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Vladislav Kupriyanov

Publications and source records attributed to Vladislav Kupriyanov.

7 recordsLinked to original sources
arXiv2026

Curved momentum space and finite Landau spectrum in $κ$-Minkowski spacetime

We derive the $κ$-Poincaré Casimir from the de Sitter geometry of momentum space and employ it as the dynamical constraint governing charged particles within the framework of Poisson gauge theory. The resulting formalism is applied to scalar and spin-$1/2$ particles in a constant magnetic field. Within the semiclassical Poisson-gauge framework, exact energy spectra are obtained without expanding in the deformation parameter $1/κ$. On the positive-energy branch in bicrossproduct momentum coordinates, identifying these coordinates with the physical momenta entering the gauge coupling imposes an upper bound on their spatial magnitude. This bound leads to a finite number of admissible Landau-level indices and hence to a Highest Landau Level (HLL). In the fermionic case, the truncation is spin dependent for the factorization adopted here, resulting in a polarized HLL. Possible implications of this ultraviolet truncation and the limitations of the framework are briefly discussed.

hep-th↗
arXiv2024

Classical Mechanics in Noncommutative Spaces: Confinement and More

We consider a semi-classical approximation to the dynamics of a point particle in a noncommutative space. In this approximation, the noncommutativity of space coordinates is described by a Poisson bracket. For linear Poisson brackets, the corresponding phase space is given by the cotangent bundle of a Lie group, with the Lie group playing the role of a curved momentum space. We show that the curvature of the momentum space may lead to rather unexpected physical phenomena such as an upper bound on the velocity of a free nonrelativistic particle, bounded motion for repulsive central force, and no-fall-into-the-centre for attractive Coulomb potential. We also consider a superintegrable Hamiltonian for the Kepler problem in $3$-space with $su(2)$ noncommutativity. The leading correction to the equations of motion due to noncommutativity is shown to be described by an effective monopole potential.

hep-th↗
arXiv2024

Non-commutative gauge symmetry from strong homotopy algebras

We explicitly construct an L$_\infty$ algebra that defines U$_{\star}(1)$ gauge transformations on a space with an arbitrary non-commutative and even non-associative star product. Matter fields are naturally incorporated in this scheme as L$_\infty$ modules. Some possibilities for including P$_\infty$ algebras are also discussed.

hep-th↗
arXiv2018

Constructions of L$_{\infty}$ algebras and their field theory realizations

We construct L$_{\infty}$ algebras for general `initial data' given by a vector space equipped with an antisymmetric bracket not necessarily satisfying the Jacobi identity. We prove that any such bracket can be extended to a 2-term L$_{\infty}$ algebra on a graded vector space of twice the dimension, with the 3-bracket being related to the Jacobiator. While these L$_{\infty}$ algebras always exist, they generally do not realize a non-trivial symmetry in a field theory. In order to define L$_{\infty}$ algebras with genuine field theory realizations, we prove the significantly more general theorem that if the Jacobiator takes values in the image of any linear map that defines an ideal there is a 3-term L$_{\infty}$ algebra with a generally non-trivial 4-bracket. We discuss special cases such as the commutator algebra of octonions, its contraction to the `R-flux algebra', and the Courant algebroid.

math-ph↗
arXiv2018

On the Uniqueness of L$_\infty$ bootstrap: Quasi-isomorphisms are Seiberg-Witten Maps

In the context of the recently proposed L$_\infty$ bootstrap approach, the question arises whether the so constructed gauge theories are unique solutions of the L$_\infty$ relations. Physically it is expected that two gauge theories should be considered equivalent if they are related by a field redefinition described by a Seiberg-Witten map. To clarify the consequences in the L$_\infty$ framework, it is proven that Seiberg-Witten maps between physically equivalent gauge theories correspond to quasi-isomorphisms of the underlying L$_\infty$ algebras. The proof suggests an extension of the definition of a Seiberg-Witten map to the closure conditions of two gauge transformations and the dynamical equations of motion.

hep-th↗
arXiv2018

Bootstrapping Non-commutative Gauge Theories from L$_\infty$ algebras

Non-commutative gauge theories with a non-constant NC-parameter are investigated. As a novel approach, we propose that such theories should admit an underlying L$_\infty$ algebra, that governs not only the action of the symmetries but also the dynamics of the theory. Our approach is well motivated from string theory. We recall that such field theories arise in the context of branes in WZW models and briefly comment on its appearance for integrable deformations of AdS$_5$ sigma models. For the SU(2) WZW model, we show that the earlier proposed matrix valued gauge theory on the fuzzy 2-sphere can be bootstrapped via an L$_\infty$ algebra. We then apply this approach to the construction of non-commutative Chern-Simons and Yang-Mills theories on flat and curved backgrounds with non-constant NC-structure. More concretely, up to the second order, we demonstrate how derivative and curvature corrections to the equations of motion can be bootstrapped in an algebraic way from the L$_\infty$ algebra. The appearance of a non-trivial A$_\infty$ algebra is discussed, as well.

hep-th↗