scholarly journals Gauge-symmetrization method for energy-momentum tensors in high-order electromagnetic field theories

2021 ◽  
Vol 104 (2) ◽  
Author(s):  
Peifeng Fan ◽  
Jianyuan Xiao ◽  
Hong Qin
Keyword(s):  
Electromagnetic Field ◽  
High Order ◽  
Field Theories ◽  
Symmetrization Method

VII.—Quantum Mechanics of Fields. I. Pure Fields

1944 ◽  
Vol 62 (1) ◽  
pp. 40-57
Author(s):  
Max Born ◽  
H. W. Peng
Keyword(s):  
Quantum Mechanics ◽  
Fourier Series ◽  
High Order ◽  
Field Theories ◽  
Matrix Elements ◽  
Matrix Mechanics ◽  
Quantum Transitions ◽  
Combination Principle ◽  
Classical Quantum ◽  
Two Indices

The difficulties met in the usual treatment of quantised field theories seem to us somewhat similar to those which occurred in Bohr's semi-classical quantum mechanics of particles. In this theory the orbits were described by Fourier series in the time; there was no exact correspondence between the periodic terms of this series and quantum transitions, but only an approximate one for terms of high order. Matrix mechanics considers not the Fourier series, but the single terms which are generalised into matrix elements having not one but two indices. This generalisation is founded on Ritz's combination principle.

Propagation of Nonlinear Electromagnetic Field Theories

1974 ◽  
Vol 52 (10) ◽  
pp. 917-918 ◽  
Author(s):  
A. Shamaly ◽  
A. Z. Capri
Keyword(s):  
Electromagnetic Field ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
The Self ◽  
Field Theories ◽  
Proca Equation ◽  
Interaction Terms ◽  
Causal Propagation ◽  
Interaction Term

It is shown that the self-interaction term λ(AμAμ)2 added to the free Lagrangian for Maxwell's equations leads to acausal propagation. Furthermore, it is found that apart from the term λAμAμ which leads back to the Proca equation, all self-interaction terms leading to causal propagation must be nonpolynomial.

MULTISYMPLECTIC GEOMETRY AND k-COSYMPLECTIC STRUCTURE FOR THE FIELD THEORIES AND THE RELATIVISTIC MECHANICS

2013 ◽  
Vol 10 (04) ◽  
pp. 1350001
Author(s):  
H. LOUMI-FERGANE ◽  
A. BELAIDI
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Physical System ◽  
Direct Relationship ◽  
Field Theories ◽  
Cosymplectic Structure ◽  
Relativistic Charged Particle

The aim of this work is twofold: First, we extend the multisymplectic geometry already done for field theories to the relativistic mechanics by introducing an appropriate configuration bundle. In particular, we developed the model to obtain the Hamilton–De Donder–Weyl equations to the movement of a relativistic charged particle immerged in an electromagnetic field. Second, we have found a direct relationship between the multisymplectic geometry and the k-cosymplectic structure of a physical system.

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