scholarly journals Quantization of κ-deformed Dirac equation

2020 ◽  
Vol 35 (25) ◽  
pp. 2050147
Author(s):  
E. Harikumar ◽  
Vishnu Rajagopal
Keyword(s):  
Dirac Equation ◽  
Particle Physics ◽  
Equations Of Motion ◽  
Space Time ◽  
Dirac Field ◽  
Oscillator Algebra ◽  
First Order ◽  
Deformed Oscillator Algebra ◽  
Mass Dependent ◽  
Conserved Currents

In this paper, we study the quantization of Dirac field theory in the [Formula: see text]-deformed space–time. We adopt a quantization method that uses only equations of motion for quantizing the field. Starting from [Formula: see text]-deformed Dirac equation, valid up to first order in the deformation parameter [Formula: see text], we derive deformed unequal time anticommutation relation between deformed field and its adjoint, leading to undeformed oscillator algebra. Exploiting the freedom of imposing a deformed unequal time anticommutation relations between [Formula: see text]-deformed spinor and its adjoint, we also derive a deformed oscillator algebra. We show that deformed number operator is the conserved charge corresponding to global phase transformation symmetry. We construct the [Formula: see text]-deformed conserved currents, valid up to first order in [Formula: see text], corresponding to parity and time-reversal symmetries of [Formula: see text]-deformed Dirac equation also. We show that these conserved currents and charges have a mass-dependent correction, valid up to first order in [Formula: see text]. This novel feature is expected to have experimental significance in particle physics. We also show that it is not possible to construct a conserved current associated with charge conjugation, showing that the Dirac particle and its antiparticle satisfy different equations in [Formula: see text] space–time.

Solution of the Dirac equation with some superintegrable potentials by the quadratic algebra approach

2014 ◽  
Vol 29 (06) ◽  
pp. 1450028 ◽  
Author(s):  
S. Aghaei ◽  
A. Chenaghlou
Keyword(s):  
Dirac Equation ◽  
Quadratic Algebra ◽  
Two Dimensional ◽  
Oscillator Algebra ◽  
Quadratic Algebras ◽  
Energy Eigenvalues ◽  
Vector Potentials ◽  
Algebra Approach ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra

The Dirac equation with scalar and vector potentials of equal magnitude is considered. For the two-dimensional harmonic oscillator superintegrable potential, the superintegrable potentials of E8 (case (3b)), S4 and S2, the Schrödinger-like equations are studied. The quadratic algebras of these quasi-Hamiltonians are derived. By using the realization of the quadratic algebras in a deformed oscillator algebra, the structure function and the energy eigenvalues are obtained.

scholarly journals Trajectory construction of Dirac evolution

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190682
Author(s):  
Peter Holland
Keyword(s):  
Dirac Equation ◽  
Evolution Operator ◽  
Exact Formula ◽  
Dirac Spinor ◽  
Mean Flow ◽  
First Order ◽  
Continuity Equations ◽  
The Mean ◽  
Trajectory Models ◽  
Mass Dependent

We extend our programme of representing the quantum state through exact stand-alone trajectory models to the Dirac equation. We show that the free Dirac equation in the angular coordinate representation is a continuity equation for which the real and imaginary parts of the wave function, angular versions of Majorana spinors, define conserved densities. We hence deduce an exact formula for the propagation of the Dirac spinor derived from the self-contained first-order dynamics of two sets of trajectories in 3-space together with a mass-dependent evolution operator. The Lorentz covariance of the trajectory equations is established by invoking the ‘relativity of the trajectory label'. We show how these results extend to the inclusion of external potentials. We further show that the angular version of Dirac's equation implies continuity equations for currents with non-negative densities, for which the Dirac current defines the mean flow. This provides an alternative trajectory construction of free evolution. Finally, we examine the polar representation of the Dirac equation, which also implies a non-negative conserved density but does not map into a stand-alone trajectory theory. It reveals how the quantum potential is tacit in the Dirac equation.

