Hamiltonian analysis of disformally coupled fermions in scalar-tensor theories
Abstract
We study disformal transformations of 𝒩 scalar fields coupled to a Dirac fermion. The resulting axial coupling generically introduces higher derivatives in the scalar field equations of motion; for field-dependent free functions, these are absent if and only if the disformal transformation acts along a single field-space direction. We show that these higher derivatives do not signal an Ostrogradsky ghost. After the transformation, the fermion registers the derivatives of the matter-frame tetrad only through the axial current, so that every coupling to the derivatives of the scalar fields multiplies a fermion bilinear, which is Grassmann even and nilpotent. Such terms do not contribute to the body of the constraint matrix, and at each level of the Grassmann expansion the field equations are linear, with the principal part of the theory without fermions. Through a Hamiltonian analysis, we show that the number of degrees of freedom is that of the bosonic theory plus that of the fermion, both in the Einstein frame, for free functions depending on the scalar fields and their kinetic matrix, and for minimally coupled fermions in multi-field DHOST theories. The same mechanism applies to disformal transformations with higher derivatives of a single scalar field, for which fermions impose no condition beyond those required by bosonic matter.
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BibTeX
@misc{ganz2026hamiltonian,
title = {{Hamiltonian analysis of disformally coupled fermions in scalar-tensor theories}},
author = {Alexander Ganz and Apostolos Tsampodimos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17501},
eprint = {2610.17501},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17501},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hamiltonian analysis of disformally coupled fermions in scalar-tensor theories
AU - Alexander Ganz
AU - Apostolos Tsampodimos
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17501
UR - https://arxiv.org/abs/2610.17501
AB - We study disformal transformations of 𝒩 scalar fields coupled to a Dirac fermion. The resulting axial coupling generically introduces higher derivatives in the scalar field equations of motion; for field-dependent free functions, these are absent if and only if the disformal transformation acts along a single field-space direction. We show that these higher derivatives do not signal an Ostrogradsky ghost. After the transformation, the fermion registers the derivatives of the matter-frame tetrad only through the axial current, so that every coupling to the derivatives of the scalar fields multiplies a fermion bilinear, which is Grassmann even and nilpotent. Such terms do not contribute to the body of the constraint matrix, and at each level of the Grassmann expansion the field equations are linear, with the principal part of the theory without fermions. Through a Hamiltonian analysis, we show that the number of degrees of freedom is that of the bosonic theory plus that of the fermion, both in the Einstein frame, for free functions depending on the scalar fields and their kinetic matrix, and for minimally coupled fermions in multi-field DHOST theories. The same mechanism applies to disformal transformations with higher derivatives of a single scalar field, for which fermions impose no condition beyond those required by bosonic matter.
ER -