2023-06-07 15:00  P7F/Online

[Journal Club] From Berry to the Momentum Phase: The Axial Anomaly and Gravity on the Phase-Space Worldline

Dr. Patrick Copinger

The Berry phase is first discussed for Weyl and Dirac fermions using the worldline formalism, or a first quantized quantum field theory representation. A relativistic and intuitive extension of the well-known fermion Hamiltonian of quantum mechanics is put forth from a novel phase space worldline construction. The axial anomaly and its appearance through kinetic theory are discussed, where it is shown for the classical worldline Dirac kinetic theory axial-vector terms are required for axial current non-conservation via a Wigner-like distribution function [1]. Motivated by the ubiquity of Berrys phase in condensed matter, we further treat its dynamical extension: a local U(1) momentum phase. The addition of a momentum phase (and Berry phase) gives rise to non-commutative degrees of freedom. Then, using a semi-classical treatment for complex scalars, it is argued Coulomb-like classical solutions for the momentum phase coupled with electromagnetism resemble an emergent Newtonian gravity [2].

[1] PC and S. Pu, Phys. Rev. D 105, 116014, (2022); 2203.00847 [hep-th].
[2] PC and P. Morales, (2022) 2211.14165 [gr-qc].