scholarly journals Dirac equation in 2-dimensional curved spacetime, particle creation, and coupled waveguide arrays

2016 ◽  
Vol 374 ◽  
pp. 162-178 ◽  
Author(s):  
Christian Koke ◽  
Changsuk Noh ◽  
Dimitris G. Angelakis
Keyword(s):  
Dirac Equation ◽  
Particle Creation ◽  
Curved Spacetime ◽  
Waveguide Arrays

scholarly journals INFLUENCE OF GRAVITY ON NONCOMMUTATIVE DIRAC EQUATION

2005 ◽  
Vol 20 (26) ◽  
pp. 1997-2005 ◽  
Author(s):  
SOFIANE BOUROUAINE ◽  
ACHOUR BENSLAMA
Keyword(s):  
Dirac Equation ◽  
Electric Field ◽  
Covariant Derivative ◽  
Strong Electric Field ◽  
Curved Spacetime ◽  
Tetrad Formalism ◽  
Dirac Particles ◽  
Modified Dirac Equation ◽  
New Form

In this paper, we investigate the influence of gravity and noncommutativity on Dirac particles. By adopting the tetrad formalism, we show that the modified Dirac equation keeps the same form. The only modification is in the expression of the covariant derivative. The new form of this derivative is the product of its counterpart given in curved spacetime with an operator which depends on the noncommutative θ-parameter. As an application, we have computed the density number of the created particles in the presence of constant strong electric field in an anisotropic Bianchi universe.

scholarly journals Quantum walking in curved spacetime: (3+1) dimensions, and beyond

2017 ◽  
Vol 17 (9&10) ◽  
pp. 810-824 ◽  
Author(s):  
Pablo Arrighi ◽  
Stefno Facchini
Keyword(s):  
Dirac Equation ◽  
Continuum Limit ◽  
Space Dimension ◽  
Quantum Walk ◽  
Internal Degree ◽  
Curved Spacetime ◽  
Arbitrary Space ◽  
Time Quantum ◽  
General Continuum ◽  
Internal Degree Of Freedom

A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). Recently it was discovered that prior grouping and encoding allows for more general continuum limit equations (e.g. the Dirac equation in (1+ 1) curved spacetime). In this paper, we extend these results to arbitrary space dimension and internal degree of freedom. We recover an entire class of PDEs encompassing the massive Dirac equation in (3 + 1) curved spacetime. This means that the metric field can be represented by a field of local unitaries over a lattice.

scholarly journals QUANTUM EFFECTS ASSOCIATED WITH AN ELECTRICALLY NEUTRAL MASSLESS PARTICLE IN A BERTOTTI-ROBINSON UNIVERSE

1994 ◽  
Vol 09 (34) ◽  
pp. 3185-3191
Author(s):  
VÍCTOR M. VILLALBA
Keyword(s):  
Exact Solution ◽  
Dirac Equation ◽  
Separation Of Variables ◽  
Particle Creation ◽  
Quantum Effects ◽  
Massless Particle

In this article we obtain, by separation of variables, an exact solution to the Dirac equation with anomalous momentum for an electrically neutral massless particle in a Bertotti-Robinson universe. We discuss the phenomenon of particle creation in this model.

scholarly journals FOUR-VECTOR VERSUS FOUR-SCALAR REPRESENTATION OF THE DIRAC WAVE FUNCTION

2012 ◽  
Vol 09 (04) ◽  
pp. 1250026 ◽  
Author(s):  
MAYEUL ARMINJON ◽  
FRANK REIFLER
Keyword(s):  
Wave Function ◽  
Dirac Equation ◽  
Minkowski Spacetime ◽  
Bundle Theory ◽  
Curved Spacetime ◽  
Unified Framework ◽  
Tetrad Field ◽  
Dirac Equations ◽  
Dirac Wave Function ◽  
General Coordinate Transformation

In a Minkowski spacetime, one may transform the Dirac wave function under the spin group, as one transforms coordinates under the Poincaré group. This is not an option in a curved spacetime. Therefore, in the equation proposed independently by Fock and Weyl, the four complex components of the Dirac wave function transform as scalars under a general coordinate transformation. Recent work has shown that a covariant complex four-vector representation is also possible. Using notions of vector bundle theory, we describe these two representations in a unified framework. We prove theorems that relate together the different representations and the different choices of connections within each representation. As a result, either of the two representations can account for a variety of inequivalent, linear, covariant Dirac equations in a curved spacetime that reduce to the original Dirac equation in a Minkowski spacetime. In particular, we show that the standard Dirac equation in a curved spacetime, with any choice of the tetrad field, is equivalent to a particular realization of the covariant Dirac equation for a complex four-vector wave function.

Zitterbewegung in cosmic string spacetime

2019 ◽  
Vol 34 (18) ◽  
pp. 1950135
Author(s):  
Natalia N. Konobeeva ◽  
Mikhail B. Belonenko
Keyword(s):  
Dirac Equation ◽  
Electric Current ◽  
Cosmic String ◽  
Curved Spacetime ◽  
Magnetic Flow ◽  
Motion Effect ◽  
Analytic Expression

In this paper, we investigate the trembling motion effect in the cosmic spacetime. The cosmic string was considered to be charged and carrying a magnetic flow. Zitterbewegung (ZB) is calculated based on the Dirac equation in the curved spacetime. An analytic expression for the electric current is obtained and analyzed.

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