arXiv subjects

Aleksandr Pinzul

Publications and source records attributed to Aleksandr Pinzul.

10 recordsLinked to original sources

arXiv2026

Geodesic equation in noncommutative space: a field theory perspective

We derive the geodesic equation for point particles propagating in Moyal-type noncommutative spacetimes using a field-theoretic approach based on the quasi-classical limit of the noncommutative Klein-Gordon equation. Starting from a twisted-geometric construction of the covariant Laplace-Beltrami operator, we obtain the noncommutative Hamilton-Jacobi equation and show that all noncommutative effects are absorbed into an effective, position-dependent mass function $M(x)$ appearing in an otherwise standard relativistic dispersion relation. The corresponding particle dynamics then acquires an additional term in the geodesic equation that takes the form of a fixed external force $F_{\text{NC}}^\mu = -\frac{1}{2} g^{\mu\nu}\partial_\nu M^2(x)$, sourced entirely by the quantum nature of spacetime. We compute this effective mass perturbatively up to fourth order in the noncommutativity parameter for a general metric, proving that all odd-order corrections vanish identically. For the specific case of an $(r-\theta)$ twist applied to spherically symmetric backgrounds, we obtain explicit expressions demonstrating that the leading correction to geodesic motion appears at $\Theta^2$ order and is proportional to the probe particle's mass, while massless particles remain unaffected.

hep-th↗

arXiv2025

On a non-geometric approach to noncommutative gauge theories

In this work, we generalize the non-geometrical construction of gauge theories, due to S. Deser, to a noncommutative setting. We show that in a free theory, along with the usual local N\"{o}ther current, there is another conserved current, which is non-local. Using the latter as a source for self-interaction, after a well-defined consistency procedure, we arrive at noncommutative gauge theories. In the non-abelian case, the standard restriction, namely that the theory should be $U(N)$ in the fundamental representation, emerges as a consequence of the requirement that the non-local current be Lie algebra valued.

hep-th↗

arXiv2023

On temperature of a diamond

We revisit the definition of the temperature of a causal diamond for the case of a free massless scalar field. The stress is given to the intrinsic, direction-dependent character of this definition. Some important limits are also discussed.

math-ph↗

arXiv2022

Multimetric Finsler Geometry

Motivated in part by the bi-gravity approach to massive gravity, we introduce and study the multimetric Finsler geometry. For the case of an arbitrary number of dimensions, we study some general properties of the geometry in terms of its Riemannian ingredients, while in the 2-dimensional case, we derive all the Cartan equations as well as explicitly find the Holmes-Thompson measure.

math-ph↗

arXiv2021

Uncertainties in Quantum Measurements: A Quantum Tomography

The observables associated with a quantum system $S$ form a non-commutative algebra ${\mathcal A}_S$. It is assumed that a density matrix $ρ$ can be determined from the expectation values of observables. But $\mathcal A_S$ admits inner automorphisms $a\mapsto uau^{-1},\; a,u\in {\mathcal A}_S$, $u^*u=u^*u=1$, so that its individual elements can be identified only up to unitary transformations. So since $\mathrm{Tr} ρ(uau^*)= \mathrm{Tr} (u^*ρu)a$, only the spectrum of $ρ$, or its characteristic polynomial, can be determined in quantum mechanics. In local quantum field theory, $ρ$ cannot be determined at all, as we shall explain. However, abelian algebras do not have inner automorphisms, so the measurement apparatus can determine mean values of observables in abelian algebras ${\mathcal A}_M\subset {\mathcal A}_S$ ($M$ for measurement, $S$ for system). We study the uncertainties in extending $ρ|_{{\mathcal A}_M}$ to $ρ|_{{\mathcal A}_S}$ (the determination of which means measurement of ${\mathcal A}_S$) and devise a protocol to determine $ρ|_{{\mathcal A}_S}\equiv ρ$ by determining $ρ|_{{\mathcal A}_M}$ for different choices of ${\mathcal A}_M$. The problem we formulate and study is a generalization of the Kadison-Singer theorem. We give an example where the system $S$ is a particle on a circle and the experiment measures the abelian algebra of a magnetic field $B$ coupled to $S$. The measurement of $B$ gives information about the state $ρ$ of the system $S$ due to operator mixing. Associated uncertainty principles for von Neumann entropy are discussed in the appendix, adapting the earlier work of Białynicki-Birula and Mycielski to the present case.

