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A. A. Deriglazov

Publications and source records attributed to A. A. Deriglazov.

At least 37 records · Page 2Linked to original sources
arXiv2005

Interpretation of Lorentz boosts in conformally deformed special relativity theory

Conformally deformed special relativity is mathematically consistent example of a theory with two observer independent scales. As compare with recent DSR proposals, it is formulated starting from the position space. In this work we propose interpretation of Lorentz boosts of the model as transformations among accelerated observers. We point further that the model can be considered as relativistic version of MOND program and thus may be interesting in context of dark matter problem.

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arXiv2005

Search for gauge symmetry generators of singular Lagrangian theory

We propose a procedure which allows one to construct local symmetry generators of general quadratic Lagrangian theory. Manifest recurrence relations for generators in terms of so-called structure matrices of the Dirac formalism are obtained. The procedure fulfilled in terms of initial variables of the theory, and do not implies either separation of constraints on first and second class subsets or any other choice of basis for constraints.

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arXiv2005

Position space versions of Magueijo-Smolin doubly special relativity proposal and the problem of total momentum

We present and discuss two different possibilities to construct position space version for Magueijo-Smolin (MS) doubly special relativity proposal. The first possibility is to start from ordinary special relativity and then to define conserved momentum in special way. It generates MS invariant as well as nonlinear MS transformations on the momentum space, leading to consistent picture for one-particle sector of the theory. The second possibility is based on the following observation. Besides the nonlinear MS transformations, the MS energy-momentum relation is invariant also under some inhomogeneous linear transformations. The latter are induced starting from linearly realized Lorentz group in five-dimensional position space. Particle dynamics and kinematics are formulated starting from the corresponding five-dimensional interval. There is no problem of total momentum in the theory. The formulation admits two observer independent scales, the speed of light, $c$, and $k$ with dimension of velocity. We speculate on different possibilities to relate $k$ with fundamental constants. In particular, expression of $k$ in terms of vacuum energy suggests emergence of (minimum) quantum of mass.

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arXiv2004

Doubly Special Relativity in Position Space Starting from the Conformal Group

We propose version of doubly special relativity theory starting from position space. The version is based on deformation of ordinary Lorentz transformations due to the special conformal transformation. There is unique deformation which does not modify rotations. In contrast to the Fock-Lorentz realization (as well as to recent position-space proposals), maximum signal velocity is position (and observer) independent scale in our formulation by construction. The formulation admits one more invariant scale identified with radius of three-dimensional space-like hypersection of space-time. We present and discuss the Lagrangian action for geodesic motion of a particle on the DSR space. For the present formulation, one needs to distinguish the canonical (conjugated to $x^μ$) momentum $p^μ$ from the conserved energy-momentum. Deformed Lorentz transformations for $x^μ$ induce complicated transformation law in space of canonical momentum. $p^μ$ is not a conserved quantity and obeys to deformed dispersion relation. The conserved energy-momentum $P^μ$ turns out to be different from the canonical one, in particular, $P^μ$-space is equipped with nontrivial commutator. The nonlinear transformations for $x^μ$ induce the standard Lorentz transformations in space of $P^μ$. It means, in particular, that composite rule for $P^μ$ is ordinary sum. There is no problem of total momentum in the theory. $P^μ$ obeys the standard energy-momentum relation (while has nonstandard dependence on velocity).

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arXiv2003

Equivalence between different classical treatments of the O(N) nonlinear sigma model and their functional Schrodinger equations

In this work we derive the Hamiltonian formalism of the O(N) non-linear sigma model in its original version as a second-class constrained field theory and then as a first-class constrained field theory. We treat the model as a second-class constrained field theory by two different methods: the unconstrained and the Dirac second-class formalisms. We show that the Hamiltonians for all these versions of the model are equivalent. Then, for a particular factor-ordering choice, we write the functional Schrodinger equation for each derived Hamiltonian. We show that they are all identical which justifies our factor-ordering choice and opens the way for a future quantization of the model via the functional Schrodinger representation.

