arXiv subjects

M. A. Kurkov

Publications and source records attributed to M. A. Kurkov.

14 recordsLinked to original sources

arXiv2026

Symmetries and Conservation Laws in Lie-Poisson Electrodynamics

Lie-Poisson electrodynamics (LPE) is a non-Abelian and nonlinear deformation of usual electrodynamics, where the gauge algebra is defined through a Lie-algebra-type Poisson bracket on space-time. We focus on the geometric approach to LPE in the absence of charged matter. We establish a non-trivial field redefinition which, under mild technical assumptions, maps the LPE dynamics to that of Maxwell theory. Using this map, for any symmetry of the Maxwell action, we construct generators of LPE symmetries and the corresponding conserved currents. In particular, we obtain deformed Poincaré transformations. We also outline a natural quantization prescription for LPE based on our field redefinition.

hep-th↗

arXiv2025

Light Propagation in $κ$-Minkowski Space-Time: Gauge Ambiguities and Invariance

We study the noncommutative $U(1)$ gauge theory on the $κ$-Minkowski space-time at the semiclassical approximation. We construct exact solutions of the deformed Maxwell equations in vacuum, describing localized signals propagating in a given direction. The propagation velocity appears to be arbitrary. We figure out that the wave packets with different values of the propagation velocity are related by noncommutative gauge transformations. Moreover, we show that spatial distances between particles are gauge-dependent as well. We explain how these two gauge dependencies compensate each other, recovering gauge invariance of measurement results. According to our analysis, the gauge ambiguity of the speed of light can be absorbed into a redefinition of the unit of length and, therefore, cannot be measured experimentally.

physics.gen-ph↗

arXiv2024

Charged Particle in Lie-Poisson Electrodynamics

Lie-Poisson electrodynamics describes the semi-classical limit of non-commutative $U(1)$ gauge theory, characterized by Lie-algebra-type non-commutativity. We focus on the mechanics of a charged point-like particle moving in a given gauge background. First, we derive explicit expressions for gauge-invariant variables representing the particle's position. Second, we provide a detailed formulation of the classical action and the corresponding equations of motion, which recover standard relativistic dynamics in the commutative limit. We illustrate our findings by exploring the exactly solvable Kepler problem in the context of the $λ$-Minkowski (or the angular) non-commutativity, along with other examples.

hep-th↗

arXiv2023

Lie-Poisson gauge theories and $κ$-Minkowski electrodynamics

We consider gauge theories on Poisson manifolds emerging as semiclassical approximations of noncommutative spacetime with Lie algebra type noncommutativity. We prove an important identity, which allows to obtain simple and manifestly gauge-covariant expressions for the Euler-Lagrange equations of motion, the Bianchi and the Noether identities. We discuss the non-Lagrangian equations of motion, and apply our findings to the $κ$-Minkowski case. We construct a family of exact solutions of the deformed Maxwell equations in the vacuum. In the classical limit, these solutions recover plane waves with left-handed and right-handed circular polarization, being classical counterparts of photons. The deformed dispersion relation appears to be nontrivial.

hep-th↗

arXiv2023

Poisson gauge theory: a review

In this paper we overview the Poisson gauge theory focusing on the most recent developments. We discuss the general construction and its symplectic-geometric interpretation. We consider explicit realisations of the formalism for all non-commutativities of the Lie algebraic type. We discuss Seiberg-Witten maps between Poisson gauge field-theoretical models.

hep-th↗

arXiv2022

Poisson gauge models and Seiberg-Witten map

The semiclassical limit of full non-commutative gauge theory is known as Poisson gauge theory. In this work we revise the construction of Poisson gauge theory paying attention to the geometric meaning of the structures involved and advance in the direction of a further development of the proposed formalism, including the derivation of Noether identities and conservation of currents. For any linear non-commutativity, $Θ^{ab}(x)=f^{ab}_c\,x^c$, with $f^{ab}_c$ being structure constants of a Lie algebra, an explicit form of the gauge Lagrangian is proposed. In particular a universal solution for the matrix $ρ$ defining the field strength and the covariant derivative is found. The previously known examples of $κ$-Minkowski, $λ$-Minkowski and rotationally invariant non-commutativity are recovered from the general formula. The arbitrariness in the construction of Poisson gauge models is addressed in terms of Seiberg-Witten maps, i.e., invertible field redefinitions mapping gauge orbits onto gauge orbits.