quant-ph↗

arXiv2021

Renormalization Group in Six-derivative Quantum Gravity

The exact one-loop beta functions for the four-derivative terms (Weyl tensor squared, Ricci scalar squared and the Gauss-Bonnet) are derived for the minimal six-derivative quantum gravity (QG) theory in four spacetime dimensions. The calculation is performed by means of the Barvinsky and Vilkovisky generalized Schwinger-DeWitt technique. With this result we gain, for the first time, the full set of the relevant beta functions in a super-renormalizable model of QG. The complete set of renormalization group (RG) equations, including also those for the Newton and the cosmological constant, is solved explicitly in the general case and for the six-derivative Lee-Wick (LW) quantum gravity proposed in a previous paper by two of the authors. In the ultraviolet regime, the minimal theory is shown to be asymptotically free and describes free gravitons in Minkowski or (anti-) de Sitter ((A)dS) backgrounds, depending on the initial conditions for the RG equations. The ghostlike states appear in complex conjugate pairs at any energy scale consistently with the LW prescription. However, owing to the running, these ghosts may become tachyons. We argue that an extension of the theory that involves operators cubic in Riemann tensor may change the beta functions and hence be capable of overcoming this problem.

hep-th↗

arXiv2020

Spectral action approach to higher derivative gravity

We study the spectral action approach to higher derivative gravity. The work focuses on the classical aspects. We derive the complete and simplified form of the purely gravitational action up to the 6-derivative terms. We also derive the equivalent forms of the action, which might prove useful in different applications, namely Riemann- and Weyl-dominated representations. The spectral action provides a rather rigid structure of the higher derivative part of the theory. We discuss the possible consequences of this rigidness. As one of the applications, we check whether the conformal backgrounds are preferred in some way on the classical level, with the conclusion that at this level, there is no obvious reason for such a preference, the space $S^1 \times S^3$ studied in earlier works being a special case. Some other possible properties of the higher derivative gravity given by the spectral action are briefly discussed.

hep-th↗

arXiv2019

Non-commutative $AdS_2/CFT_1$ duality: the case of massive and interacting scalar fields

We continue the study of the nocommutative $AdS_2 / CFT_1$ correspondence. We extend our previous results obtained for a free massless scalar field to the case of a massive scalar field. Both the free and interacting cases are considered. For both cases it is confirmed that to the leading order in noncommutative corrections the 2- and 3-point correlation functions have the form that is assumed by some (yet unspecified) dual $CFT$. We also argue that there does not exist a map which connects the commutative model to its non-commutative counterpart, and therefore the conformal behaviour of the noncommutative correlators is a non-trivial result.

hep-th↗

arXiv2017

Dimensional Deception from Noncommutative Tori: An alternative to Horava-Lifschitz

We study the dimensional aspect of the geometry of quantum spaces. Introducing a physically motivated notion of the scaling dimension, we study in detail the model based on a fuzzy torus. We show that for a natural choice of a deformed Laplace operator, this model demonstrates quite non-trivial behaviour: the scaling dimension flows from 2 in IR to 1 in UV. Unlike another model with the similar property, the so-called Horava-Lifshitz model, our construction does not have any preferred direction. The dimension flow is rather achieved by a rearrangement of the degrees of freedom. In this respect the number of dimensions is deceptive. Some physical consequences are discussed.

hep-th↗

arXiv2006

On Dark Matter Self-Interactions from Higher Dimensional Gravity

It has recently been suggested that in a brane world scenario with large extra dimensions, short distance gravitational interactions can enhance the dark matter scattering cross-section in a velocity dependent way. Such a modification may then help to address possible problems with non-interacting cold dark matter on galactic and sub-galactic scales. We argue that, considering the singular character of the higher dimensional Newtonian potential, the scattering cross-section is UV-dependent, depending ultimately on the underlying quantum gravity theory considered. We demonstrate that for a wide class of unitary short distance regularizations, the actual cross-section is velocity-independent and does not significantly affect dark matter substructure. We comment on the problem of thermalization of ultra-light cold dark matter by gravitational interactions in the early universe.

astro-ph↗