GP2 - Birmingham Workshop Program: Quantum Phase Theorem for Cyclic Evolution

Session Information

Location: Physics West 117 | School of Physics and Astronomy, University of Birmingham
Day: 1. Tuesday 21st April
Time: 15:00-15:20
Chairperson: Chair: Iacopo Carusotto

Presentation Details

Presentation Type: Oral | 
Title: Quantum Phase Theorem for Cyclic Evolution
Abstract: Geometric phases of charged particles arise as holonomies of the electromagnetic gauge connection. The archetype is the Aharonov–Bohm effect, in which the wave function of a charged particle acquires a topological phase upon encircling a confined magnetic flux. Standard accounts model the particle as a test charge coupled to prescribed external potentials, while giving no explicit role to the electromagnetic fields it generates.

This talk presents a quantum phase theorem that restores this missing ingredient. It shows that the geometric phase accumulated by a charged particle over a cycle splits into two separately gauge-invariant contributions: (i) a bulk phase arising from the interaction between the particle’s Liénard–Wiechert fields and the external electromagnetic fields throughout the region containing the particle, and (ii) a boundary phase arising from the coupling between the particle’s fields and the external electromagnetic potentials on the enclosing surface and at the temporal endpoints of the particle trajectory. The bulk phase promotes the particle’s fields to active elements of quantum evolution, while the boundary term reveals a distinct class of quantum phases generated by boundary interactions.

The theorem identifies the Aharonov–Bohm phase as a purely boundary phase: a surface interaction between the external vector potential and the particle’s magnetic field generates the phase and makes it proportional to a winding number. This formulation yields a new expression for the Aharonov–Bohm phase and provides a local, causal account of its origin.

Overall, the theorem unifies geometric, bulk, and boundary contributions within a single physical programme, clarifying how sources, fields, and boundaries jointly shape quantum phases in electromagnetic systems. A notable outcome of the theorem is that it reveals gauge invariance as a boundary symmetry: gauge freedom confines to the boundary phase, while the bulk contribution remains gauge-free.

Presenter

Mr Ricardo Heras
University of Birmingham | United Kingdom

Authors

1. Heras, Ricardo | School of Physics and Astronomy, University of Birmingham