Quantum field theory with scale-dependent weighted measures: nonlinear momentum representations, vacuum fluctuations, and causal structure
Abstract
We reconsider the construction of free quantum fields through momentum-space weighted measures, introducing an independent energy scale that restores the conventional theory at low momenta. The resulting family is characterized by a dimensionless spectral function and includes, as a distinguished case, the spatial weight associated with the Euclidean Snyder algebra. We discuss its relation to modified dispersion relations and nonlinear momentum coordinates, and introduce an observer-covariant spectral weight defined using a timelike four-velocity. For the complex Klein-Gordon field we obtain the equal-time algebra, conserved weighted observables, vacuum fluctuations, and two-point functions in arbitrary spatial dimension. The ultraviolet conditions for their finiteness are established, and the nonlocal causal structure is analyzed in terms of a spatial convolution of the ordinary Pauli-Jordan distribution. An illustrative interacting extension and numerical profiles of the kernels and amplitudes are also presented.
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BibTeX
@misc{gonzalezsalud2026quantum,
title = {{Quantum field theory with scale-dependent weighted measures: nonlinear momentum representations, vacuum fluctuations, and causal structure}},
author = {S. González-Salud and R. Cartas-Fuentevilla},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39285},
eprint = {2610.39285},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39285},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum field theory with scale-dependent weighted measures: nonlinear momentum representations, vacuum fluctuations, and causal structure
AU - S. González-Salud
AU - R. Cartas-Fuentevilla
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39285
UR - https://arxiv.org/abs/2610.39285
AB - We reconsider the construction of free quantum fields through momentum-space weighted measures, introducing an independent energy scale that restores the conventional theory at low momenta. The resulting family is characterized by a dimensionless spectral function and includes, as a distinguished case, the spatial weight associated with the Euclidean Snyder algebra. We discuss its relation to modified dispersion relations and nonlinear momentum coordinates, and introduce an observer-covariant spectral weight defined using a timelike four-velocity. For the complex Klein-Gordon field we obtain the equal-time algebra, conserved weighted observables, vacuum fluctuations, and two-point functions in arbitrary spatial dimension. The ultraviolet conditions for their finiteness are established, and the nonlocal causal structure is analyzed in terms of a spatial convolution of the ordinary Pauli-Jordan distribution. An illustrative interacting extension and numerical profiles of the kernels and amplitudes are also presented.
ER -