https://doi.org/10.1140/epjc/s10052-020-08442-5
Regular Article – Theoretical Physics
Coleman–Weinberg potential in p-adic field theory
1
Department of Mathematical Methods for Quantum Technologies, Steklov Mathematical Institute of Russian Academy of Sciences, Gubkin Str. 8, 119991, Moscow, Russia
2
Department of Physics and Astronomy, Uppsala University, Box 516, 75120, Uppsala, Sweden
3
Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ, Nijmegen, The Netherlands
Received:
6
July
2020
Accepted:
6
September
2020
Published online:
18
September
2020
In this paper, we study 
scalar field theory defined on the unramified extension of p-adic numbers 
. For different “space-time” dimensions n, we compute one-loop quantum corrections to the effective potential. Surprisingly, despite the unusual properties of non-Archimedean geometry, the Coleman–Weinberg potential of p-adic field theory has structure very similar to that of its real cousin. We also study two formal limits of the effective potential, 
and 
. We show that the 
limit allows to reconstruct the canonical result for real field theory from the p-adic effective potential and provide an explanation of this fact. On the other hand, in the 
limit, the theory exhibits very peculiar behavior with emerging logarithmic terms in the effective potential, which has no analogue in real theories.
© The Author(s) 2020
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