Extending the Geometric Phase to Relativistic Spacetime

Authors

• Sajid Raihan Akash, University of Nebraska-LincolnFollow

First Advisor

Herman Batelaan

Second Advisor

Ilya Kravchenko

Date of this Version

3-25-2026

Document Type

Thesis

Citation

Senior thesis, March 25, 2026

Department of Physics and Astronomy, University of Nebraska-Lincoln

Advisors: Herman Batelaan and Ilya Kravchenko

Comments

Copyright 2026, Sajid Raihan Akash. Used by permission

Abstract

The Berry phase [3] is traditionally understood as a geometric phase acquired during cyclic adiabatic evolution, often interpreted as the flux of an effective “magnetic field” through a solid angle in parameter space. In this thesis, we investigate situations in which a geometric phase arises even when no spatial solid angle is enclosed, revealing the limitations of the standard purely spatial interpretation. We first review the Berry phase for a spin-½ particle in a slowly varying magnetic field and analyze scenarios in which the system’s eigenstate is changed during the adiabatic evolution. We show that the resulting phase can be understood through a spacetime formulation analogous to the electrodynamic Aharonov–Bohm effect [1], where both “analogous magnetic” and “analogous electric” fields contribute through a spacetime surface integral. This framework clarifies how nonzero geometric phases can occur even when the projected spatial solid angle vanishes. We then extend this perspective to the Jahn–Teller 𝐸 ⊗ 𝑒 system. While a closed loop around the conical intersection yields the familiar π phase, we show that nontrivial geometric phases can also emerge in paths with zero net enclosed solid angle.

Advisors: Herman Batelaan and Ilya Kravchenko