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Spectral Density of the Causal Propagator
Abstract
The causal propagator (or Pauli-Jordan function), which multiplied by i is the spacetime commutator of the field $[ϕ(x),ϕ(x')]$, plays an essential role in scalar quantum field theory. We discuss the role of the causal propagator and its spectrum in recent developments in defining quantum field theory in a more explicitly covariant manner, as well as in causal set theory. We then present a conjecture for its asymptotic spectral density in a free theory, and give examples that lend evidence to the conjectured scaling. Our work has implications for Lorentzian spectral geometry in much the same way as Weyl's asymptotic law has for Riemannian spectral geometry.
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BibTeX
@misc{jones2026spectral,
title = {{Spectral Density of the Causal Propagator}},
author = {Joshua Y. L. Jones and Yasaman K. Yazdi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.00311},
eprint = {2606.00311},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.00311},
}
RIS
TY - UNPB
TI - Spectral Density of the Causal Propagator
AU - Joshua Y. L. Jones
AU - Yasaman K. Yazdi
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2606.00311
UR - https://arxiv.org/abs/2606.00311
AB - The causal propagator (or Pauli-Jordan function), which multiplied by i is the spacetime commutator of the field $[ϕ(x),ϕ(x')]$, plays an essential role in scalar quantum field theory. We discuss the role of the causal propagator and its spectrum in recent developments in defining quantum field theory in a more explicitly covariant manner, as well as in causal set theory. We then present a conjecture for its asymptotic spectral density in a free theory, and give examples that lend evidence to the conjectured scaling. Our work has implications for Lorentzian spectral geometry in much the same way as Weyl's asymptotic law has for Riemannian spectral geometry.
ER -