Hamiltonian framework for Chiral Gauge Theories on a Disk Boundary
Abstract
I propose a Hamiltonian framework for chiral gauge theories (CGT) based on an existing Euclidean formulation, that uses 2n dimensional chiral fermions on the boundary of a 2n+1 dimensional disk. In the original Euclidean formulation, boundary gauge fields were extended into the bulk using 2n + 1 dimensional gauge field equations of motion (EOM). This creates a bottleneck for constructing a Hamiltonian. I present an alternate proposal for extending the gauge fields into the bulk that is compatible with both a Hamiltonian framework and a Euclidean path integral. Applying this to Abelian gauge fields produces exact expressions of interior fields as a functional of the boundary fields, which can be directly used in a Hamiltonian formulation. Euclidean analysis of the new gauge field extension shows that it can preserve the non-perturbative content of the original construction, including the behavior of topological charge, associated chiral fermion zero modes and an absence of the strong CP problem when applied to the Standard Model. This construction opens up a route to a Hamiltonian treatment and future quantum simulation of CGTs on a disk boundary.
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BibTeX
@misc{sen2026hamiltonian,
title = {{Hamiltonian framework for Chiral Gauge Theories on a Disk Boundary}},
author = {Srimoyee Sen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11035},
eprint = {2610.11035},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11035},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hamiltonian framework for Chiral Gauge Theories on a Disk Boundary
AU - Srimoyee Sen
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.11035
UR - https://arxiv.org/abs/2610.11035
AB - I propose a Hamiltonian framework for chiral gauge theories (CGT) based on an existing Euclidean formulation, that uses 2n dimensional chiral fermions on the boundary of a 2n+1 dimensional disk. In the original Euclidean formulation, boundary gauge fields were extended into the bulk using 2n + 1 dimensional gauge field equations of motion (EOM). This creates a bottleneck for constructing a Hamiltonian. I present an alternate proposal for extending the gauge fields into the bulk that is compatible with both a Hamiltonian framework and a Euclidean path integral. Applying this to Abelian gauge fields produces exact expressions of interior fields as a functional of the boundary fields, which can be directly used in a Hamiltonian formulation. Euclidean analysis of the new gauge field extension shows that it can preserve the non-perturbative content of the original construction, including the behavior of topological charge, associated chiral fermion zero modes and an absence of the strong CP problem when applied to the Standard Model. This construction opens up a route to a Hamiltonian treatment and future quantum simulation of CGTs on a disk boundary.
ER -