Model Of Relativistic Particle Research Articles

Heisenberg versus the Covariant String

A Poincaré multiplet of mass eigenstates (P2-m2)Ψ=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\bigl (P^2 - m^2\\bigr )\\Psi = 0$$\\end{document} cannot be a subspace of a space with a D-vector position operator X=(X0,⋯XD-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X=(X_0,\\dots X_{D-1})$$\\end{document}: the Heisenberg algebra [Pm,Xn]=iδmn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[P^m, X_n] = \ extrm{i}\\delta ^m{}_n$$\\end{document} implies by a simple argument that each Poincaré multiplet of definite mass vanishes. The same conclusion follows from the Stone-von Neumann theorem. In a quantum theory the constraint of an absolutely continuous spectrum to a lower dimensional submanifold yields zero even if Dirac’s treatment of the corresponding classical constraint defines a symplectic submanifold with a consistent corresponding quantum model. Its Hilbert space is not a subspace of the unconstrained theory. Hence the operator relations of the unconstrained model need not carry over to the constrained model. Our argument excludes quantized worldline models of relativistic particles and the physical states of the covariant quantum string. We correct misconceptions about the generators of Lorentz transformations acting on particles.

Fractional Laplacian Spinning Particle in External Electromagnetic Field

We construct a fractional Laplacian spinning particle model in an external electromagnetic field that generalizes a standard relativistic spinning particle model without anti-commuting spin variables. The one-dimensional fractional Laplacian in world-line variable λ governs the kinetic energy that is non-local in λ. The interaction between the particle’s charge and the electromagnetic four-potential is non-local in λ, while the interaction between the particle’s spin tensor and the electromagnetic field is standard. By applying the variational principle, we obtain the equations of motion for particle coordinates. We solve analytically the equations of motion in two particular cases: the constant electric and magnetic field. For more complex field configurations, the equations are, in general, non-local and non-linear. By making the assumption of a much weaker interaction term between the charge and four-potential compared with the interaction between spinning degrees of freedom and the electromagnetic field, we obtain approximate analytical solutions in the case of a quadratic electromagnetic potential.

Investigating the effect of density variation on pitch angle scattering events of runaway electrons as observed through electron cyclotron emission diagnostic at Aditya-upgrade tokamak.

Nascent observations about the influence of kinetic instabilities on electron cyclotron emission (ECE) from runaway electrons (REs) have been detected and explored at the Aditya-Upgrade (Aditya-U) tokamak. The developed broadband ECE radiometer system offers wideband measurements by integrating several radio frequency units with a fixed intermediate frequency receiver with multiple channels, which is a novel approach to meet the needs of the localized measurements at various toroidal fields and extend the system dynamic range. The low density (ne ≤ 1 × 10-19m-3) plasma discharges at Aditya-U are consistently accompanied by a 20%-40% increase in the ECE radiometer signal amplitude within 100 µs and sporadic step-like modulations. The Pitch Angle Scattering (PAS) of REs induced by kinetic instabilities is a potential candidate for their occurrence. This steep jump in the radiometer signals was detected due to its high temporal resolution of 10 µs. A "PREDICT" code that employs the relativistic test particle model validates these experimental findings of the radiometer diagnostic for the first time for Aditya-U tokamak. Preliminary observations of the ECE radiometer signals also show that additional gas puffs can be used to vary the trigger timings of such PAS events or even lead to their complete avoidance.

On the dynamics of relativistic particles with torsion in warped product spacetimes

In this work, we study spacelike trajectories of a relativistic particle model whose Lagrangian is given by the total torsion of its worldline. Once the field equations are established, we investigate the trajectories in two physically relevant families of four-dimensional spacetimes: generalized Robertson–Walker and standard static spacetimes. For the former we obtain both characterization as well as non-existence results for Frenet curves of different orders, which are the curves capable of modeling trajectories. For standard static spacetimes, we obtain a full characterization of the critical curves and present an example in which we can explicitly compute non-trivial trajectories.

