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Generalized Proca Equations and Vacuum Current from Breaking of U(1) × U(1) Gauge Symmetry
, 2006
"... We consider a U(1)×U(1) ElectricMagnetic theory with minimal coupling between both gauge fields A and C. We consider two possible mechanism of symmetry breaking that generate generalized Proca masses for the gauge field A. By considering a vacuumexpectationvalue for the C field in the full U(1) ..."
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We consider a U(1)×U(1) ElectricMagnetic theory with minimal coupling between both gauge fields A and C. We consider two possible mechanism of symmetry breaking that generate generalized Proca masses for the gauge field A. By considering a vacuumexpectationvalue for the C field in the full U(1) × U(1) theory we obtain both a mass term and a vacuum current. By considering the broken electric theory U(1) we obtain a remaining free field on the solution for C, upon a vev to this remaining field we obtain only a mass term. The interpretation for the vev is given in terms of constant currents and holonomy cycles of the underlying space manifold. The number of degrees of freedom before and after gauge symmetry breaking are discussed, similarly to Schwinger and Anderson we consider the gauge freedom to constitute degrees of freedom that upon gauge symmetry breaking by non trivial vacuum currents hold three massive photons. PACS: 40., 03.50.De, 11.15.q, 12.60.Nz
Explicit Actions for Electromagnetism with Two Gauge Fields with Only one Electric and one Magnetic Physical Fields
, 2006
"... We extend the work of Mello et al. based in Cabbibo and Ferrari concerning the description of electromagnetism with two gauge fields from a variational principle, i.e. an action. We provide a systematic independent derivation of the allowed actions which have only one magnetic and one electric physi ..."
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We extend the work of Mello et al. based in Cabbibo and Ferrari concerning the description of electromagnetism with two gauge fields from a variational principle, i.e. an action. We provide a systematic independent derivation of the allowed actions which have only one magnetic and one electric physical fields and are invariant under the discrete symmetries P and T. We conclude that neither the Lagrangian, nor the Hamiltonian, are invariant under the electromagnetic duality rotations. This agrees with the weakstrong coupling mixing characteristic of the duality due to the Dirac quantization condition providing a natural way to differentiate dual theories related by the duality rotations (the energy is not invariant). Also the standard electromagnetic duality rotations considered in this work violate both P and T by inducing Hopf terms (theta terms) for each sector and a mixed Maxwell term. The canonical structure of the theory is briefly addressed and the magnetic gauge sector is interpreted as a ghost sector.