Are there any Landau poles in wavelet-based quantum field theory? - INSPIRE

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Are there any Landau poles in wavelet-based quantum field theory?

Mikhail Altaisky
(
- Moscow, Space Res. Inst. and
- Mahatma Gandhi U.
)
,
Michal Hnatich
(
- Dubna, JINR and
- Kosice U. and
- Kosice, IEF
)

Feb 21, 2023

13 pages

Published in:

Phys.Rev.D 108 (2023) 8, 085023

Published: Oct 15, 2023

e-Print:

2302.11340 [hep-th]

DOI:

10.1103/PhysRevD.108.085023 (publication)

View in:

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Abstract: (APS)

Following previous work by one of the authors [M. V. Altaisky, Unifying renormalization group and the continuous wavelet transform, Phys. Rev. D 93, 105043 (2016).], we develop a new approach to the renormalization group, where the effective action functional

Γ_{A} [ϕ]

is a sum of all fluctuations of scales from the size of the system

L

down to the scale of observation

A

. It is shown that the renormalization flow equation of the type

\frac{\partial Γ_{A}}{\partial \ln A} = - Y (A)

is a limiting case of such consideration, when the running coupling constant is assumed to be a differentiable function of scale. In this approximation, the running coupling constant, calculated at one-loop level, suffers from the Landau pole. In general, when the scale-dependent coupling constant is a nondifferentiable function of scale, the Feynman loop expansion results in a difference equation. This keeps the coupling constant finite for any finite value of scale

A

. As an example, we consider Euclidean

ϕ^{4}

field theory.

Note:

RevTeX, 13 pages, 3 eps figures

coupling constant: energy dependence
effective action
pole
renormalization
Euclidean
fluctuation
flow
Feynman
wavelet
renormalization group

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