scholarly journals DIRAC–COULOMB SCATTERING WITH PLANE WAVE ENERGY EIGENSPINORS ON DE SITTER EXPANDING UNIVERSE

2008 ◽  
Vol 23 (09) ◽  
pp. 1351-1359 ◽  
Author(s):  
ION I. COTĂESCU ◽  
COSMIN CRUCEAN
Keyword(s):  
Dirac Equation ◽  
Plane Wave ◽  
Wave Energy ◽  
De Sitter Space ◽  
Space Time ◽  
Dirac Field ◽  
Coulomb Scattering ◽  
Final States ◽  
De Sitter ◽  
Scattering Process

The lowest order contribution of the amplitude of Dirac–Coulomb scattering in de Sitter space–time is calculated assuming that the initial and final states of the Dirac field are described by exact solutions of the free Dirac equation on de Sitter space–time with a given energy and helicity. We find that the total energy is conserved in the scattering process.

scholarly journals ON FAIRLIE'S MOYAL FORMULATION OF M(ATRIX)-THEORY

2001 ◽  
Vol 16 (31) ◽  
pp. 4969-4984
Author(s):  
M. HSSAINI ◽  
M. B. SEDRA ◽  
M. BENNAI ◽  
B. MAROUFI
Keyword(s):  
Poisson Bracket ◽  
Explicit Form ◽  
Simple Form ◽  
Equations Of Motion ◽  
Yang Mills ◽  
First Order ◽  
Large N ◽  
Special Cases ◽  
M Theory ◽  
Conserved Currents

Starting from the Moyal formulation of M theory in the large N-limit, we propose to reexamine the associated membrane equations of motion in ten dimensions formulated in terms of Poisson bracket. Among the results obtained, we rewrite the coupled first order Nahm equations into a simple form leading in turn to their systematic relation with SU (∞) Yang–Mills equations of motion. The former are interpreted as the vanishing condition of some conserved currents which we propose. We develop also an algebraic analysis in which an ansatz is considered and find an explicit form for the membrane solution of our problem. Typical solutions known in literature can also emerge as special cases of the proposed solution.

scholarly journals E11, brane dynamics and duality symmetries

2018 ◽  
Vol 33 (13) ◽  
pp. 1850080 ◽  
Author(s):  
Peter West
Keyword(s):  
Direct Product ◽  
Equations Of Motion ◽  
Space Time ◽  
Vector Representation ◽  
First Order ◽  
Duality Relations ◽  
The One

Following arXiv:hep-th/0412336 we use the nonlinear realisation of the semi-direct product of [Formula: see text] and its vector representation to construct brane dynamics. The brane moves through a space-time which arises in the nonlinear realisation from the vector representation and it contains the usual embedding coordinates as well as the worldvolume fields. The resulting equations of motion are first order in derivatives and can be thought of as duality relations. Each brane carries the full [Formula: see text] symmetry and so the Cremmer–Julia duality symmetries. We apply this theory to find the dynamics of the IIA and IIB strings, the M2 and M5 branes, the IIB D3 brane as well as the one and two branes in seven dimensions.

scholarly journals EXPLICIT DERIVATION OF THE FLUCTUATION-DISSIPATION RELATION OF THE VACUUM NOISE IN THE N-DIMENSIONAL DE SITTER SPACE–TIME

2001 ◽  
Vol 16 (16) ◽  
pp. 2841-2857 ◽  
Author(s):  
T. MURATA ◽  
K. TSUNODA ◽  
K. YAMAMOTO
Keyword(s):  
Equations Of Motion ◽  
De Sitter Space ◽  
Space Time ◽  
Dirac Field ◽  
De Sitter ◽  
Fluctuation Dissipation ◽  
Dissipative Coefficient ◽  
Retarded Green Function ◽  
Kms Condition ◽  
Explicit Derivation

