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Ue(1) × Ug(1) actions in 2+1dimensions: Full vectorial electric and magnetic
"... It is considered a dimensional reduction of Ue(1) × Ug(1) 3 + 1dimensional electromagnetism to 2 + 1dimensions. It is shown that all the six electric and magnetic field vectorial components are present in the reduced theory and that they can be described in terms of vector gauge fields. The quant ..."
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It is considered a dimensional reduction of Ue(1) × Ug(1) 3 + 1dimensional electromagnetism to 2 + 1dimensions. It is shown that all the six electric and magnetic field vectorial components are present in the reduced theory and that they can be described in terms of vector gauge fields. The quantum structure is maintained in the absence of boundary effects. In the case where boundary effects are present a cross ChernSimons term between both gauge fields is present such that the quantum structure of the reduced theory changes. The dimensional reduced action is invariant under parity (P) and timeinversion (T). PACS: 03.50.De, 12.20.m, 41.20.q, 13.40.f Keywords: Electromagnetism, Two Dimensions, pseudophoton
A PseudoPhoton in NonTrivial Background
"... We show that in the presence of external fields for which either ˙ B ext = 0 or ∇ × E ext = 0 it is not possible to derive the classical Maxwell equations from an action with only one gauge field. We suggest that one possible solution is to consider a second physical pseudovector gauge field C. ..."
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We show that in the presence of external fields for which either ˙ B ext = 0 or ∇ × E ext = 0 it is not possible to derive the classical Maxwell equations from an action with only one gauge field. We suggest that one possible solution is to consider a second physical pseudovector gauge field C. The action for this theory is originally motivated by the inclusion of magnetic monopoles. These particles play no role in this work and our argument is only based in, that the violation of the Bianchi identities, cannot be accounted at the action level with only the standard gauge field. We give a particular example for a periodic rotating external magnetic field. Our construction holds that at classical level both the vector and pseudovector gauge fields A and C are regular. We compare pseudophoton with paraphoton (graviphoton) theories concluding that, besides the mechanisms of gauge symmetry already studied by the authors, the Bianchi identities violation are a crucial difference between both theories. We also show that the effects in PVLAS experiment due to the inclusion of pseudophotons cannot be distinguished from the usual classical induced electric and magnetic fields due to the standard Maxwell equations. Therefore, although this kind of optical experiments cannot test the existence of pseudophotons, they do not exclude its existence. PACS: 03.50.De, 12.20.m,11.15.q
September 2006 A PseudoPhoton in NonTrivial Background Fields
, 2006
"... We show that in the presence of external fields for which either ˙ B ext = 0 or ∇ × E ext = 0 it is not possible to derive the classical Maxwell equations from an action with only one gauge field. We suggest that one possible solution is to consider a second physical pseudovector gauge field C. ..."
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We show that in the presence of external fields for which either ˙ B ext = 0 or ∇ × E ext = 0 it is not possible to derive the classical Maxwell equations from an action with only one gauge field. We suggest that one possible solution is to consider a second physical pseudovector gauge field C. The action for this theory is originally motivated by the inclusion of magnetic monopoles. These particles play no role in this work and our argument is only based in, that the violation of the Bianchi identities, cannot be accounted at the action level with only the standard gauge field. We give a particular example for a periodic rotating external magnetic field. Our construction holds that at classical level both the vector and pseudovector gauge fields A and C are regular. We compare pseudophoton with paraphoton (graviphoton) theories concluding that, besides the mechanisms of gauge symmetry already studied by the authors, the Bianchi identities violation are a crucial difference between both theories. We also show that the effects in PVLAS experiment due to the inclusion of pseudophotons cannot be distinguished from the usual classical induced electric and magnetic fields due to the standard Maxwell equations. Therefore, although this kind of optical experiments cannot test the existence of pseudophotons, they do not exclude its existence. PACS:?03.50.De,?03.70.+k,?11.15.q
July 2007, hepth/0601171 Generalized Proca Equations and Vacuum Current from Breaking of Ue(1) × Ug(1) Gauge Symmetry
, 2007
"... We study a Ue(1) × Ug(1) ElectricMagnetic theory with minimal coupling between both gauge fields A (photon) and C (pseudophoton). We consider two possible mechanism of symmetry breaking that generate generalized Proca masses for the gauge field A. By considering a vacuumexpectationvalue (vev) fo ..."
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We study a Ue(1) × Ug(1) ElectricMagnetic theory with minimal coupling between both gauge fields A (photon) and C (pseudophoton). We consider two possible mechanism of symmetry breaking that generate generalized Proca masses for the gauge field A. By considering a vacuumexpectationvalue (vev) for the C field in the full Ue(1) ×Ug(1) theory we obtain both a mass term and a vacuum current. By considering the broken electric theory Ue(1) we obtain as a solution for the C field a remaining free field c such that, upon be given a vev, renders a mass term for the photon field A. The interpretation for the vev is given in terms of constant currents and homology cycles of the underlying space manifold. The number of degrees of freedom, before and after gauge symmetry breaking, are discussed. As a particular case of this construction the authors have already shown that this mechanism reproduces the SchwingerAnderson mechanism such that upon gauge symmetry breaking due to non trivial vacuum generates mass for the standard photon (plasmon). We show that, although generally, Lorentz symmetry may be broken in the pseudophoton sector due to its vev, the effective theory for the standard photon still preserves Lorentz invariance.
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.