hep-th↗

arXiv2021

Heat Kernel, Spectral Functions and Anomalies in Weyl Semimetals

Being motivated by applications to the physics of Weyl semimetals we study spectral geometry of Dirac operator with an abelian gauge field and an axial vector field. We impose chiral bag boundary conditions with variable chiral phase $θ$ on the fermions. We establish main properties of the spectral functions which ensure applicability of the $ζ$ function regularization and of the usual heat kernel formulae for chiral and parity anomalies. We develop computational methods, including a perturbation expansion for the heat kernel. We show that the terms in both anomalies which include electromagnetic potential are independent of $θ$.

math-ph↗

arXiv2013

High energy bosons do not propagate

We discuss the propagation of bosons (scalars, gauge fields and gravitons) at high energy in the context of the spectral action. Using heat kernel techniques, we find that in the high-momentum limit the quadratic part of the action does not contain positive powers of the derivatives. We interpret this as the fact that the two point Green functions vanish for nearby points, where the proximity scale is given by the inverse of the cutoff.

hep-th↗

arXiv2013

Universal Landau Pole

Our understanding of quantum gravity suggests that at the Planck scale the usual geometry loses its meaning. If so, the quest for grand unification in a large non-abelian group naturally endowed with the property of asymptotic freedom may also lose its motivation. Instead we propose an unification of all fundamental interactions at the Planck scale in the form of a Universal Landau Pole (ULP), at which all gauge couplings diverge. The Higgs quartic coupling also diverges while the Yukawa couplings vanish. The unification is achieved with the addition of fermions with vector gauge couplings coming in multiplets and with hypercharges identical to those of the the Standard Model. The presence of these particles also prevents the Higgs quartic coupling from becoming negative, thus avoiding the instability (or metastability) of the SM vacuum.

hep-th↗

arXiv2012

Higgs-Dilaton Lagrangian from Spectral Regularization

In this letter we calculate the full Higgs-Dilaton action describing the Weyl anomaly using the bosonic spectral action. This completes the work we started in our previous paper (JHEP 1110 (2011) 001). We also clarify some issues related to the dilaton and its role as collective modes of fermions under bosonization.

hep-th↗

arXiv2011

Spectral action, Weyl anomaly and the Higgs-Dilaton potential

We show how the bosonic spectral action emerges from the fermionic action by the renormalization group flow in the presence of a dilaton and the Weyl anomaly. The induced action comes out to be basically the Chamseddine-Connes spectral action introduced in the context of noncommutative geometry. The entire spectral action describes gauge and Higgs fields coupled with gravity. We then consider the effective potential and show, that it has the desired features of a broken and an unbroken phase, with the roll down.

hep-th↗

arXiv2011

Spectral Action from Anomalies

Starting from a theory of fermions moving in a fixed gauge and gravitational background we implement the scale invariance of the theory. Upon quantization the theory is anomalous but the anomaly can be cancelled by the addition of another term to the action. This term comes out to be basically the Chamseddine Connes spectral action introduced in the context of noncommutative geometry. An alternative realization of the dilaton may involve a collective scalar mode of all fermions accumulated in a {scale-noninvariant} dilaton action. The entire spectral action describes gauge and Higgs fields coupled with gravity. Here this action is coupled with a dilaton and we discuss how it relates to the transition from the radiation to the electroweak broken phase via condensation of Higgs fields.

hep-th↗

arXiv2010

Black stars induced by matter on a brane: exact solutions

New exact asymptotically flat solutions of five-dimensional Einstein equations with horizon are found to describe multidimensional black stars generated by matter on the brane, conceivably on high energy colliders. The five-dimensional space-time is realized as an orbifold against reflection of a special extra-space coordinate and matter on the brane is induced by tailoring of the five-dimensional Schwarzschild-Tangherlini black hole metric.

hep-th↗

arXiv2009

Local Fields without Restrictions on the Spectrum of 4-Momentum Operator and Relativistic Lindblad Equation

Quantum theory of Lorentz invariant local scalar fields without restrictions on 4-momentum spectrum is considered. The mass spectrum may be both discrete and continues and the square of mass as well as the energy may be positive or negative. Such fields can exist as part of a hidden matter in the Universe if they interact with ordinary fields very weakly. Generalization of Kallen-Lehmann representation for propagators of these fields is found. The considered generalized fields may violate CPT- invariance. Restrictions on mass-spectrum of CPT-violating fields are found. Local fields that annihilate vacuum state and violate CPT- invariance are constructed in this scope. Correct local relativistic generalization of Lindblad equation for density matrix is written for such fields. This generalization is particulary needed to describe the evolution of quantum system and measurement process in a unique way. Difficulties arising when the field annihilating the vacuum interacts with ordinary fields are discussed.

hep-th↗