Exact solutions of Dirac equation on a static curved space–time

Oliveira, M. D. de; Schmidt, Alexandre G. M.

doi:10.1016/j.aop.2018.11.025

Cited by 26 publications

(17 citation statements)

References 22 publications

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“…However, comparing Equations (16) and 17, we see that the tachyonic mass operator, analogous to the Dirac one, is 0 5 . Using this matrix as the operator and changing the sign in the right hand-side of Equation (19), the similarity transformation returns the tachyonic equation, since ( 0 5 ) −1 ( 0 5 ) = − and ( 0 5 ) −1 5 ( 0 5 ) = 5 .…”

Section: Tachyonic Dirac Equation From the Tanaka Lagrangianmentioning

confidence: 94%

“…For the ordinary Dirac equation, this symmetry is assured by the operator = 1 3 [32]. Since the first terms of Equations (16) and (17) are identical, symmetry is expected to be verified also by the tachyonic equation through the same operator . By performing the similarity transformation on the conjugate time-reversed tachyonic equation, one gets:…”

Section: Tachyonic Dirac Equation From the Tanaka Lagrangianmentioning

confidence: 99%

“…In its non-linear version [5][6][7], the Dirac equation is used in condensed matter physics [8][9][10] and quantum optics [11][12][13][14]. The Dirac equation has also been generalised for curved space-time in order to study the behaviour of fermions in gravitational fields [15][16][17]. In the framework of mathematical physics, the Dirac equation has been studied for different potentials (e.g., Coulomb, Yukawa, and Poschl-Teller) in order to test or find new methods of solving the associated Cauchy problem [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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Tachyonic Dirac Equation Revisited

Nanni¹

2020

Acta Phys. Pol. B

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In this paper, we revisit the two theoretical approaches for the formulation of the tachyonic Dirac equation. The first approach works within the theory of restricted relativity, starting from a Lorentz invariant Lagrangian consistent with a spacelike four-momentum. The second approach uses the theory of relativity extended to superluminal motions and works directly on the ordinary Dirac equation through superluminal Lorentz transformations. The equations resulting from the two approaches show mostly different, if not opposite, properties. In particular, the first equation violates the invariance under the action of the parity and charge conjugation operations. Although it is a good mathematical tool to describe the dynamics of a space-like particle, it also shows that the mean particle velocity is subluminal. In contrast, the second equation is invariant under the action of parity and charge conjugation symmetries, but the particle it describes is consistent with the classical dynamics of a tachyon. This study shows that it is not possible with the currently available theories to formulate a covariant equation that coherently describes the neutrino in the framework of the physics of tachyons, and depending on the experiment, one equation rather than the other should be used.

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Section: Tachyonic Dirac Equation From the Tanaka Lagrangianmentioning

confidence: 94%

Section: Tachyonic Dirac Equation From the Tanaka Lagrangianmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tachyonic Dirac Equation Revisited

Nanni¹

2020

Acta Phys. Pol. B

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“…The behavior of particles obeying the covariant Dirac equation in the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime has given rise to many investigations ( [2,18,8,12,21,22,31]). On the other hand, the solution of the semilinear Dirac equation describing self-interacting Dirac fields in general FLRW spacetime according to our best knowledge, haven't been discussed in literature.…”

Section: Introductionmentioning

confidence: 99%

The self-interacting Dirac fields in FLRW spacetime

Galstian¹,

Yagdjian²

2021

Preprint

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We prove the existence of global in time solution with the small initial data for the semilinear equation of the spin-1 2 particles in the Friedmann-Lemaître-Robertson-Walker spacetime. Moreover, we also prove that if the initial function satisfies the Lochak-Majorana condition, then the global solution exists for arbitrary large initial value. The solution scatters to free solution for large time. The mass term is assumed to be complex-valued. The conditions on the imaginary part of mass are discussed by proving nonexistence of the global solutions if certain relation between scale function and the mass are fulfilled.

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“…One of the most important problems in mathematical physics is to study the properties of the Dirac spinor field equations by assigning a specific potential and finding its exact solutions, according to various methods [1][2][3][4][5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

A Square-Integrable Spinor Solution to Non-Interacting Dirac Equations

Fabbri,

Cianci,

Vignolo

2021

Preprint

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Exact solutions of Dirac equation on a static curved space–time

Cited by 26 publications

References 22 publications

Tachyonic Dirac Equation Revisited

Tachyonic Dirac Equation Revisited

The self-interacting Dirac fields in FLRW spacetime

A Square-Integrable Spinor Solution to Non-Interacting Dirac Equations

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