Underdeterminacy and Redundance in Maxwell’s Equations. I. The Origin of Gauge Freedom

Underdeterminacy and Redundance in Maxwell’s Equations. Origin of Gauge Freedom - Transversality of Free Electromagnetic Waves - Gaugefree Canonical Treatment without Constraints

Maxwell’s (1864) original equations are redundant in their description of charge conservation. In the nowadays used, ’rationalized’ Maxwell equations, this redundancy is removed through omitting the continuity equation. Alternatively, one can Helmholtz decompose the original set and omit instead the longitudinal part of the flux law. This provides at once a natural description of the transversa...

The conceptual origins of Maxwell’s equations and gauge theory

ar X iv : 1 51 2 . 02 09 4 v 1 [ he p - ph ] 7 D ec 2 01 5 Unification of Force and Substance ∗

Maxwell’s mature presentation of his equations emphasized the unity of electromagnetism and mechanics, subsuming both as “dynamical systems”. That intuition of unity has proved both fruitful, as a source of pregnant concepts, and broadly inspiring. A deep aspect of Maxwell’s work is its use of redundant potentials, and the associated requirement of gauge symmetry. Those concepts have become cen...

سیستمهای الکترونی همبسته قوی در شبکه‌های ناکام

 We give an overview of recent work on charge degrees of freedom of strongly correlated electrons on geometrically frustrated lattices. Special attention is paid to the checkerboard lattice, i.e., the two-dimensional version of a pyrochlore lattice and to the kagomé lattice. For the checkerboard lattice it is shown that at half filling when spin degrees of freedom are neglected and at quarter f...

Trace Anomaly and Quantization of Maxwell’s Theory on Non-commutative Spaces

The canonical and symmetrical energy-momentum tensors and their non-zero traces in Maxwell’s theory on non-commutative spaces have been found. Dirac’s quantization of the theory under consideration has been performed. I have found the extended Hamiltonian and equations of motion in the general gauge covariant form.