The Dirac oscillator in a spinning cosmic string spacetime

Abstract

We examine the effects of gravitational fields produced by topological defects on a Dirac field and a Dirac oscillator in a spinning cosmic string spacetime. We obtain the eigenfunctions and the energy levels of the relativistic field in that background and consider the effect of various parameters, such as the frequency of the rotating frame, the oscillator's frequency, the string density and other quantum numbers. DIRAC EQUATION IN THE COSMIC STRING SPACETIMEbetween quarks as well as the confining part of the phenomenological Cornell potential), the Dirac oscillator and related models have been applied in many other contexts as well, such as quantum optics [7][8][9], supersymmetry [5, 10, 11], nuclear reactions [12], the hadronic spectrum (with the two-body Dirac oscillator) [13,14], the Clifford algebra [15,16], noncommutative space [17,18], thermodynamic properties [19], Lie algebras [20], supersymmetric (non-relativistic) quantum mechanics [21], the supersymmetric path-integral formalism [22], chiral phase transitions in presence of a constant magnetic field [8], the relativistic Landau levels in presence of external magnetic field [23], the Aharonov-Bohm effect [24], and condensed matter physics phenomena and graphene [25]. Similar studies for the Duffin-Kemmer-Petiau (DKP) oscillator, which is analogous to the Dirac oscillator for spinless and spin-one particles, are in Refs. [26,27]. Finally, let us mention many studies of the Dirac oscillator with topological defects and cosmic string spacetimes in Refs. [28][29][30][31][32][33][34] and analogous investigations for scalar fields in Refs. [35][36][37][38][39]. Some studies of relativistic oscillators are in Refs. [40][41][42][43][44][45][46][47].In this work, we examine the relativistic quantum dynamics of Dirac oscillator on the curved spacetime of a rotating cosmic string. From the corresponding Dirac equation, we analyze the influence of the topological defect on the equation of motion, the energy spectrum and the wave-functions. An analogous study for the Klein-Gordon equation is in Ref. [49]. In Sec. 2, we write down the covariant Dirac equation without oscillator in a spinning cosmic string spacetime, and find its wave-functions and energy eigenvalues. In Sec. 3, we present the covariant Dirac oscillator in the same spacetime and obtain the wave-functions and energy spectrum. We present concluding remarks in Sec. 4.

Topological and rotating effects on the Dirac field in the spiral dislocation spacetime

“…In this case, since the physical region of the spacetime is defined in the range 0 ≤ r < √ 1−β 2 ω 2 ω , therefore, the geometry of the spacetime has played the role of the hard-wall confining potential. Observe that there is no influence of the topology of the spiral dislocation spacetime on the relativistic energy levels (39). Despite having effects of the topology of the spacetime on the radial coordinate as shown in Eq.…”

“…Furthermore, due to the effects of rotation, there is a contribution to the relativistic energy levels that corresponds to the coupling between the angular velocity ω and the angular momentum l given in the first term of Eq. (39). It corresponds to a Sagnac-type effect [74].…”

Particle Production via Dirac Dipole Moments in the Magnetized and Nonmagnetized Exponentially Expanding Universe

“…Similarly, substituting (17) and its conjugate in (32) and (33), the components of the polarization densities and the magnetization density are written as follows:…”

“…So, he computed the number density of the created particles by means of the Bogolibov transformation by using the out vacuum states constructed from the solutions of the relativistic particles wave equations. After these important works of Parker, the solutions of the relativistic particle wave equations have extensively been studied in various 3+1 dimensional spacetime backgrounds [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Using the WKB approach, the number density and renormalized energy-momentum tensor of the created spin-1/2 particle in the spatially flat (3+1)-dimensional Friedmann-Robertson-Walker (FRW) spacetime have been calculated [20].…”

Aharonov–Bohm-type effect in the background of a distortion of a vertical line into a vertical spiral

“…[10,16], the main effect of the presence of the distortion of a circular curve into a vertical spiral is the shift in the angular momentum quantum number that gives rise to an analogue effect of the Aharonov-Bohm effect for bound states [21,22]. With the interface between general relativity and relativistic quantum mechanics, spacetime with dislocations have drawn attention to relativistic analogue effects of the Aharonov-Bohm effect [23][24][25][26]. In the present work, we deal with another type of screw dislocation that corresponds to the distortion of a vertical line into a vertical spiral [7].…”