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2 + 1-dimensional system of thickness δ ⊥ , with boundaries Σ1 and Σ2, embedded in a 3 + 1-dimensional system.
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It is considered a dimensional reduction of Ue(1)×Ug(1) (3+1)-dimensional electromagnetism with a gauge field (photon) and a pseudo-vector gauge field (pseudo-photon) to (2+1) dimensions. In the absence of boundary effects, the quantum structure is maintained, while when boundary effects are considered, as have been previously studied, a cross Cher...
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... this section we address a possible dimensional reduction scheme for action (3). We consider a planar system of a certain thickness δ ⊥ with two boundaries Σ1 and Σ2 as represented in figure 1. Let us take in consideration the regularity of the each of the gauge fields, such that the constants rA = 0, 1 and ...
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Citations
... We note that these quantities are evaluated in a 2-dimensional spatial hyper-plane, hence M has units of mass over length and S z of mass such that when embedded into a 3-dimensional spatial manifold it is further required to integrated over the thickness of the 2-dimensional embedding along the orthogonal direction (z) to retrieve the standard 3-dimensional quantities with units of mass and angular momentum, respectively. It is relevant to stress that, as discussed in [50], from a 3 + 1-dimensional perspective these computations are valid and consistent only for systems with constant fields along the direction orthogonal to the planar system as it is the case of systems with cylindrical symmetry (for further discussions on embedded 2 + 1-dimensional systems see for example [14] and [63]). ...
... We resume the main configuration types discussed in table 2. As a final remark we note that the magnetic string-like configuration corresponding to solution III for the range of the parameter p ∈] − ∞, −1[ describing a ghost gauge sector suggests that, for extended gauge theories containing a ghost gauge sector coupled to magnetic charge [60,61], similar magnetically charged solutions may be computed in 3 + 1-dimensions [62] and 2 + 1-dimensions [63]. ...
In this article are computed magnetic solutions of Einstein Maxwell Chern-Simons theory coupled to a dilaton-like scalar field. These solutions are computed by applying a space-time duality suggested by the author to known electric solutions of the same theory. As a redundancy check for the space-time duality it is explicitly shown that the magnetic configurations obtained are, as expected, solutions of the equations of motion. The magnetic configurations have metric determinant sqrt(−g)∼r^p for the range of the parameter p∈]−∞,+∞[/{−1} and are interpreted either as magnetic string-like configurations, configurations driven by an externally applied magnetic field or cosmological-like solutions with background magnetic fields.
... Finally some works [68] have fixed the value of our constant ξ to 1 2 for the action of TMGT of the BF type (1.23) in 2+1 dimensions, modulo surface terms. One of the convincing arguments is that upon setting ξ = 1 2 , this action may be obtained through the dimensional reduction of U e (1) × U g (1) Maxwell theory in 3+1 dimensions with a gauge field and a pseudo-gauge field 2 . ...
... In stellar plasma (e.g. the Sun) has also been put forward within magnetohydrodynamics [13] that singular magnetic field lines may explain the heating of the stellar corona due to magnetic reconnection mechanisms [14]. These results are also consistent with the field content obtained in planar system for which planar magnetic fields and orthogonal electric fields exist in pseudo-photon theories (as opposed to the pure Maxwell theory) [15]. ...
Extended $U_e(1)\times U_g(1)$ electromagnetism containing both a photon and a pseudo-photon is introduced at variational level and is justified by the violation of the Bianchi identities in conceptual systems, either in the presence of magnetic monopoles or non-regular external fields, not being accounted by the standard Maxwell action. It is shown that in the perturbative quantum field theory regimes there are observable consequences both for the magnetic momenta and second order vacuum polarization radiative corrections in the presence of non-regular strong electromagnetic fields (e.g. rotating magnetic fields).
... As for the relative sign between the Einstein term and the Maxwell term imposes whether the gauge field˜Afield˜ field˜A is interpreted as a standard gauge field (opposite sign) or a ghost field (same sign). Specifically for standard gauge fields the quantum states have positive energy eigenvalues while for ghost fields have negative energy eigenstates (see [19] and references therein for a discussion of relative sign choices and derivation of Hamiltonian quantization in 2 + 1-and 3 + 1-dimensional embeddings). ...
