Covariant differential calculus on quantum Minkowski space and theq-analogue of Dirac equation

1992 ◽  
Vol 55 (3) ◽  
pp. 417-422 ◽  
Author(s):  
Xing-Chang Song
Keyword(s):  
Dirac Equation ◽  
Minkowski Space ◽  
Differential Calculus

scholarly journals Nature itself in a mirror space–time

2015 ◽  
Vol 93 (10) ◽  
pp. 1005-1008 ◽  
Author(s):  
Rasulkhozha S. Sharafiddinov
Keyword(s):  
Dirac Equation ◽  
Minkowski Space ◽  
Space Time ◽  
Point Of View ◽  
Classical Solutions ◽  
Left Handed ◽  
Minkowski Space Time ◽  
Energy And Momentum ◽  
The Right ◽  
Structure Of Matter

The unity of the structure of matter fields with flavor symmetry laws involves that the left-handed neutrino in the field of emission can be converted into a right-handed one and vice versa. These transitions together with classical solutions of the Dirac equation testify in favor of the unidenticality of masses, energies, and momenta of neutrinos of the different components. If we recognize such a difference in masses, energies, and momenta, accepting its ideas about that the left-handed neutrino and the right-handed antineutrino refer to long-lived leptons, and the right-handed neutrino and the left-handed antineutrino are short-lived fermions, we would follow the mathematical logic of the Dirac equation in the presence of the flavor symmetrical mass, energy, and momentum matrices. From their point of view, nature itself separates Minkowski space into left and right spaces concerning a certain middle dynamical line. Thereby, it characterizes any Dirac particle both by left and by right space–time coordinates. It is not excluded therefore that whatever the main purposes each of earlier experiments about sterile neutrinos, namely, about right-handed short-lived neutrinos may serve as the source of facts confirming the existence of a mirror Minkowski space–time.

scholarly journals DIFFERENTIAL STRUCTURE ON κ-MINKOWSKI SPACE, AND κ-POINCARÉ ALGEBRA

2011 ◽  
Vol 26 (20) ◽  
pp. 3385-3402 ◽  
Author(s):  
STJEPAN MELJANAC ◽  
SAŠA KREŠIĆ-JURIĆ
Keyword(s):  
Power Series ◽  
Hopf Algebra ◽  
Minkowski Space ◽  
Differential Calculus ◽  
Weyl Algebra ◽  
Algebra Structure ◽  
Exterior Derivative ◽  
Lorentz Algebra ◽  
Poincaré Algebra ◽  
Formal Power

We construct realizations of the generators of the κ-Minkowski space and κ-Poincaré algebra as formal power series in the h-adic extension of the Weyl algebra. The Hopf algebra structure of the κ-Poincaré algebra related to different realizations is given. We construct realizations of the exterior derivative and one-forms, and define a differential calculus on κ-Minkowski space which is compatible with the action of the Lorentz algebra. In contrast to the conventional bicovariant calculus, the space of one-forms has the same dimension as the κ-Minkowski space.

scholarly journals THE DIRAC–HESTENES EQUATION FOR SPHERICAL SYMMETRIC POTENTIALS IN THE SPHERICAL AND CARTESIAN GAUGES

2006 ◽  
Vol 21 (19n20) ◽  
pp. 4071-4082 ◽  
Author(s):  
ROLDÃO DA ROCHA ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Dirac Equation ◽  
Minkowski Space ◽  
Spherical Symmetry ◽  
Separation Of Variables ◽  
Differential Forms ◽  
Space Time ◽  
Minkowski Space Time ◽  
Clifford Bundle

In this paper, using the apparatus of the Clifford bundle formalism, we show how straightforwardly solve in Minkowski space–time the Dirac–Hestenes equation — which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation — by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that, contrary to what is expected at a first sight, the solution of the Dirac–Hestenes equation in both gauges has exactly the same mathematical difficulty.

The Lorentz–Dirac equation in Minkowski space

1994 ◽  
Vol 35 (7) ◽  
pp. 3482-3489 ◽  
Author(s):  
Violeta Gaftoi ◽  
José L. López‐Bonilla ◽  
Jesús Morales ◽  
Marco A. Rosales
Keyword(s):  
Dirac Equation ◽  
Minkowski Space

scholarly journals Chiral symmetry breaking as a geometrical process

2014 ◽  
Vol 29 (26) ◽  
pp. 1450145 ◽  
Author(s):  
E. Bittencourt ◽  
S. Faci ◽  
M. Novello
Keyword(s):  
Dirac Equation ◽  
Symmetry Breaking ◽  
Minkowski Space ◽  
Chiral Symmetry ◽  
Spinor Field ◽  
Chiral Symmetry Breaking ◽  
Curved Space ◽  
Left Handed ◽  
Chiral Component ◽  
The Right

This paper is an extension for spinor fields the recently developed Dynamical Bridge formalism which relates a linear dynamics in a curved space to a nonlinear dynamics in Minkowski space. This leads to a new geometrical mechanism to generate a chiral symmetry breaking without mass, providing an alternative explanation for the absence of right-handed neutrinos. We analyze a spinor field obeying the Dirac equation in a curved space which is constructed by its own current. This way, both chiralities of the spinor field satisfy the same dynamics in the curved space. Afterward, the dynamical equation is re-expressed in terms of the flat Minkowski space and then each chiral component behaves differently. The left-handed part of the spinor field satisfies the Dirac equation while the right-handed part is trapped by a Nambu–Jona-Lasinio type potential.

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