Motivated by a recent work by Terashima (Phys. Rev.D60, 084001), we revisit the fluctuation-dissipation (FD) relation between the dissipative coefficient of a detector and the vacuum noise of fields in curved space–time. In an explicit manner we show that the dissipative coefficient obtained from classical equations of motion of the detector and the scalar (or Dirac) field satisfies the FD relation associated with the vacuum noise of the field, which demonstrates that Terashima's prescription works properly in the N-dimensional de Sitter space–time. This practice is useful not only to reconfirm the validity of the use of the retarded Green function to evaluate the dissipative coefficient from the classical equations of motion but also to understand why the derivation works properly, which is discussed in connection with previous investigations on the basis of the Kubo–Martin–Schwinger (KMS) condition. Possible application to black hole space–time is also briefly discussed.

GENERALIZED VOLKOV PROBLEM

1991 ◽  
Vol 06 (27) ◽  
pp. 4831-4841
Author(s):  
GERMAN V. SHISHKIN ◽  
MOHAMMED A. YASIN
Keyword(s):  
Dirac Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Minkowski Space ◽  
Space Time ◽  
Wave Fields ◽  
Cartesian Coordinates ◽  
First Order ◽  
Minkowski Space Time ◽  
External Wave

We consider the Dirac equation in Minkowski space-time in Cartesian coordinates with external wave fields of different tensor structures, namely in the presence of scalar, vector, pseudoscalar, pseudovector, coupled vector and tensor, and coupled vector and pseudovector waves, i.e. we consider the generalized Volkov problem. The solution of the Dirac equation is reduced to that of a system of four equations, two of which are first-order ordinary differential equations and two are algebraic ones. Series of new solutions of the Dirac equation are obtained.

An Interview with the Physicist that Her Head in the Universe and Both Feet on the Earth

2019 ◽  
Author(s):  
Adib Rifqi Setiawan
Keyword(s):  
Standard Model ◽  
Particle Physics ◽  
Space Time ◽  
Additional Dimension ◽  
The Earth ◽  
The Standard Model ◽  
The Universe

Put simply, Lisa Randall’s job is to figure out how the universe works, and what it’s made of. Her contributions to theoretical particle physics include two models of space-time that bear her name. The first Randall–Sundrum model addressed a problem with the Standard Model of the universe, and the second concerned the possibility of a warped additional dimension of space. In this work, we caught up with Randall to talk about why she chose a career in physics, where she finds inspiration, and what advice she’d offer budding physicists. This article has been edited for clarity. My favourite quote in this interview is, “Figure out what you enjoy, what your talents are, and what you’re most curious to learn about.” If you insterest in her work, you can contact her on Twitter @lirarandall.

An Interview with the Physicist that Her Head in the Universe and Both Feet on the Earth

2019 ◽  
Author(s):  
Adib Rifqi Setiawan
Keyword(s):  
Standard Model ◽  
Particle Physics ◽  
Space Time ◽  
Additional Dimension ◽  
The Earth ◽  
The Standard Model ◽  
The Universe

Put simply, Lisa Randall’s job is to figure out how the universe works, and what it’s made of. Her contributions to theoretical particle physics include two models of space-time that bear her name. The first Randall–Sundrum model addressed a problem with the Standard Model of the universe, and the second concerned the possibility of a warped additional dimension of space. In this work, we caught up with Randall to talk about why she chose a career in physics, where she finds inspiration, and what advice she’d offer budding physicists. This article has been edited for clarity. My favourite quote in this interview is, “Figure out what you enjoy, what your talents are, and what you’re most curious to learn about.” If you insterest in her work, you can contact her on Twitter @lirarandall.

Kinetic theory

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Distribution Function ◽  
Kinetic Theory ◽  
Liouville Equation ◽  
Vlasov Equation ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Hamiltonian Form ◽  
First Order ◽  
Number Of Particles

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.

Sign in / Sign up

Export Citation Format

Share Document