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Sequential exponential-motivic periods in spatially cut-off ϕ42
Abstract
We represent constructive integrals in spatially cut-off ϕ42 by sequences of exponential-motivic periods. For a nonzero spatial cutoff, a single Galois transformation makes the partition periods diverge in modulus along every sequence of approximations satisfying the constructive estimates. For a fixed cutoff presentation, we characterize the subgroup of transformations admitting a bounded realization on the free field's L1 space and prove that all fixed-observable limits on this subgroup are a common scalar multiple of their physical values. A one-variable quartic example shows that all transformed fixed-observable sequences can converge without such a bounded realization, with limits that are not proportional to the physical values.
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BibTeX
@misc{sampedro2026sequential,
title = {{Sequential exponential-motivic periods in spatially cut-off $ϕ^4_2$}},
author = {Juan Carlos Sampedro},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04148},
eprint = {2610.04148},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04148},
}
RIS
TY - UNPB
TI - Sequential exponential-motivic periods in spatially cut-off ϕ^4_2
AU - Juan Carlos Sampedro
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.04148
UR - https://arxiv.org/abs/2610.04148
AB - We represent constructive integrals in spatially cut-off ϕ^4_2 by sequences of exponential-motivic periods. For a nonzero spatial cutoff, a single Galois transformation makes the partition periods diverge in modulus along every sequence of approximations satisfying the constructive estimates. For a fixed cutoff presentation, we characterize the subgroup of transformations admitting a bounded realization on the free field's L^1 space and prove that all fixed-observable limits on this subgroup are a common scalar multiple of their physical values. A one-variable quartic example shows that all transformed fixed-observable sequences can converge without such a bounded realization, with limits that are not proportional to the physical values.
ER -