Conformal Symmetry and Planck's Thermal Radiation in Classical Physics
Abstract
Thermal radiation is discussed for a classical scalar field. Dilation and acceleration appear in conformal symmetry, and so are treated in connection with zero-point radiation and equilibrium thermal radiation. Classical zero-point radiation is completely invariant under dilation in a inertial frame. However, in a Rindler frame, zero-point radiation takes a different form which is related to Planck's thermal spectrum with temperature T related to acceleration. Traditionally, zero-point radiation is said to take a thermal (Unruh) form in a Rindler frame. However, the classical viewpoint indicates that zero-point radiation in a Rindler frame requires a divergent frequency spectrum and so is not thermal radiation. The Unruh form suggests an additional classical thermal spectrum satisfying the Stefan-Boltzmann relation.
Related
- Direct tests of conformal symmetry with Rydberg atoms: assessment and proposals
- Scaling similarity and generalised conformal symmetry in D2-brane holography
- Emergent Conformal Symmetry on Superfluid Vortices in Two-Color QCD and Pseudoreal Gauge Theories
- New time-periodic solutions to the cubic conformal wave equation on 𝕊3: I Spherical symmetry
- Classical conformal invariance and superhorizon dynamics in de Sitter
BibTeX
@misc{boyer2026conformal,
title = {{Conformal Symmetry and Planck's Thermal Radiation in Classical Physics}},
author = {Timothy H. Boyer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07904},
eprint = {2609.07904},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07904},
}
RIS
TY - UNPB
TI - Conformal Symmetry and Planck's Thermal Radiation in Classical Physics
AU - Timothy H. Boyer
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07904
UR - https://arxiv.org/abs/2609.07904
AB - Thermal radiation is discussed for a classical scalar field. Dilation and acceleration appear in conformal symmetry, and so are treated in connection with zero-point radiation and equilibrium thermal radiation. Classical zero-point radiation is completely invariant under dilation in a inertial frame. However, in a Rindler frame, zero-point radiation takes a different form which is related to Planck's thermal spectrum with temperature T related to acceleration. Traditionally, zero-point radiation is said to take a thermal (Unruh) form in a Rindler frame. However, the classical viewpoint indicates that zero-point radiation in a Rindler frame requires a divergent frequency spectrum and so is not thermal radiation. The Unruh form suggests an additional classical thermal spectrum satisfying the Stefan-Boltzmann relation.
ER -