arXiv subjects

Mikhail Altaisky

Publications and source records attributed to Mikhail Altaisky.

7 recordsLinked to original sources

arXiv2026

Combinatorial Spacetime from Loop Quantum Gravity

Loop quantum gravity is a perspective candidate for the quantum theory of gravity. However, there is a conceptual controversy in it: having started from the Einstein-Hilbert action and describing spacetime without matter, we can hardly define spacetime as anything other than a set of relations between matter fields. Here, following the Penrose idea of combinatorial spacetime we reformulate loop quantum gravity theory solely in terms of the matter fields.

gr-qc↗

arXiv2023

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

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 case, when the scale-dependent coupling constant is a non-differentiable 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.

hep-th↗

arXiv2022

Can our spacetime emerge from anti -- de Sitter space?

We present a model showing that our four-dimensional spacetime with the signature $(+,-,-,-)$ and almost vanishing positive curvature may have originated from a $b$-ary tree-like branching of a single discrete entity, and the $AdS_5$ space related to this branching process.

gr-qc↗

arXiv2022

Multiresolution quantum field theory in light-front coordinates

We analyse the use of wavelet transform in quantum field theory models written in light-front coordinates. In a recent paper [W.N Polyzou, Phys. Rev. D 101(2020) 096004] W.N.Polyzou used $x^+$ variable as 'time', and applied wavelet transform to the 'spatial' coordinates only. This makes the theory asymmetric with respect to space and time coordinates. In present paper we generalise the concept of continuous causal path, which is the basis of path integration, to the sequences of causally ordered spacetime regions, and present evaluation rules for Feynman path integrals over such sequences in terms of wavelet transform. Both the path integrals and the wavelet transform in our model are symmetric with respect to the light-front variables ($x^+,x^-$). The definition of a spacetime event in our generalization is very much like the definition of event in probability theory.

hep-th↗

arXiv2020

Wavelet regularization of Euclidean QED

The regularization of quantum electrodynamics in the space of functions $ψ_a(x)$, which depend on both the position $x$ and the scale $a$, is presented. The scale-dependent functions are defined in terms of the continuous wavelet transform in $\mathbb{R}^4$ Euclidean space, with the derivatives of Gaussian served as basic wavelets. The vacuum polarization and the dependence of the effective coupling constant on the scale parameters are calculated in one-loop approximation in the limit $p^2 \gg 4m^2$.

hep-th↗

arXiv2011

On the corrections to the Casimir effect depending on the resolution of measurement

The Casimir force $\cF = -\frac{π^2\hbar c}{240a^4}$, which attracts to each other two perfectly conducting parallel plates separated by the distance $a$ in vacuum, is one of the blueprints of the reality of vacuum fluctuations. Following the recent conjecture, that quantum fields should be described in terms of the fields depending on the resolution of measurement, rather than the position alone (M.V.Altaisky, Phys. Rev. D 81(2010)125003), we derive the correction to the Casimir energy depending on the ratio of the plate displacement amplitude to the distance between plates.

hep-th↗

arXiv2005

Scale-dependent stochastic quantization

Based on the wavelet-defined multiscale random noise proposed in [Doklady Physics 2003, v.48, 478], a multiscale version of the stochastic quantization procedure is considered. A new type of the commutation relations emerging from the multiscale decomposition of the operator-valued fields is derived

hep-th↗