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Dusko Latas

Publications and source records attributed to Dusko Latas.

8 recordsLinked to original sources
arXiv2024

Quantum Scalar Field on Fuzzy de Sitter Space I. Field Modes and Vacua

We study a scalar field on a noncommutative model of spacetime, the fuzzy de Sitter space, which is based on the algebra of the de Sitter group $SO(1,d)$ and its unitary irreducible representations. We solve the Klein-Gordon equation in $d=2,4$ and show, using a specific choice of coordinates and operator ordering, that all commutative field modes can be promoted to solutions of the fuzzy Klein-Gordon equation. To explore completeness of this set of modes, we specify a Hilbert space representation and study the matrix elements (integral kernels) of a scalar field: in this way the complete set of solutions of the fuzzy Klein-Gordon equation is found. The space of noncommutative solutions has more degrees of freedom than the commutative one, whenever spacetime dimension is $d>2$. In four dimensions, the new non-geometric, internal modes are parametrised by $S^2\times W$, where $W$ is a discrete matrix space. Our results pave the way to analysis of quantum field theory on the fuzzy de~Sitter space.

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arXiv2021

Laplacian on fuzzy de Sitter space

We study details of geometry of noncommutative de Sitter space: we determine the Riemann and Ricci curvature tensors, the energy and the Laplacian. We find, in particular, that fuzzy de Sitter space is an Einstein space, $R_{ab}=-3ζ\,η_{ab}$. The Laplacian, defined in the noncommutative frame formalism, is not hermitian and gives nonunitary evolution. When symmetrically ordered, it has the usual quadratic form $Δ=Π_aΠ^a$ (when acting on functions in representation space, $Ψ\in {\cal H}$): we find its eigenstates and discuss its spectrum. This result is a first step in a study of the scalar field Laplacian, $Δ= [Π_a, [Π^a,\ ]]$, and its propagator.

hep-th↗
arXiv2020

Light-by-Light Scattering and Spacetime Noncommutativity

The aim of this article is to explore a potential usability of a photon-photon self-interaction from the noncommutative quantum electrodynamics (NCQED) in the case of light-by-light scattering ($γγ\toγγ$) in ultraperipheral Pb+Pb collisions, a reaction measured recently by ATLAS and planned for future experiments in hadron-hadron colliders. We compute the total cross section from both, the full one-loop standard model (SM) and the tree-level NCQED amplitudes, in the equivalent photon approximation with impact parameters, for various noncommutative scales, $\rmΛ_{NC}$, and incoming nuclear spin-energy combinations. We find that NCQED contribution to the cross section has considerable increase at diphoton invariant mass range higher than $\rmΛ_{NC}$, while the SM contribution is strongly suppressed in such region. Our results show that the current ATLAS $\rm\sqrt{s_{NN}} = 5.02$ TeV experiment can only probe $\rmΛ_{NC}<100$ GeV region. On the other hand, future hadron-hadron collider proposals could have the potential to extend to $\rmΛ_{NC}\lesssim 300$ GeV region, making the performance of $\rm Pb+Pb(γγ)\to Pb+Pbγγ$ scattering on testing space-time noncommutativity close to that of the previously proposed photon-photon mode of linear electron-positron collider.

hep-ph↗
arXiv2019

Discrete fuzzy de Sitter cosmology

We analyze the spectrum of time observable in noncommutative cosmological model introduced in [5], defined by $(ρ, s=\frac 12)\,$ representation of the de Sitter group. We find that time has peculiar property: it is not self-adjoint, but appropriate restrictions to the space of physical states give self-adjoint extensions. Extensions have discrete spectrum with logarithmic distribution of eigenvalues, $\,t_n \sim \ell\, \log\, n$+const, where $\ell$ characterizes noncommutativity and the usual assumption is $\,\ell=\ell_{Planck}$. When calculated on physical states, radius of the universe is bounded below by $\, \ell\, \sqrt{\frac 34\, \left( \frac 14 +ρ^2\right)}\, $, which resolves the big bang singularity. An immediate consequence of the model is a specific breaking of the original symmetry at the Planck scale.

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arXiv2018

Fuzzy de Sitter Space

We discuss properties of fuzzy de Sitter space defined by means of algebra of the de Sitter group $\mathrm{SO}(1,4)$ in unitary irreducible representations. It was shown before that this fuzzy space has local frames with metrics that reduce, in the commutative limit, to the de Sitter metric. Here we determine spectra of the embedding coordinates for $(ρ,s=\frac 12)$ unitary irreducible representations of the principal continuous series of the $\mathrm{SO}(1,4)$. The result is obtained in the Hilbert space representation, but using representation theory it can be generalized to all representations of the principal continuous series.

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arXiv2013

The role of the Seiberg-Witten field redefinition in renormalization of noncommutative chiral electrodynamics

It has been conjectured in the literature that renormalizability of the $θ$-expanded noncommutative gauge theories improves when one takes into account full nonuniqueness of the Seiberg-Witten expansion, which relates noncommutative (`high-energy') with commutative (`low-energy') fields. In order to check this conjecture we analyze renormalizability of the noncommutative chiral electrodynamics: we quantize the action which contains all possible terms implied by the SW map. After renormalization we arrive at a different theory in which the relation between the coupling constants is changed. This means that the $θ$-expanded chiral electrodynamics is not renormalizable: when fermions are included, the SW expansion is not preserved in quantization.

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arXiv2007

Non-commutative SU(N) gauge theories and asymptotic freedom

In this paper we analyze the one-loop renormalization of the $θ$-expanded $\rm SU(N)$ Yang-Mills theory. We show that the {\it freedom parameter} $a$, key to renormalization, originates from higher order non-commutative gauge interaction, represented by a higher derivative term $ b h θ^{μν}\hat F_{μν}\star\hat F_{ρσ}\star\hat F^{ρσ}$. The renormalization condition fixes the allowed values of the parameter $a$ to one of the two solutions: $a=1$ or $a=3$, i.e. to $b=0$ or to $b=1/2$, respectively. When the higher order interaction is switched on, ($a=3$), pure non-commutative SU(N) gauge theory at first order in $θ$-expansion becomes one-loop renormalizable for various representations of the gauge group. We also show that, in the case $a=3$ and the adjoint representation of the gauge fields, the non-commutative deformation parameter $h$ has to be renormalized and it is asymptotically free.

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