New method of integration for the Dirac equation on a curved space‐time

1992 ◽  
Vol 33 (6) ◽  
pp. 2279-2289 ◽  
Author(s):  
V. G. Bagrov ◽  
V. V. Obukhov
Keyword(s):  
Dirac Equation ◽  
Space Time ◽  
New Method ◽  
Curved Space

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

2019 ◽  
Vol 401 ◽  
pp. 21-39 ◽  
Author(s):  
M.D. de Oliveira ◽  
Alexandre G.M. Schmidt
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
Space Time ◽  
Curved Space

New Routines for Algebraic Programming of the Dirac Equation

1997 ◽  
Vol 08 (02) ◽  
pp. 273-286 ◽  
Author(s):  
Ion I. Cotăescu ◽  
Dumitru N. Vulcanov
Keyword(s):  
Dirac Equation ◽  
Main Part ◽  
Space Time ◽  
Curved Space ◽  
Algebraic Programming ◽  
Matrix Algebras ◽  
Dirac Matrix ◽  
New Procedures

We present new procedures in the REDUCE language for algebraic programming of the Dirac equation on curved space-time. The main part of the program is a package of routines defining the Pauli and Dirac matrix algebras. Then the Dirac equation is obtained using the facilities of the EXCALC package. Finally we present some results obtained after running our procedures for the Dirac equation on several curved space-times.

Spinor under space-time gauge and Dirac equation in curved space-time

1985 ◽  
Vol 86 (1) ◽  
pp. 1-10
Author(s):  
R. C. Wang ◽  
J. F. Lu ◽  
S. P. Xiang
Keyword(s):  
Dirac Equation ◽  
Space Time ◽  
Curved Space

scholarly journals DIMENSIONAL REDUCTION

1999 ◽  
Vol 14 (02) ◽  
pp. 99-103 ◽  
Author(s):  
CORINNE A. MANOGUE ◽  
TEVIAN DRAY
Keyword(s):  
Dirac Equation ◽  
Space Time ◽  
Particle Spectrum ◽  
Spin States ◽  
Helicity State ◽  
Curved Space ◽  
Massless Spin ◽  
Generation Structure ◽  
Massive Spin ◽  
Opposite Helicity

Using an octonionic formalism, we introduce a new mechanism for reducing ten space–time dimensions to four without compactification. Applying this mechanism to the free, ten-dimensional, massless (momentum space) Dirac equation results in a particle spectrum consisting of exactly three generations. Each generation contains one massive spin-1/2 particle with two spin states, one massless spin-1/2 particle with only one helicity state, and their antiparticles — precisely one generation of leptons. There is also a single massless spin-1/2 particle/antiparticle pair with the opposite helicity and no generation structure. We conclude with a discussion of some further consequences of this approach, including those which could arise when using the formalism on a curved space–time background, as well as the implications for the nature of space–time itself.

scholarly journals Antimatter Gravity: Second Quantization and Lagrangian Formalism

Physics ◽  
2020 ◽  
Vol 2 (3) ◽  
pp. 397-411
Author(s):  
Ulrich D. Jentschura
Keyword(s):  
Dirac Equation ◽  
Flat Space ◽  
Space Time ◽  
Charge Conjugation ◽  
Lagrangian Formalism ◽  
Curved Space ◽  
The Earth ◽  
Antimatter Gravity ◽  
Quantized Field ◽  
Charge Conjugation Parity

The application of the CPT (charge-conjugation, parity, and time reversal) theorem to an apple falling on Earth leads to the description of an anti-apple falling on anti–Earth (not on Earth). On the microscopic level, the Dirac equation in curved space-time simultaneously describes spin-1/2 particles and their antiparticles coupled to the same curved space-time metric (e.g., the metric describing the gravitational field of the Earth). On the macroscopic level, the electromagnetically and gravitationally coupled Dirac equation therefore describes apples and anti-apples, falling on Earth, simultaneously. A particle-to-antiparticle transformation of the gravitationally coupled Dirac equation therefore yields information on the behavior of “anti-apples on Earth”. However, the problem is exacerbated by the fact that the operation of charge conjugation is much more complicated in curved, as opposed to flat, space-time. Our treatment is based on second-quantized field operators and uses the Lagrangian formalism. As an additional helpful result, prerequisite to our calculations, we establish the general form of the Dirac adjoint in curved space-time. On the basis of a theorem, we refute the existence of tiny, but potentially important, particle-antiparticle symmetry breaking terms in which possible existence has been investigated in the literature. Consequences for antimatter gravity experiments are discussed.

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