scholarly journals Finsler geometry as a model for relativistic gravity

2018 ◽  
Vol 15 (supp01) ◽  
pp. 1850166 ◽  
Author(s):  
Claus Lämmerzahl ◽  
Volker Perlick
Keyword(s):  
General Relativity ◽  
Dirac Equation ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Gordon Equation ◽  
Finsler Geometry ◽  
Experimental Tests ◽  
The Status ◽  
Klein Gordon ◽  
Klein Gordon Equation

We give an overview on the status and on the perspectives of Finsler gravity, beginning with a discussion of various motivations for considering a Finslerian modification of General Relativity. The subjects covered include Finslerian versions of Maxwell’s equations, of the Klein–Gordon equation and of the Dirac equation, and several experimental tests of Finsler gravity.

Relativistic Wave Equations

2019 ◽  
pp. 25-42
Author(s):  
Michael E. Peskin
Keyword(s):  
Dirac Equation ◽  
Maxwell’S Equations ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Gordon Equation ◽  
Relativistic Wave Equations ◽  
Quantum Mechanical ◽  
Relativistic Wave ◽  
Klein Gordon ◽  
Klein Gordon Equation

This chapter presents the wave equations that govern the behavior of quantum mechanical particles with spin 0, 1/2, and 1 in relativistic theories. These equations are the Klein-Gordon equation, the Dirac equation, and Maxwell’s equations.

scholarly journals The Helmholtzian Operator and Maxwell-Cassano Equations of an Electromagnetic-nuclear Field

2019 ◽  
pp. 8-12
Author(s):  
Claude Michael Cassano
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Gordon Equation ◽  
Nuclear Field ◽  
Klein Gordon ◽  
Klein Gordon Equation

This article demonstrates that when acting on a four-vector doublet, the Helmholtzian may be factored into two 4×4/8×8 differential matrices, resulting in a four-vector doublet Klein-Gordon equation with source. This factorization enables yielding of a mass-generalized set of Maxwell’s equations.

scholarly journals Dirac Equation in Cosmological Inertial Frame

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Wave Equation ◽  
Dirac Equation ◽  
Inertial Frame ◽  
Gordon Equation ◽  
Probability Amplitude ◽  
Function Type ◽  
Klein Gordon ◽  
Klein Gordon Equation

Dirac equation is a one order-wave equation. Wave function uses as a probability amplitude in quantum mechanics. We make Dirac Equation from wave function, Type A in cosmological inertial frame.The Dirac equation satisfy Klein-Gordon equation in cosmological inertial frame.

scholarly journals Implementation of a Quantized Line Element in Klein-Gordon and Dirac Fields

2015 ◽  
Vol 48 ◽  
pp. 68-86
Author(s):  
D.L. Bulathsinghala ◽  
K.A.I.L. Wijewardena Gamalath
Keyword(s):  
Dirac Equation ◽  
Gordon Equation ◽  
Line Element ◽  
Coarse Grained ◽  
Relativistic Energy ◽  
Time Intervals ◽  
Quantization Rule ◽  
Time Space ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this paper an ansatz that the anti-commutation rules hold only as integrated average over time intervals and not at every instant giving rise to a time-discrete form of Klein-Gordon equation is examined. This coarse-grained validation of the anti-commutation rules enables us to show that the relativistic energy-momentum relation holds only over discrete time intervals, fitting well with the time-energy uncertainty relation. When this time-discrete scheme is applied to four vector notations in relativity, the line-element can be quantized and thereby how the physical attributes associated with time, space and matter can be quantized is sketched. This potentially enables us to discuss the Zeno’s arrow paradox within the classical limit. As the solutions of the Dirac equation can be used to construct solutions to the Klein-Gordon equation, this temporal quantization rule is applied to the Dirac equation and the solutions associated with the Dirac equation under such conditions are interpreted. Finally, the general relativistic effects are introduced to a line-element associated with a particle in relativistic motion and a time quantized line-element associated with gravity is obtained.

scholarly journals Derivation of a Relativistic Wave Equation more Profound than Dirac’s Relativistic Wave Equation

2018 ◽  
Vol 10 (6) ◽  
pp. 102
Author(s):  
Koshun Suto
Keyword(s):  
Wave Equation ◽  
Hydrogen Atom ◽  
Dirac Equation ◽  
Potential Energy ◽  
Gordon Equation ◽  
Relativistic Wave Equation ◽  
Relativistic Wave ◽  
Departure Point ◽  
Klein Gordon ◽  
Klein Gordon Equation

The author has previously derived an energy-momentum relationship applicable in a hydrogen atom. Since this relationship is taken as a departure point, there is a similarity with the Dirac’s relativistic wave equation, but an equation more profound than the Dirac equation is derived. When determining the coefficients  and β of the Dirac equation, Dirac assumed that the equation satisfies the Klein-Gordon equation. The Klein-Gordon equation is an equation which quantizes Einstein's energy-momentum relationship. This paper derives an equation similar to the Klein-Gordon equation by quantizing the relationship between energy and momentum of the electron in a hydrogen atom. By looking to the Dirac equation, it is predicted that there is a relativistic wave equation which satisfies that equation, and its coefficients are determined. With the Dirac equation it is necessary to insert a term for potential energy into the equation when describing the state of the electron in a hydrogen atom. However, in this paper, a potential energy term is not introduced into the relativistic wave equation. Instead, potential energy is incorporated into the equation by changing the coefficient  of the Dirac equation.

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