4,166 research outputs found

    Electromagnetism and multiple-valued loop-dependent wave functionals

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    We quantize the Maxwell theory in the presence of a electric charge in a "dual" Loop Representation, i.e. a geometric representation of magnetic Faraday's lines. It is found that the theory can be seen as a theory without sources, except by the fact that the wave functional becomes multivalued. This can be seen as the dual counterpart of what occurs in Maxwell theory with a magnetic pole, when it is quantized in the ordinary Loop Representation. The multivaluedness can be seen as a result of the multiply-connectedness of the configuration space of the quantum theory.Comment: 5 page

    Dirac equation for membranes

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    Dirac's idea of taking the square root of constraints is applied to the case of extended objects concentrating on membranes in D=4 space-time dimensions. The resulting equation is Lorentz invariant and predicts an infinite hierarchy of positive and negative masses (tension). There are no tachyonic solutions.Comment: 5 pages, 1 figure, v2: improved version, accepted for publication as a Brief Report in Physical Review

    The 'Square Root' of the Interacting Dirac Equation

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    The 'square root' of the interacting Dirac equation is constructed. The obtained equations lead to the Yang-Mills superfield with the appropriate equations of motion for the component fields.Comment: 6 page

    Properties of noncommutative axionic electrodynamics

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    Using the gauge-invariant but path-dependent variables formalism, we compute the static quantum potential for noncommutative axionic electrodynamics, and find a radically different result than the corresponding commutative case. We explicitly show that the static potential profile is analogous to that encountered in both non-Abelian axionic electrodynamics and in Yang-Mills theory with spontaneous symmetry breaking of scale symmetry.Comment: 4 pages. To appear in PR

    The dynamical equation of the spinning electron

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    We obtain by invariance arguments the relativistic and non-relativistic invariant dynamical equations of a classical model of a spinning electron. We apply the formalism to a particular classical model which satisfies Dirac's equation when quantised. It is shown that the dynamics can be described in terms of the evolution of the point charge which satisfies a fourth order differential equation or, alternatively, as a system of second order differential equations by describing the evolution of both the center of mass and center of charge of the particle. As an application of the found dynamical equations, the Coulomb interaction between two spinning electrons is considered. We find from the classical viewpoint that these spinning electrons can form bound states under suitable initial conditions. Since the classical Coulomb interaction of two spinless point electrons does not allow for the existence of bound states, it is the spin structure that gives rise to new physical phenomena not described in the spinless case. Perhaps the paper may be interesting from the mathematical point of view but not from the point of view of physics.Comment: Latex2e, 14 pages, 5 figure

    Nonlinear QED and Physical Lorentz Invariance

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    The spontaneous breakdown of 4-dimensional Lorentz invariance in the framework of QED with the nonlinear vector potential constraint A_{\mu}^{2}=M^{2}(where M is a proposed scale of the Lorentz violation) is shown to manifest itself only as some noncovariant gauge choice in the otherwise gauge invariant (and Lorentz invariant) electromagnetic theory. All the contributions to the photon-photon, photon-fermion and fermion-fermion interactions violating the physical Lorentz invariance happen to be exactly cancelled with each other in the manner observed by Nambu a long ago for the simplest tree-order diagrams - the fact which we extend now to the one-loop approximation and for both the time-like (M^{2}>0) and space-like (M^{2}<0) Lorentz violation. The way how to reach the physical breaking of the Lorentz invariance in the pure QED case taken in the flat Minkowskian space-time is also discussed in some detail.Comment: 16 pages, 2 Postscript figures to be published in Phys. Rev.

    Interacting dark energy in f(R)f(R) gravity

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    The field equations in f(R)f(R) gravity derived from the Palatini variational principle and formulated in the Einstein conformal frame yield a cosmological term which varies with time. Moreover, they break the conservation of the energy--momentum tensor for matter, generating the interaction between matter and dark energy. Unlike phenomenological models of interacting dark energy, f(R)f(R) gravity derives such an interaction from a covariant Lagrangian which is a function of a relativistically invariant quantity (the curvature scalar RR). We derive the expressions for the quantities describing this interaction in terms of an arbitrary function f(R)f(R), and examine how the simplest phenomenological models of a variable cosmological constant are related to f(R)f(R) gravity. Particularly, we show that Λc2=H2(12q)\Lambda c^2=H^2(1-2q) for a flat, homogeneous and isotropic, pressureless universe. For the Lagrangian of form R1/RR-1/R, which is the simplest way of introducing current cosmic acceleration in f(R)f(R) gravity, the predicted matter--dark energy interaction rate changes significantly in time, and its current value is relatively weak (on the order of 1% of H0H_0), in agreement with astronomical observations.Comment: 8 pages; published versio

    P.A.M. Dirac and the Discovery of Quantum Mechanics

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    Dirac's contributions to the discovery of non-relativistic quantum mechanics and quantum electrodynamics, prior to his discovery of the relativistic wave equation, are described

    Lagrangian and Hamiltonian formulations of higher order Chern-Simons theories

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    We consider models involving the higher (third) derivative extension of the abelian Chern-Simons (CS) topological term in D=2+1 dimensions. The polarisation vectors in these models reveal an identical structure with the corresponding expressions for usual models which contain, at most, quadratic structures. We also investigate the Hamiltonian structure of these models and show how Wigner's little group acts as gauge generator.Comment: 13 pages, Late

    On the transformations of hamiltonian gauge algebra under rotations of constraints

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    By explicit calculation of the effect of a ghost-dependent canonical transformation of BRST-charge, we derive the corresponding transformation law for structure coefficients of hamiltonian gauge algebra under rotation of constraints.We show the transformation law to deviate from the behaviour (expected naively) characteristic to a genuine connection.Comment: 11 pages, some misprints remove
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