2016/10/04 by Brendan Z. Foster, Ted Jacobson
Physics and Astronomy · #Amplitude #Dirac equation #Fermion #Feynman diagram #MAJORANA #Noncommutative and Quantum Gravity Theories #Path integral formulation #Projection (relational algebra) #Propagator #Quantum Mechanics and Non-Hermitian Physics #Sign (mathematics) #Spin (aerodynamics) #Topological Materials and Phenomena #gr-qc #hep-th #quant-ph
paper · pdf · doi:10.1007/s10773-016-3170-0
Extends in several ways our earlier paper, arXiv:hep-th/0310166
arxiv created 2016/10/04 · openalex created_date 2016/10/14 · openalex publication_date 2016/11/30 · arxiv updated 2016/12/21 · openalex updated_date 2026/08/05
We discretize the Weyl equation for a massless, spin-1/2 particle on a time-diagonal, hypercubic spacetime lattice with null faces. The amplitude for a step of right-handed chirality is proportional to the spin projection operator in the step direction, while for left-handed it is the orthogonal projector. Iteration yields a path integral for the retarded propagator, with matrix path amplitude proportional to the product of projection operators. This assigns the amplitude i± T 3-B/2 2-N to a path with N steps, B bends, and T right-handed minus left-handed bends, where the sign corresponds to the chirality. Fermion doubling does not occur in this discrete scheme. A Dirac mass m introduces the amplitude iεm to flip chirality in any given time step ε, and a Majorana mass similarly introduces a charge conjugation amplitude.