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Mass for Plasma Photons from Gauge Symmetry Breaking
, 2009
"... We derive the effective masses for photons in unmagnetized plasma waves using a quantum field theory with two vector fields (gauge fields). In order to properly define the quantum field degrees of freedom we rederive the classical wave equations on lightfront gauge. This is needed because the usua ..."
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We derive the effective masses for photons in unmagnetized plasma waves using a quantum field theory with two vector fields (gauge fields). In order to properly define the quantum field degrees of freedom we rederive the classical wave equations on lightfront gauge. This is needed because the usual scalar potential of electromagnetism is, in quantum field theory, not a physical degree of freedom that renders negative energy eigenstates. We also consider a background local fluid metric that allows for a covariant treatment of the problem. The different masses for the longitudinal (plasmon) and transverse photons are in our framework due to the local fluid metric. We apply the mechanism of mass generation by gauge symmetry breaking recently proposed by the authors by giving a nontrivial vacuumexpectationvalue to the second vector field (gauge field). The Debye length λD is interpreted as an effective compactification length and we compute an explicit solution for the large gauge transformations that correspond to the specific mass eigenvalues derived here. Using an usual quantum field theory canonical quantization we obtain the usual results in the literature. Although none of these ingredients are new to physicist, as far as the authors are aware it is the first time that such constructions are applied to Plasma Physics. Also we give a physical interpretation (and realization) for the second vector field in terms of the plasma background in terms of known physical phenomena. Addendum: It is given a short proof that equation (10) is wrong, therefore equations (1217) are meaningless. The remaining results are correct being generic derivations for nonmagnetized plasmas derived in a covariant QFT framework. PACS: 03.50.De, 03.70.+k, 11.15.q
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
Effective Electric and Magnetic Local Actions for Electromagnetism with two Gauge Fields
"... A simple mechanism of dynamical symmetry breaking of electromagnetism with two gauge fields (U(1) × U(1)) is considered. By considering the action variations with respect to the gauge connections F = dA and G = dC we obtain an electric and a magnetic effective actions (U(1)) that have an extra coup ..."
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A simple mechanism of dynamical symmetry breaking of electromagnetism with two gauge fields (U(1) × U(1)) is considered. By considering the action variations with respect to the gauge connections F = dA and G = dC we obtain an electric and a magnetic effective actions (U(1)) that have an extra coupling to the magnetic and electric currents (respectivelly) that decouple from the classical theory, meaning that it does not contribute to the standard equations of motion obtained by varying A and C, i.e. Maxwell equations. The extra gauge field C(or A) effectivelly is fixed by the physical effective field A(or C) constituting a nontrivial configuration C = C(A) (or A = A(C)) such that the field discontinuities (Dirac string or WuYang nontrivial fiberbundle) are encoded in the extra gauge field C (or A). Our construction is only compactible with local current densities. 1 work supported by SFRH/BPD/17683/2004 and POCTI PFIS57547/2004; also at Centra1 Introduction and Discussion The seminal works of Dirac [1] introduced the famous charge quantization relation eg = n
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
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.
1 Rotating Magnetic Solutions for 2+1D Einstein Maxwell ChernSimons from SpaceTime Duality
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Electronic Journal of Theoretical Physics LandauGinzburg ChernSimons model with Ue(1) × Ug(1) Gauge Symmetry and Internal PseudoPhotons
, 2011
"... Abstract: In this article it is studied, at variational level, a mathematical setup given by the LandauGinzburg ChernSimons model for anyons in 2+1dimensions within the framework of dimensional reduced Ue(1) × Ug(1) extended electromagnetism with both vector gauge fields (photons) and pseudovec ..."
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Abstract: In this article it is studied, at variational level, a mathematical setup given by the LandauGinzburg ChernSimons model for anyons in 2+1dimensions within the framework of dimensional reduced Ue(1) × Ug(1) extended electromagnetism with both vector gauge fields (photons) and pseudovector gauge fields (pseudophotons) such that both magnetic and electric vortexes coexist in the planar system. This model exhibits explicit planar P and T discrete symmetries being the Hall conductivity consistently a tensor and the Dirac quantization on the electric and magnetic coupling constants is equivalent to the quantization of magnetic flux. It is also discussed a thickening to 4dimensions of the model with explicit 4dimensional P violation which allows either for electric and magnetic charge separation, either for the Meissner effect. Although mathematically consistent, the electromagnetic field content for this model does not coincide with the standard Hall effect being present an extra orthogonal electric and longitudinal magnetic fields. c ○ Electronic Journal of Theoretical Physics. All rights reserved.