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arXiv2003

Poincare covariant mechanics on noncommutative space

The Dirac approach to constrained systems can be adapted to construct relativistic invariant theories on a noncommutative (NC) space. As an example, we propose and discuss relativistic invariant NC particle coupled to electromagnetic field by means of the standard term $A^μ\dot x_μ$. Poincare invariance implies deformation of the free particle NC algebra in the interaction theory. The corresponding corrections survive in the nonrelativistic limit.

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arXiv2003

Noncommutative relativistic particle on the electromagnetic background

Noncommutative version of D-dimensional relativistic particle is proposed. We consider the particle interacting with the configuration space variable $θ^{μν}(τ)$ instead of the numerical matrix. The corresponding Poincare invariant action has a local symmetry, which allows one to impose the gauge $θ^{0i}=0, ~ θ^{ij}=const$. The matrix $θ^{ij}$ turns out to be the noncommutativity parameter of the gauge fixed formulation. Poincare transformations of the gauge fixed formulation are presented in the manifest form. Consistent coupling of NC relativistic particle to the electromagnetic field is constructed and discussed.

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arXiv2002

Noncommutative version of an arbitrary nondegenerated mechanics

A procedure to obtain noncommutative version for any nondegenerated dynamical system is proposed and discussed. The procedure is as follow. Let $S=\int dt L(q^A, ~ \dot q^A)$ is action of some nondegenerated system, and $L_1(q^A, ~ \dot q^A, ~ v_A)$ is the corresponding first order Lagrangian. Then the corresponding noncommutative version is $S_N=\int dt[ L_1(q^A, ~ \dot q^A, \~ v_A)+ \dot v_Aθ^{AB}v_B]$. Namely, the system $S_N$ has the following properties: 1) It has the same number of physical degrees of freedom as the initial system $S$. 2) Equations of motion of the system are the same as for the initial system $S$, modulo the term which is proportional to the parameter $θ^{AB}$. 3) Configuration space variables have the noncommutative brackets: $\{q^A, ~ q^B\}=-2θ^{AB}$. It is pointed also that quantization of the system $S_N$ leads to quantum mechanics with ordinary product replaced by the Moyal product.

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arXiv2002

Noncommutative relativistic particle

Noncommutative version of D-dimensional relativistic particle is proposed. We consider the particle interacting with the configuration space variable $θ^{μν}(τ)$ instead of the numerical matrix. The corresponding Poincare invariant action has a local symmetry, which allows one to impose the gauge $θ^{0i}=0, ~ θ^{ij}=const$. The matrix $θ^{ij}$ turns out to be the noncommutativity parameter of the gauge fixed formulation. Poincare transformations of the gauge fixed formulation are presented in the manifest form.

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arXiv2002

Quantum mechanics on noncommutative plane and sphere from constrained systems

It is shown that quantum mechanics on noncommutative (NC) spaces can be obtained by canonical quantization of some underlying constrained systems. Noncommutative geometry arises after taking into account the second class constraints presented in the models. It leads, in particular, to a possibility of quantization in terms of the initial NC variables. For a two-dimensional plane we present two Lagrangian actions, one of which admits addition of an arbitrary potential. Quantization leads to quantum mechanics with ordinary product replaced by the Moyal product. For a three-dimensional case we present Lagrangian formulations for a particle on NC sphere as well as for a particle on commutative sphere with a magnetic monopole at the center, the latter is shown to be equivalent to the model of usual rotor. There are several natural possibilities to choose physical variables, which lead either to commutative or to NC brackets for space variables. In the NC representation all information on the space variable dynamics is encoded in the NC geometry. Potential of special form can be added, which leads to an example of quantum mechanics on the NC sphere.

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arXiv2002

Noncommutative quantum mechanics as a constrained system

It is shown that quantum mechanics on noncommutative spaces (NQM) can be obtained by the canonical quantization of some underlying second class constrained system formulated in extended configuration space. It leads, in particular, to an intriguing possibility of quantization in terms of the initial (noncommutative) variables. Two different formulations are discissed. The first one is appropriate for at most quadratic potential. The noncommutativity parameter and rank of matrix of the constraint brackets depend on the potential. It explains appearance of two phases of the resulting NQM. The second formulation is appropriate for an arbitrary potential. In both cases the corresponding Lagrangian action is presented and quantized, which leads to quantum mechanics with ordinary product replaced by the Moyal product.

