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Spin-1/2 Maxwell Fields | | Rollin S. Armour Jr
; | | Date: |
12 May 2003 | | Journal: | Found.Phys. 34 (2004) 815-842 | | Subject: | hep-th | | Abstract: | Requiring covariance of Maxwell’s equations without {it a priori} imposing charge invariance allows for both spin-1 and spin-1/2 transformations of the complete Maxwell field and current. The spin-1/2 case yields new transformation rules, with new invariants, for all traditional Maxwell field and source quantities. The accompanying spin-1/2 representations of the Lorentz group employ the Minkowski metric, and consequently the primary spin-1/2 Maxwell invariants are also spin-1 invariants; for example, $Phi^2 - {f A}^2$, ${f E}^2 - {f B}^2 + 2i {f E} m{cdot} {f B} - ({partial}_{0}{Phi} + {m{
abla cdot}}{f A})^2$. The associated Maxwell Lagrangian density is also the same for both spin-1 and spin-1/2 fields. However, in the spin-1/2 case, standard field and source quantities are complex and both charge and gauge invariance are lost. Requiring the potentials to satisfy the Klein-Gordon equation equates the Maxwell and field-potential equations with two Dirac equations of the Klein-Gordon mass, and thus one complex Klein-Gordon Maxwell field describes either two real vector fields or two Dirac fields, all of the same mass. | | Source: | arXiv, hep-th/0305084 | | Services: | Forum | Review | PDF | Favorites | |
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