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Khazret S. Nirov

Publications and source records attributed to Khazret S. Nirov.

10 recordsLinked to original sources
arXiv2019

Vertex Models and Spin Chains in Formulas and Pictures

We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are introduced. Their explicit analytical forms for the case of integrable systems associated with the quantum loop algebra ${\mathrm U}_q(\mathcal L(\mathfrak{sl}_{l + 1}))$ are given. The commutativity conditions for the transfer operators of lattices with a boundary are derived by the graphical method. Our consideration reveals useful advantages of the graphical approach for certain problems in the theory of quantum integrable systems.

math-ph↗
arXiv2017

Highest $\ell$-Weight Representations and Functional Relations

We discuss highest $\ell$-weight representations of quantum loop algebras and the corresponding functional relations between integrability objects. In particular, we compare the prefundamental and $q$-oscillator representations of the positive Borel subalgebras of the quantum group $\mathrm{U}_q(\mathcal L(\mathfrak{sl}_{l+1}))$ for arbitrary values of $l$. Our article has partially the nature of a short review, but it also contains new results. These are the expressions for the $L$-operators, and the exact relationship between different representations, as a byproduct resulting in certain conclusions about functional relations.

math-ph↗
arXiv2010

Exercises with the universal R-matrix

Using the formula for the universal $R$-matrix proposed by Khoroshkin and Tolstoy, we give a detailed derivation of $L$-operators for the quantum groups associated with the generalized Cartan matrices $A_1^{(1)}$ and $A_2^{(1)}$.

math-ph↗
arXiv2003

W-algebras for non-abelian Toda systems

We construct the classical W-algebras for some non-abelian Toda systems associated with the Lie groups GL(2n,R) and Sp(n,R). We start with the set of characteristic integrals and find the Poisson brackets for the corresponding Hamiltonian counterparts. The convenient block matrix representation for the Toda equations is used. The infinitesimal symmetry transformations generated by the elements of the W-algebras are presented.

hep-th↗
arXiv2002

Higher Symmetries of Toda Equations

The symmetries of the simplest non-abelian Toda equations are discussed. The set of characteristic integrals whose Hamiltonian counterparts form a W-algebra, is presented.

hep-th↗
arXiv1998

Pseudoclassical mechanics and hidden symmetries of 3d particle models

We discuss hidden symmetries of three-dimensional field configurations revealed at the one-particle level by the use of pseudoclassical particle models. We argue that at the quantum field theory level, these can be naturally explained in terms of manifest symmetries of the reduced phase space Hamiltonian of the corresponding field systems.

hep-th↗
arXiv1997

The Ostrogradsky prescription for BFV formalism

Gauge-invariant systems of a general form with higher order derivatives of gauge parameters are investigated within the framework of the BFV formalism. Higher order terms of the BRST charge and BRST-invariant Hamiltonian are obtained. It is shown that the identification rules for Lagrangian and Hamiltonian ghost variables depend on the choice of the extension of constraints from the primary constraint surface.

hep-th↗
arXiv1995

Strings as a Model for Parent and Baby Universes: Total Splitting Rates

Emission of hard microscopic string (graviton) by an excited macroscopic string may be viewed as a model of branching of a $(1+1)$-dimensional baby universe off large parent one. We show that, apart from a trivial factor, the total emission rate is not suppressed by the size of the macroscopic string. This implies unsuppressed loss of quantum coherence in $(1+1)$-dimensional parent universe.

hep-th↗
arXiv1994

BRST formalism for systems with higher order derivatives of gauge parameters

For a wide class of mechanical systems, invariant under gauge transformations with higher (arbitrary) order time derivatives of gauge parameters, the equivalence of Lagrangian and Hamiltonian BRST formalisms is proved. It is shown that the Ostrogradsky formalism establishes the natural rules to relate the BFV ghost canonical pairs with the ghosts and antighosts introduced by the Lagrangian approach. Explicit relation between corresponding gauge-fixing terms is obtained.

hep-th↗