Reparameterization Invariant Model of a Supersymmetric System: BRST and Supervariable Approaches

We carry out the Becchi-Rouet-Stora-Tyutin (BRST) quantization of the one 0 + 1 -dimensional (1D) model of a free massive spinning relativistic particle (i.e., a supersymmetric system) by exploiting its classical infinitesimal and continuous reparameterization symmetry transformations. We use the modified Bonora-Tonin (BT) supervariable approach (MBTSA) to BRST formalism to obtain the nilpotent (anti-)BRST symmetry transformations of the target space variables and the (anti-)BRST invariant Curci-Ferrari- (CF-) type restriction for the 1D model of our supersymmetric (SUSY) system. The nilpotent (anti-)BRST symmetry transformations for other variables of our model are derived by using the (anti-)chiral supervariable approach (ACSA) to BRST formalism. Within the framework of the latter, we have shown the existence of the CF-type restriction by proving the (i) symmetry invariance of the coupled Lagrangians and (ii) the absolute anticommutativity property of the conserved (anti-)BRST charges. The application of the MBTSA to a physical SUSY system (i.e., a 1D model of a massive spinning particle) is a novel result in our present endeavor. In the application of ACSA, we have considered only the (anti-)chiral super expansions of the supervariables. Hence, the observation of the absolute anticommutativity of the (anti-)BRST charges is a novel result. The CF-type restriction is universal in nature as it turns out to be the same for the SUSY and non-SUSY reparameterization (i.e., 1D diffeomorphism) invariant models of the (non-)relativistic particles.

Model of massless relativistic particle with continuous spin and its twistorial description

We propose a new world-line Lagrangian model of the D= 4 massless relativistic particle with continuous spin and develop its twistorial formulation. The description uses two Penrose twistors subjected to four first class constraints. After the first quantization of the world-line twistorial model, the wave function is defined by an unconstrained function on the two-dimensional complex affine plane. We find the twistor transform that determines the space-time field of the continuous spin particle through the corresponding twistor one, which plays the role of a prepotential. It is shown that this space-time field is an exact solution of the space-time constraints defining the irreducible massless representation of the Poincaré group with continuous spin.

Particle model with generalized Poincaré symmetry

Using the techniques of nonlinear coset realization with a generalized Poincaré group, we construct a relativistic particle model, invariant under the generalized symmetries, providing a dynamical realization of the B5 algebra.

Gauging the Relativistic Particle Model on the Noncommutative Plane

We construct a new model for relativistic particle on the noncommutative plane, using the symplectic formalism of constrained systems. We suggest a shortcut approach to construct the gauged Lagrangian, using the Poisson algebra of constraints, without calculating the whole procedure of symplectic formalism. We also propose an approach for the systems, in which the symplectic formalism is not applicable, due to the truncation of production of secondary constraints at the first level. After gauging the model, we obtain the corresponding generators of gauge transformations of the physical system. Finally, by extracting the Poisson structure of all constraints, we show the effect of gauging on the canonical structure of the phase spaces of both primary and gauged models.

Implication of the geodesic equation in the generalized uncertainty principle framework

The generalized uncertainty principle (GUP) corrected modified relativistic particle model has been derived in curved space-time. From this modified model, the equation of motion (EM) has been constructed relativistically in terms of the affine parameter ($\lambda$) or proper time ($\tau$) and nonrelativistically in terms of coordinate time ($t$). In this context, the constraint analysis technique has been applied to get the EM. Interestingly, the EM obtained in both cases is the usual one. This result clearly indicates an important fact, that is, consistency of the equivalence principle in the GUP framework, and furthermore it can be concluded that with the GUP-corrected modified algebra it is impossible to get the GUP effect in point particle motion.

Electrodynamics of a generalized charged particle in doubly special relativity framework

In the present paper, dynamics of generalized charged particles are studied in the presence of external electromagnetic interactions. This particular extension of the free relativistic particle model lives in Non-Commutative κ-Minkowski space–time, compatible with Doubly Special Relativity, that is motivated to describe Quantum Gravity effects. Furthermore we have also considered the electromagnetic field to be dynamical and have derived the modified forms of Lienard–Wiechert like potentials for these extended charged particle models. In all the above cases we exploit the new and extended form of κ-Minkowski algebra where electromagnetic effects are incorporated in the lowest order, in the Dirac framework of Hamiltonian constraint analysis.

Rigid particle revisited: Extrinsic curvature yields the Dirac equation

We reexamine the model of relativistic particle with higher-derivative linear term on the first extrinsic curvature (rigidity). The passage from classical to quantum theory requires a number of rather unexpected steps which we report here. We found that, contrary to common opinion, quantization of the model in terms of so ( 3.2 ) -algebra yields massive Dirac equation. • New way of canonical quantization of relativistic rigid particle is proposed. • Quantization made in terms of so ( 3.2 ) angular momentum algebra. • Quantization yields massive Dirac equation.

GUP-BASED AND SNYDER NONCOMMUTATIVE ALGEBRAS, RELATIVISTIC PARTICLE MODELS, DEFORMED SYMMETRIES AND INTERACTION: A UNIFIED APPROACH

We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space–time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.

Massless particles in generalized Robertson–Walker 4-spacetimes

The model of massless relativistic particle relying in a curvature-dependent action functional is considered in the framework of generalized Robertson–Walker 4-spacetimes. The discussion is based on the number of nonvanishing Frenet curvatures, and we obtain characterizations, examples, and nonexistence results for the critical points of the action functional, which are included in the fibers.

