Modular theory and affine representations on the Rindler horizon
Abstract
We develop a group-theoretic interpretation of the Unruh effect based on affine symmetry on a light ray and relate it to modular theory. For a massless scalar field in two spacetime dimensions inertial and uniformly accelerated observers select two different flows within the same chiral one-particle structure, respectively, null translations and dilations. Minkowski modes are adapted to translations, while Rindler modes are adapted to dilations, with the Mellin transform providing the natural bridge between them. When a Minkowski positive-frequency mode is restricted to a single Rindler wedge, its comparison with Rindler modes is non-unitary within the positive-frequency sector. Modular theory gives the corresponding operator-algebraic interpretation: on the horizon the modular flow of the half-line algebra is implemented by dilations, and the restricted vacuum satisfies the KMS condition. The affine group thus appears as the minimal symmetry structure underlying thermality on the Rindler horizon.
Versions
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BibTeX
@misc{arzano2026modular,
title = {{Modular theory and affine representations on the Rindler horizon}},
author = {Michele Arzano and Paolo Palumbo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.01071},
eprint = {2606.01071},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.01071},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Modular theory and affine representations on the Rindler horizon
AU - Michele Arzano
AU - Paolo Palumbo
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2606.01071
UR - https://arxiv.org/abs/2606.01071
AB - We develop a group-theoretic interpretation of the Unruh effect based on affine symmetry on a light ray and relate it to modular theory. For a massless scalar field in two spacetime dimensions inertial and uniformly accelerated observers select two different flows within the same chiral one-particle structure, respectively, null translations and dilations. Minkowski modes are adapted to translations, while Rindler modes are adapted to dilations, with the Mellin transform providing the natural bridge between them. When a Minkowski positive-frequency mode is restricted to a single Rindler wedge, its comparison with Rindler modes is non-unitary within the positive-frequency sector. Modular theory gives the corresponding operator-algebraic interpretation: on the horizon the modular flow of the half-line algebra is implemented by dilations, and the restricted vacuum satisfies the KMS condition. The affine group thus appears as the minimal symmetry structure underlying thermality on the Rindler horizon.
ER -