... In 2+1-dimensions the magnetic field is a scalar (corresponding tõ B (3D) = ˜ F rϕ ) and planar system can be interpreted either as a projected 3 + 1-dimensional system or as embedded systems [19]. So far the dualities (2.2), (3.1) and (4.1) apply to both these frameworks and implicitly the angular component of the electric field is necessarily null, ˜ E ϕ (3D) = ˜ F 0ϕ = 0. ...
In this paper it is studied a space-time duality web that maps electric into magnetic (and magnetic into electric) charged classical stationary rotating solutions for 2+1-dimensional Abelian Einstein Maxwell Chern-Simons theories. A first duality map originally suggested by Kogan for static charged solutions is extended to stationary rotating space-times and are suggested two new space-time dualities maps. The three dualities complete a close duality web. It is also shown that in 3+1-dimensions these dualities are only possible for systems which exhibit non-projected cylindrical symmetry and are not related to the standard electromagnetic duality of Maxwell equations which acts on the physical fields and charges. Generalization to N-form theories in higher dimensional space-times is briefly discussed.
We have investigated the wave dynamics of a vector field perturbation
coupling to Einstein tensor in the four-dimensional Reissner-Nordstr\"{o}m
black hole spacetime. Our results show that besides the dependence on the
coupling between the vector field and Einstein tensor, the wave dynamic
equation of the vector field perturbation strongly depends on the parity of the
perturbation itself, which is quite different from that of the usual vector
field perturbation without the coupling in the four-dimensional spacetime.
Moreover, we also find that the vector field perturbation with odd parity grows
with exponential rate if the coupling strength is stronger than certain a
critical value. However, the vector field perturbation with even parity always
decays in the Reissner-Nordstr\"{o}m black hole spacetime.
In 1983, Laughlin reported a wave function which while using the first-principles kinetic energy and Coulomb interactions fractionalizes the charge of the electron so that a charge such as 1/3 occurs. Since then this wave function has been applied to many problems in condensed matter physics. An effort is made to review the literature dealing with Aharonov–Bohm effect, ground state, confinement, phase transitions, Wigner and Luttinger solids, edge states, Anderson's theory, statistics and anyons, etc. The importance of the angular momentum is pointed out and it is shown that Landau levels play an important role in understanding the fractions at which the plateaus occur in the quantum Hall effect.
We show that in the presence of external fields for which either
$\dot{\vb{B}}^{\mathrm{ext}}\neq 0$ or $\nabla\times\vb{E}^{\mathrm{ext}}\neq
0$ 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 pseudo-vector 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 pseudo-vector gauge fields $A$ and $C$ are regular. We compare
pseudo-photon with paraphoton (graviphoton) theories concluding that, besides
the mechanisms of gauge symmetry breaking already studied, the Bianchi
identities violation are a crucial difference between both theories. We also
show that, due to Dirac's quantization condition, at quantum field theory level
the effects due to pseudo-photons and photons can be distinguished by the
respective contributions to the magnetic moment of fermions and vacuum
polarization. These effects may be relevant in astrophysical environments,
namely close and inside neutron stars and magnetars. [Erratum: The construction
in this work must, at most, be considered as a conceptual system or toy model.
Are discussed systems where the results may have relevance.]
The paper offers the full action for an electromagnetic field with electrical and magnetic charges; Feynman laws are formulated
for the calculation of the interaction cross-sections for electrically and magnetically charged particles on the base of offered
action within relativistic quantum field theory. Derived with formulated Feynman rules cross-section of the interaction between
an elementary particle with magnetic charge and an elementary particle with electrical charge proves to be equal zero.
KeywordsMagnetic monopole–Full action–Lagrangian
In this article it is studied, at variational level, a mathematical setup
given by the Landau-Ginzburg Chern-Simons model for anyons in 2+1-dimensions
within the framework of dimensional reduced Ue(1)xUg(1) extended
electromagnetism with both vector gauge fields (photons) and pseudo-vector
gauge fields (pseudo-photons) 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 4-dimensions of the model with explicit 4-dimensional 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.
