Year: 2025
Type: preprint
Abstract: Changes in magnetic helicity are often discussed across a variety of fields, from condensed matter physics to early universe cosmology. It is frequently stated that the helicity change is given by the integral of the gauge field strength tensor and its dual over spacetime, $\int F \wedge F$. However, this is incorrect when magnetic monopoles once exist in the spacetime. In this paper, we show the correct formula of the helicity change in such a case for the Maxwell theory with the magnetic monopoles. We also discuss what happens when we embed the Maxwell theory with magnetic monopoles into non-Abelian gauge theories. We show that a similar formula holds for the 't Hooft--Polyakov monopole. In particular, we find the winding numbers and the zeroes of the Higgs field in the non-Abelian gauge theory play a crucial role in the helicity change. The same discussion is also applicable to the electroweak theory, and we discuss the implication of our findings to the baryon number change via the chiral anomaly in the early universe.
Source: arXiv (Cornell University)
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: Towards the real-time analysis of phase transition, 比較的重いアクシオン物理の再検証, G1839532492, Systematic enumeration of string theory vacua based on modern numerical techniques, G4766011574, G5847793060, Wideband dark matter search using novel sensing technologies based on superconducting qubits, Revealing constraints of quantum gravity on elementary particle models through classification of six-dimensional supergravity theories
OpenAlex ID: W7084446508
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