Relativistic quantum particle in a time-dependent homogeneous field

Abstract A model of the relativistic quantum particle under the action of a time-dependent force is considered. This exactly solvable model is realized in the one-dimensional relativistic configurational x-space and is described by the finite-difference equation. The momentum p-space is one-dimensional Lobachevsky space. We have explicitly constructed the wave functions and propagators for this model in both x- and p-representations. We have also found a solution of a definite class of partial differential and finite-difference equations, which can be interpreted as the operator identities.

New particle model in extended space–time and covariantization of planar Landau dynamics

We introduce the Maxwell-invariant extension of D=4 relativistic free particle model into ten-dimensional Maxwell tensorial space. The new model after first quantization describes in particular Lorentz frame the planar dynamics providing Landau orbits in the presence of constant magnetic field.

A semiclassical description of relativistic spin without the use of Grassmann variables and the Dirac equation

We propose a relativistic particle model without Grassmann variables which, being canonically quantized, leads to the Dirac equation. Both Γ -matrices and the relativistic spin tensor are produced through the canonical quantization of the classical variables which parametrize the properly constructed relativistic spin surface. Although there is no mass–shell constraint in our model, our particle’s speed cannot exceed the speed of light. The classical dynamics of the model is in correspondence with the dynamics of mean values of the corresponding operators in the Dirac theory. In particular, the position variable experiences Zitterbewegung in noninteracting theory. The classical equations for the spin tensor are the same as those of the Barut–Zanghi model of a spinning particle.

Spinning-particle model for the Dirac equation and the relativistic Zitterbewegung

We construct the relativistic particle model without Grassmann variables which meets the following requirements. A) Canonical quantization of the model implies the Dirac equation. B) The variable which experiences Zitterbewegung, represents a gauge non-invariant variable in our model. Hence our particle does not experience the undesirable Zitterbewegung. C) In the non-relativistic limit spin is described by three-vector, as it could be expected.

On the semiclassical approach to quantum cosmology: relational particle model

The emergent semiclassical time approach to resolving the problem of time in quantum gravity involves heavy slow degrees of freedom providing via an approximately Hamilton–Jacobi equation an approximate time standard with respect to which the quantum mechanics of light fast degrees of freedom can run. More concretely, this approach involves Born–Oppenheimer and WKB ansätze and some accompanying approximations. In this paper, I investigate this approach for concrete scaled relational particle mechanics models, i.e. models featuring only relative separations, relative angles and relative times. I consider the heavy–light interaction term in the light quantum equation—necessary for the semiclassical approach to work, first as an emergent-time-dependent perturbation of the emergent-time-dependent Schrödinger equation for the light subsystem. Secondly, I consider a scheme in which the backreaction is small but non-negligible, so that the l-subsystem also affects the form of the emergent time. I also suggest that the many terms involving expectation values of the light wavefunctions in both the (unapproximated) heavy and light equations might require treatment in parallel to the Hartree–Fock self-consistent approach rather than merely being discarded; for the moment this paper provides a counterexample to such terms being smaller than their unaveraged counterparts. Investigation of these ideas and methods will give us a more robust understanding of the suggested quantum-cosmological origin of microwave background inhomogeneities and galaxies.

Symmetries of Snyder-de Sitter space and relativistic particle dynamics

We study the deformed conformal-Poincaré symmetries consistent with the Snyder-de Sitter space. A relativistic particle model invariant under these deformed symmetries is given. This model is used to provide a gauge independent derivation of the Snyder-de Sitter algebra. Our results are valid in the leading order in the parameters appearing in the model.

Quantum cosmological relational model of shape and scale in 1D

Relational particle models are useful toy models for quantum cosmology and the problem of time in quantum general relativity. This paper shows how to extend existing work on concrete examples of relational particle models in 1D to include a notion of scale. This is useful as regards forming a tight analogy with quantum cosmology and the emergent semiclassical time and hidden time approaches to the problem of time. This paper shows furthermore that the correspondence between relational particle models and classical and quantum cosmology can be strengthened using judicious choices of the mechanical potential. This gives relational particle mechanics models with analogues of spatial curvature, cosmological constant, dust and radiation terms. A number of these models are then tractable at the quantum level. These models can be used to study important issues (1) in canonical quantum gravity: the problem of time, the semiclassical approach to it and timeless approaches to it (such as the naive Schrödinger interpretation and records theory) and (2) in quantum cosmology, such as in the investigation of uniform states, robustness and the qualitative understanding of the origin of structure formation.