

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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.

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