Parity-violating scalar-tensor theory revisited: complete basis up to d=4 and Hamiltonian analysis
Abstract
We construct complete bases of parity-violating generally covariant scalar-tensor (GST) and spatially covariant gravity (SCG) monomials up to derivative grade d=4. Including all derivative partitions, each description contains one d=3 and thirteen d=4 linearly independent monomials. At the level of Lagrangians, we find six integration-by-parts relations that reduce polynomial-type Lagrangians to combinations of one d=3 and seven d=4 monomials with general coefficient functions. We derive the correspondence between the two bases, retaining general coefficients and total derivatives, and establish their independence under integrations by parts. Among the seven d=4 SCG monomials, five contain neither the lapse velocity nor the time derivative of the extrinsic curvature. For the two remaining monomials, we perform a Hamiltonian constraint analysis with a standard Einstein-Hilbert kinetic term and a lapse-dependent potential. On the regular branches considered, the lapse-velocity term propagates four degrees of freedom (DOFs), while the extrinsic-curvature-velocity term propagates six DOFs, whether present alone or together with the lapse-velocity term. These results provide a complete basis for constructing parity-violating scalar-tensor theories with three DOFs up to d=4 within this setting, with the parity-violating Lagrangian spanned by six GST polynomials: one d=3 and five d=4 polynomials.
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BibTeX
@misc{zhang2026parityviolating,
title = {{Parity-violating scalar-tensor theory revisited: complete basis up to $d=4$ and Hamiltonian analysis}},
author = {Yun-Chuan Zhang and Yu-Min Hu and Xian Gao},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08191},
eprint = {2611.08191},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08191},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Parity-violating scalar-tensor theory revisited: complete basis up to d=4 and Hamiltonian analysis
AU - Yun-Chuan Zhang
AU - Yu-Min Hu
AU - Xian Gao
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08191
UR - https://arxiv.org/abs/2611.08191
AB - We construct complete bases of parity-violating generally covariant scalar-tensor (GST) and spatially covariant gravity (SCG) monomials up to derivative grade d=4. Including all derivative partitions, each description contains one d=3 and thirteen d=4 linearly independent monomials. At the level of Lagrangians, we find six integration-by-parts relations that reduce polynomial-type Lagrangians to combinations of one d=3 and seven d=4 monomials with general coefficient functions. We derive the correspondence between the two bases, retaining general coefficients and total derivatives, and establish their independence under integrations by parts. Among the seven d=4 SCG monomials, five contain neither the lapse velocity nor the time derivative of the extrinsic curvature. For the two remaining monomials, we perform a Hamiltonian constraint analysis with a standard Einstein-Hilbert kinetic term and a lapse-dependent potential. On the regular branches considered, the lapse-velocity term propagates four degrees of freedom (DOFs), while the extrinsic-curvature-velocity term propagates six DOFs, whether present alone or together with the lapse-velocity term. These results provide a complete basis for constructing parity-violating scalar-tensor theories with three DOFs up to d=4 within this setting, with the parity-violating Lagrangian spanned by six GST polynomials: one d=3 and five d=4 polynomials.
ER -