On the Electric-Magnetic Duality Symmetry: Quantum Anomaly, Optical Helicity, and Particle Creation (original) (raw)
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The dual symmetry between electric and magnetic fields is an important intrinsic property of Maxwell equations in free space. This symmetry underlies the conservation of optical helicity and, as we show here, is closely related to the separation of spin and orbital degrees of freedom of light (the helicity flux coincides with the spin angular momentum). However, in the standard field-theory formulation of electromagnetism, the field Lagrangian is not dual symmetric. This leads to problematic dual-asymmetric forms of the canonical energy-momentum, spin and orbital angular-momentum tensors. Moreover, we show that the components of these tensors conflict with the helicity and energy conservation laws. To resolve this discrepancy between the symmetries of the Lagrangian and Maxwell equations, we put forward a dualsymmetric Lagrangian formulation of classical electromagnetism. This dual electromagnetism preserves the form of Maxwell equations, yields meaningful canonical energy-momentum and angular-momentum tensors, and ensures a self-consistent separation of the spin and orbital degrees of freedom. This provides a rigorous derivation of the results suggested in other recent approaches.
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Journal of Physics: Conference Series, 2007
effectively modify the classical picture of light rays as the null geodesics of spacetime. After a short introduction on the main aspects of the quantum gravitational optics, as a nontrivial example, we study this effect in the background of NUT space characterizing the spacetime of a spherical mass endowed with a gravitomagnetic monopole charge, the so called NUT factor. * Electronic address: nahmadi@ut.ac.ir † Electronic address: saloumeh@mehr.sharif.edu ‡ Electronic address: nouri@theory.ipm.ac.ir
POSSIBLE POLARIZATION AND SPIN-DEPENDENT ASPECTS OF QUANTUM GRAVITY
International Journal of Modern Physics D, 2008
We argue that quantum gravity theories that carry a Lie algebraic modification of the Poincaré and Heisenberg algebras inevitably provide inhomogeneities that may serve as seeds for cosmological structure formation. Furthermore, in this class of theories one must expect a strong polarisation and spin dependence of various quantum-gravity effects.
Possible polarisation and spin dependent aspects of quantum gravity
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Annals of Physics, 1980
I discuss cosmological particle production in spaces with spectral asymmetry. A change in the amount of spectral symmetry sufficient to produce a level crossing will result in the creation of neutrino pairs rather than neutrino, antineutrino pairs; the net excess of fermions being given by the number of level crossings. A symmetric Bianchi IX model is treated in detail and for large initial anisotropy the number of neutrinos produced is (l/256) exp 128, where /3+ is a measure of the initial anisotropy. The relation of this phenomenon to chiral anomalies and to the Atiyah-Patodi-Singer index theorem for manifolds with boundary is described. The effect of spectral asymmetry on photons is discussed and it is shewn that no level crossing can occur. This paper is an elaboration of some ideas described briefly in [I] which relate the "handedness" of space to the behaviour of quantum particles moving in that space. The class of spacetimes considered in [I ] are topologically R x Z,, , where 2, is a compact spacelike hypersurface and can be decomposed to three regions, M-, Alo, M+-. M-and M+ are past and future static regions and MO is an intervening region of spacetime in which the geometry depends upon time. Since M+ and Mare static there is a well defined notion of vacuum state, I 0,) and j O-), respectively. In MO no such notion exists because the time dependent gravitational field can create particles. This particle creation will, in general, imply that / 0,) f 1 OK). In M t and M-one may consider solutions of the Dirac or Maxwell equations which are proportional to exp &tiEt where {E) are the eigenvalues of the threedimensional Dirac operator (for neutrinos) or of the three-dimensional curl operator (for photons). The sign of the eigenvalue determines the helicity of the particle state which the solution describes. The space manifold & is said to be "handed" if it does not admit an orientation reversing isometry" or "parity" operation P: Z,,. The absence of a parity symmetry leads to "spectral asymmetry," that is, the absence of a 1-1 correspondence between the states of positive and of negative helicity. If, as can occur, the energy eigenvalues { 1 E I} are systematically higher for one helicity than for the other the expectation value of the helicity in a Gibbs state at some temperature T = /5-l can be nonzero. In the case of neutrinos for which helicity and fermion number are proportional this means that the mean neutrino number in the Gibbs state is nonzero. These effects occur in static spaces and are quite different from the 0003-4916/80/030098-19805.00/O
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The theory of quantum fields propagating on an isotropic cosmological quantum spacetime is reexamined by generalizing the scalar test field to an electromagnetic (EM) vector field. For any given polarization of the EM field on the classical background, the Hamiltonian can be written in the form of the Hamiltonian of a set of decoupled harmonic oscillators, each corresponding to a single mode of the field. In transition from the classical to quantum spacetime background, following the technical procedure given by Ashtekar et al. [Phys. Rev. D 79, 064030 (2009)], a quantum theory of the test EM field on an effective (dressed) spacetime emerges. The nature of this emerging dressed geometry is independent of the chosen polarization, but it may depend on the energy of the corresponding field mode. Specifically, when the backreaction of the field on the quantum geometry is negligible (i.e., a test field approximation is assumed), all field modes probe the same effective background independent of the mode's energy. However, when the backreaction of the field modes on the quantum geometry is significant, by employing a Born-Oppenheimer approximation, it is shown that a rainbow (i.e., a mode-dependent) metric emerges. The emergence of this mode-dependent background in the Planck regime may have a significant effect on the creation of quantum particles. The production amount on the dressed background is computed and is compared with the familiar results on the classical geometry.
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We show that if we start with the free Dirac Lagrangian, and demand local phase invariance, considering the total phase coming from two independent contributions associated with the charge and mass degrees of freedom of charged Dirac particles, then we are forced to introduce two massless independent vector fields for charged Dirac particles that generate all of electrodynamics and gravitodynamics of Heaviside's Gravity of 1893 or Maxwellian Gravity and specify the charge and mass currents produced by charged Dirac particles. From this approach we found (i) a new mathematical representation of Lorentz-Maxwell's equations of electrodynamics physically equivalent to the standard equations and (ii) two equivalent sets of gravito-Lorentz-Maxwell's equations of vector gravity by correcting Heaviside's speculative gravito-Lorentz force. The gravito-Lorentz-Maxwell equations obtained here match with several classical (Galilean or Special or General Relativistic) versions of...
At first, we discuss parallels electric and magnetic fields solutions in a gravitational background. Then, considering eletromagnetic and gravitational waves symmetries we show a particular solution for stationary gravitational waves. Finally we consider gravitation as a gauge theory (effective gravitational theory), evaluate the propagators of the model, analyze the corresponding quantum excitations and verify (confirm) the tree-level unitarity-at many places of the model.