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arXiv2001

Open string with a background B-field as the first order mechanics and noncommutativity

To study noncommutativity properties of the open string with constant B-field we construct a mechanical action which reproduces classical dynamics of the string sector under consideration. It allows one to apply the Dirac quantization procedure for constrained systems in a direct and unambiguous way. The mechanical action turns out to be the first order system without taking the strong field limit $B\longrightarrow\infty$. In particular, it is true for zero mode of the string coordinate which means that the noncommutativity is intrinsic property of this mechanical system. We describe the arbitrariness in the relation existent between the mechanical and the string variables and show that noncommutativity of the string variables on the boundary can be removed. It is in correspondence with the result of Seiberg and Witten on relation among noncommutative and ordinary Yang-Mills theories.

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arXiv2001

Supplementation of reducible constraints and the Green-Schwarz superstring

We apply the supplementation trick [26] to the Green-Schwarz superstring. For type IIB theory both first and second class constraints are covariantly separated and then arranged into irreducible sets in the initial formulation. For N=1 Green-Schwarz superstring we propose a modified action which is equivalent to the initial one. Fermionic first and second class constraints are covariantly separated, the first class constraints turn out to be irreducible. We discuss also equations of motion in the covariant gauge for $κ$-symmetry. For type IIA theory the same modification leads to formulation with irreducible second class constraints.

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arXiv2001

String action with multiplet of $Θ$-terms and the hidden Poincare symmetry

We study string action with multiplet of $Θ$-terms added, which turns out to be closely related with the bosonic sector of D=11 superstring action [3,4]. Alternatively, the model can be considered as describing class of special solutions of the membrane. An appropriate set of variables is find, in which the light-cone quantization turns out to be possible. It is shown that anomaly terms in the algebra of the light-cone Poincare generators are absent for the case D=27.

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arXiv2001

Modified N=1 Green-Schwarz superstring with irreducible first class constraints

We propose modified action which is equivalent to N=1 Green-Schwarz superstring and which allows one to realize the supplementation trick [26]. Fermionic first and second class constraints are covariantly separated, the first class constraints (1CC) turn out to be irreducible. We discuss also equations of motion in the covariant gauge for $κ$-symmetry. It is shown how the usual Fock space picture can be obtained in this gauge.

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arXiv2000

On consistency of the closed bosonic string with different left-right ordering constants

Closed bosonic string with different normal ordering constants $a \ne \bar a$ for the right and the left moving sectors is considered. One immediate consequence of this choice is absence of tachyon in the physical state spectrum. Selfconsistency of the resulting model in the "old covariant quantization" (OCQ) framework is studyed. The model is manifestly Poincare invariant, it has non trivial massless sector and is ghost free for $D=26, ~ a=1, ~\bar a=0$. A possibility to obtain the light-cone formulation for the model is also discussed.

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arXiv2000

Local symmetries in the Hamiltonian framework. 1. Hamiltonian form of the symmetries and the Noether identities

We study in the Hamiltonian framework the local transformations $δ_εq^A(τ)=\sum^{[k]}_{k=0}\partial^k_τε^a{} R_{(k)a}{}^A(q^B, \dot q^C)$ which leave invariant the Lagrangian action: $δ_εS=div$. Manifest form of the symmetry and the corresponding Noether identities is obtained in the first order formalism as well as in the Hamiltonian one. The identities has very simple form and interpretation in the Hamiltonian framework. Part of them allows one to express the symmetry generators which correspond to the primarily expressible velocities through the remaining one. Other part of the identities allows one to select subsystem of constraints with a special structure from the complete constraint system. It means, in particular, that the above written symmetry implies an appearance of the Hamiltonian constraints up to at least $([k]+1)$ stage. It is proved also that the Hamiltonian symmetries can always be presented in the form of canonical transformation for the phase space variables. Manifest form of the resulting generating function is obtained.

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