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[en] When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. A gravitational field can be incorporated as a background spacetime if the back-action of matter on the field can be neglected, resulting in modifications of the Dirac or Klein–Gordon equations for elementary fermions and bosons respectively. The semi-classical description predicts particle creation in many situations, including the expanding-universe scenario, near the event horizon of a black hole (the Hawking effect), and an accelerating observer in flat spacetime (the Unruh effect). In this work, we give a pedagogical introduction to the Dirac equation in a general 2D spacetime and show examples of spinor wave packet dynamics in flat and curved background spacetimes. In particular, we cover the phenomenon of particle creation in a time-dependent metric. Photonic analogs of these effects are then proposed, where classical light propagating in an array of coupled waveguides provides a visualisation of the Dirac spinor propagating in a curved 2D spacetime background. The extent to which such a single-particle description can be said to mimic particle creation is discussed.
[en] A divergence-free asymptotic approximation is developed for constructing an equation of motion for a radiating classical relativistic charged particle. The formulation employs the point particle limit in a sequence of solutions and the method developed by Dirac in his theory of classical charged particle. Since the initial-value approach proposed by Schultz is used, no runaway solutions exist and the irreversible nature of the particle motion is naturally derived. It is pointed out that the derived Lorentz-Dirac equation should not be regarded as an exact description of the motion of the charged particle holding at all times
[en] It is show that the classical Maxwell theory admits a simple and natural renormalization of the self-interaction energy. This leads to a consistent, local and causal, relativistic theory of the Maxwell field interacting with classical, charged, point-like particles. The theory may be regarded as a simple and necessary completion of special relativity. The renormalization method proposed here is a realization of Einstein's idea of ''deriving equation of motion from field equation''. It is shown that Dirac's ''3-dots'' equation does not describe a fundamental law of physics, but only a specific family of solution of our theory, corresponding to a specific choice of the field initial data. (author). 13 refs
[en] I study the existence of smooth, static nontrivial solutions to Einstein-Yang-Mills-Klein-Gordon equations. The absence of static solutions is proven if the Klein-Gordon field is linear and the asymptotic falloff of g00 to unity is quicker than 1/r. In the case when g00 = 1+0(1/r) the system is shown to reduce to the pure gravity, under certain conditions. Possible applications of bifurcation theory for finding solutions which are close to the trivial one in the case when the scalar field is of Higgs type are discussed. 12 refs. (author)
[en] We explore the multisymplectic Fourier pseudospectral discretizations for the (3+1)-dimensional Klein-Gordon equation in this paper. The corresponding multisymplectic conservation laws are derived. Two kinds of explicit symplectic integrators in time are also presented
[en] Quantum singularities considered in the 3D Banados-Teitelboim-Zanelli (BTZ) spacetime by Pitelli and Letelier [Phys. Rev. D 77, 124030 (2008)] is extended to charged BTZ and 3D Einstein-Maxwell-dilaton gravity spacetimes. The occurrence of naked singularities in the Einstein-Maxwell extension of the BTZ spacetime both in linear and nonlinear electrodynamics as well as in the Einstein-Maxwell-dilaton gravity spacetimes are analyzed with the quantum test fields obeying the Klein-Gordon and Dirac equations. We show that with the inclusion of the matter fields, the conical geometry near r=0 is removed and restricted classes of solutions are admitted for the Klein-Gordon and Dirac equations. Hence, the classical central singularity at r=0 turns out to be quantum mechanically singular for quantum particles obeying the Klein-Gordon equation but nonsingular for fermions obeying the Dirac equation. Explicit calculations reveal that the occurrence of the timelike naked singularities in the considered spacetimes does not violate the cosmic censorship hypothesis as far as the Dirac fields are concerned. The role of horizons that clothes the singularity in the black hole cases is replaced by repulsive potential barrier against the propagation of Dirac fields.
[en] Interaction of the unified Einstein-Maxwell field with the Dirac spinor field is investigated. A variational principle is found which is of a first differential order and, contrary to the standard variational derivation of the Dirac equation, does not lead to any second type of constraints. (orig./HSI)
[en] The Dirac equation in four dimension is studied describing fermions, both as 4 x 4 matrices and differential forms. It is discussed in both formalisms its properties under transformations of the group SU(4). (A.C.A.S.)
[pt]Estuda-se a equacao de Dirac a quatro dimensoes descrevendo fermions tanto como matrizes 4 x 4 quanto na forma diferencial. Neste trabalho, discutem-se em ambos os formalismos, suas propriedades sob transformacoes do grupo SU(4). (A.C.A.S.)