The Maxwell and Proca equations in spaces with torsion

1982 ◽  
Vol 25 (1) ◽  
pp. 26-30
Author(s):  
E. V. Smetanin
Keyword(s):  
Proca Equations

scholarly journals A Derivation of Proca Equations on Cantor Sets: A Local Fractional Approach

2014 ◽  
Vol 10 ◽  
pp. 48-56 ◽  
Author(s):  
Victor Christianto ◽  
Biruduganti Rahul
Keyword(s):  
Maxwell Equations ◽  
High Energy Physics ◽  
Stokes Equations ◽  
High Energy ◽  
Cantor Sets ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fractal Media ◽  
Vector Calculus ◽  
Proca Equations

In a recent paper published at Advances in High Energy Physics (AHEP) journal, Yang Zhao et al. derived Maxwell equations on Cantor sets from the local fractional vector calculus. It can be shown that Maxwell equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields. Using the same approach, elsewhere Yang, Baleanu & Tenreiro Machado derived systems of Navier-Stokes equations on Cantor sets. However, so far there is no derivation of Proca equations on Cantor sets. Therefore, in this paper we present for the first time a derivation of Proca equations and GravitoElectroMagnetic (GEM) Proca-type equations on Cantor sets. Considering that Proca equations may be used to explain electromagnetic effects in superconductor, We suggest that Proca equations on Cantor sets can describe electromagnetic of fractal superconductors; besides GEM Proca-type equations on Cantor sets may be used to explain some gravitoelectromagnetic effects of superconductor for fractal media. It is hoped that this paper may stimulate further investigations and experiments in particular for fractal superconductor. It may be expected to have some impact to fractal cosmology modeling too.

Spin-1 Fields: The Maxwell and Proca Equations

1996 ◽  
pp. 141-170 ◽  
Author(s):  
Walter Greiner ◽  
Joachim Reinhardt
Keyword(s):  
Proca Equations

scholarly journals CAUSAL PROPAGATION OF SPIN-CASCADES

2006 ◽  
Vol 21 (39) ◽  
pp. 2961-2969 ◽  
Author(s):  
L. M. RICO ◽  
M. KIRCHBACH
Keyword(s):  
Differential Equation ◽  
Electromagnetic Field ◽  
Dirac Equation ◽  
Direct Product ◽  
Electromagnetic Environment ◽  
Wave Fronts ◽  
Causal Propagation ◽  
Proca Equations

We gauge the direct product of the Proca with the Dirac equation that describes the coupling to the electromagnetic field of the spin-cascade (1/2, 3/2) residing in the four-vector spinor ψμ and analyze propagation of its wave fronts in terms of the Courant–Hilbert criteria. We show that the differential equation under consideration is unconditionally hyperbolic and the propagation of its wave fronts unconditionally causal. In this way we prove that the irreducible spin-cascade embedded within ψμ is free from the Velo–Zwanziger problem that plagues the Rarita–Schwinger description of spin-3/2. The proof extends also to the direct product of two Proca equations and implies causal propagation of the spin-cascade (0, 1, 2) within an electromagnetic environment.

scholarly journals London-Proca-Hirsch Equations for Electrodynamics of Superconductors on Cantor Sets

2015 ◽  
Vol 4 ◽  
pp. 1-7 ◽  
Author(s):  
Victor Christianto
Keyword(s):  
Magnetic Fields ◽  
Maxwell Equations ◽  
High Energy Physics ◽  
High Energy ◽  
Cantor Sets ◽  
Vector Calculus ◽  
Electric And Magnetic Fields ◽  
Proca Equations ◽  
First Time ◽  
Energy Physics

In a recent paper published at Advances in High Energy Physics (AHEP) journal, Yang Zhao et al. derived Maxwell equations on Cantor sets from the local fractional vector calculus. It can be shown that Maxwell equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields. However, so far there is no derivation of equations for electrodynamics of superconductor on Cantor sets. Therefore, in this paper I present for the first time a derivation of London-Proca-Hirsch equations on Cantor sets. The name of London-Proca-Hirsch is proposed because the equations were based on modifying Proca and London-Hirsch’s theory of electrodynamics of superconductor. Considering that Proca equations may be used to explain electromagnetic effects in superconductor, I suggest that the proposed London-Proca-Hirsch equations on Cantor sets can describe electromagnetic of fractal superconductors. It is hoped that this paper may stimulate further investigations and experiments in particular for fractal superconductor. It may be expected to have some impact to fractal cosmology modeling too.

The wave equation for spin 1 in Hamiltonian form

1955 ◽  
Vol 229 (1176) ◽  
pp. 39-43 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Differential Equations ◽  
Matrix Equation ◽  
Hamiltonian Form ◽  
Initial Value ◽  
Potential Vector ◽  
Spin Number ◽  
Proca Equations ◽  
Derivatives Of

If from the differential equations that hold in a Proca field you select the ten that express the time derivatives of the ten components involved, i. e. of the ‘electromagnetic’ field and its potential vector, you obtain right away for the ten-componental entity an equation that may be said to be at the same time of the Schrödinger, the Dirac and the Kemmer type. The four 10 x 10-matrices that occur as coefficients are Hermitian and satisfy Kemmer’s commutation rules. The fifth is easily constructed. Those of the Proca equations that were not included are merely injunctions on the initial value. They are expressed by one matrix equation, that makes it evident that, once posited, they are preserved. The three spin matrices are indicated. The spin number is 1 or 0, but the aforesaid injunctions exclude 0.

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