Relativistic Covariance from Hamiltonian Hydrodynamics in the Chiral Limit
Abstract
We derive the covariant equations of nondissipative chiral hydrodynamics from their equal-time Hamiltonian formulation and identify the Lie--Poisson structure implicit in the chiral brackets. This structure combines fluid motion with local chiral transformations. For a parity-invariant Hamiltonian quadratic in chiral charge densities and pion gradients, without external backgrounds, we derive and solve the constraints imposed by Lorentz boosts. Their coupled nonlinear sector is equivalent to the linear boost transformation laws of a symmetric tensor, which determine the velocity dependence from rest-frame data. For finite, positive rest-frame coefficients, finite ordinary-fluid energy density and thermodynamic derivatives, and a momentum--velocity relation that can be solved in either direction, the chiral Hamiltonian coefficients remain finite at every fluid speed below light speed if and only if the rest-frame pion propagation speed does not exceed the speed of light. This formulation makes symmetry constraints explicit and provides a starting point for future thermodynamically consistent dissipative extensions.
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BibTeX
@misc{liu2026relativistic,
title = {{Relativistic Covariance from Hamiltonian Hydrodynamics in the Chiral Limit}},
author = {Zi-Hao Liu and Mei Huang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16095},
eprint = {2610.16095},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16095},
}
RIS
TY - UNPB
TI - Relativistic Covariance from Hamiltonian Hydrodynamics in the Chiral Limit
AU - Zi-Hao Liu
AU - Mei Huang
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16095
UR - https://arxiv.org/abs/2610.16095
AB - We derive the covariant equations of nondissipative chiral hydrodynamics from their equal-time Hamiltonian formulation and identify the Lie--Poisson structure implicit in the chiral brackets. This structure combines fluid motion with local chiral transformations. For a parity-invariant Hamiltonian quadratic in chiral charge densities and pion gradients, without external backgrounds, we derive and solve the constraints imposed by Lorentz boosts. Their coupled nonlinear sector is equivalent to the linear boost transformation laws of a symmetric tensor, which determine the velocity dependence from rest-frame data. For finite, positive rest-frame coefficients, finite ordinary-fluid energy density and thermodynamic derivatives, and a momentum--velocity relation that can be solved in either direction, the chiral Hamiltonian coefficients remain finite at every fluid speed below light speed if and only if the rest-frame pion propagation speed does not exceed the speed of light. This formulation makes symmetry constraints explicit and provides a starting point for future thermodynamically consistent dissipative extensions.
ER -