Algebraic And Dirac-hestenes Spinors And Spinor Fields

Almost all presentations of Dirac theory in first or second quantization in physics (and mathematics) textbooks make use of covariant Dirac spinor fields. An exception is the presentation of that theory (first quantization) offered originally by Hestenes and now used by many authors. There, a new concept of spinor field (as a sum of nonhomogeneous even multivectors fields) is used. However, a careful analysis (detailed below) shows that the original Hestenes definition cannot be correct since it conflicts with the meaning of the Fierz identities. In this paper we start a program dedicated to the examination of the mathematical and physical basis for a comprehensive definition of the objects used by Hestenes. In order to do that we give a preliminary definition of algebraic spinor fields (ASF) and Dirac-Hestenes spinor fields (DHSF) on Minkowski space-time as some equivalence classes of pairs (ξu, ψu), where ξu is a spinorial frame field and ψu is an appropriate sum of multivectors fields (to be specified below). The necessity of our definitions are shown by a careful analysis of possible formulations of Dirac theory and the meaning of the set of Fierz identities associated with the bilinear covariants (on Minkowski space-time) made with ASF or DHSF. We believe that the present paper clarifies some misunderstandings (past and recent) appearing on the literature of the subject. It will be followed by a sequel paper where definitive definitions of ASF and DHSF are given as appropriate sections of a vector bundle called the left spin-Clifford bundle. The bundle formulation is essential in order to be possible to produce a coherent theory for the covariant derivatives of these fields on arbitrary Riemann-Cartan space-times. 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Electronic Correlations In Narrow-band Solids

The Hubbard Hamiltonian is rederived from the full many-body Hamiltonian with the assumption that only intrasite correlations are important. It is shown to be exact in both the Hartree-Fock and narrow-band limits, provided the appropriate linearization procedure is adopted in the former case. Real-time and imaginary-time Green's functions are derived for the cases intermediate between the Hartree-Fock and narrow-band limits, and a long-standing puzzle with regard to the number of electrons in the upper pseudoparticle band is cleared up. The chemical potential and total energy of the system are calculated in the narrow-band limit and are shown to be identical with those derived from an effective one-electron representation. It is shown that because these quantities depend only on the number of doubly occupied sites, important transport parameters such as electrical conductivity and thermoelectric power can be calculated from the effective one-electron representation, without the necessity of evaluating the two-particle Green's function. For finite bands, the total energy in the Hubbard model is shown to give the exact result, in contradiction to a previous calculation. It is shown that thermodynamic quantities such as the total energy and chemical potential which depend only on derivatives of the grand partition function are independent of the presence or absence of magnetic ordering, but that the entropy is not. Thus a study of the insulatormetal phase transitions is very sensitive to magnetic ordering. © 1979 The American Physical Society.1921203121

Magnetic Monopoles Without String In The Kähler-clifford Algebra Bundle: A Geometrical Interpretation

In substitution for Dirac monopoles with string (and for topological monopoles), "monopoles without string" have recently been introduced on the basis of a generalized potential, the sum of a vector A, and a pseudovector γ5 B potential. By making recourse to the Clifford bundle script c sign(τM,g) [ ( TxM,g) = ℝ1,3; script c sign(TxM,g) = ℝ1,3 ], which just allows adding together for each x∈M tensors of different ranks, in a previous paper a Lagrangian and Hamiltonian formalism was constructed for interacting monopoles and charges that can be regarded as satisfactory from various points of view. In the present article, after having "completed" the formalism, a purely geometrical interpretation of it is put forth within the Kähler-Clifford bundle script K(τ*M,ĝ) of differential forms, essential ingredients being a generalized curvature and the Hodge decomposition theorem. Thus the way is paved for the extension of our "monopoles without string" to non-Abelian gauge groups. The analogy with supersymmetric theories is apparent. © 1990 American Institute of Physics.31250250

Superluminal Localized Solutions to Maxwell Equations propagating along a waveguide: The finite-energy case

In a previous paper of ours [Phys. Rev. E64 (2001) 066603, e-print physics/0001039] we have shown localized (non-evanescent) solutions to Maxwell equations to exist, which propagate without distortion with Superluminal speed along normal-sized waveguides, and consist in trains of "X-shaped" beams. Those solutions possessed therefore infinite energy. In this note we show how to obtain, by contrast, finite-energy solutions, with the same localization and Superluminality properties. [PACS nos.: 41.20.Jb; 03.50.De; 03.30.+p; 84.40.Az; 42.82.Et. Keywords: Wave-guides; Localized solutions to Maxwell equations; Superluminal waves; Bessel beams; Limited-dispersion beams; Finite-energy waves; Electromagnetic wavelets; X-shaped waves; Evanescent waves; Electromagnetism; Microwaves; Optics; Special relativity; Localized acoustic waves; Seismic waves; Mechanical waves; Elastic waves; Guided gravitational waves.]Comment: plain LaTeX file (12 pages), plus 10 figure

An assessment of Evans' unified field theory I

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe theta and a (metric compatible) Lorentz connection Gamma. These two potentials yield the field strengths torsion T and curvature R. Evans tried to infuse electromagnetic properties into this geometrical framework by putting the coframe theta to be proportional to four extended electromagnetic potentials A; these are assumed to encompass the conventional Maxwellian potential in a suitable limit. The viable Einstein-Cartan(-Sciama-Kibble) theory of gravity was adopted by Evans to describe the gravitational sector of his theory. Including also the results of an accompanying paper by Obukhov and the author, we show that Evans' ansatz for electromagnetism is untenable beyond repair both from a geometrical as well as from a physical point of view. As a consequence, his unified theory is obsolete.Comment: 39 pages of latex, modified because of referee report, mistakes and typos removed, partly reformulated, taken care of M.W.Evans' rebutta

Langstroth hive construction with cement-vermiculite

Exfoliated vermiculite is a light-weight and cheap product that, because of its thermal resistance, has become a valuable insulating material. With regard to its use in beekeeping, this research tested whether the box for honey bees constructed with cement-vermiculite mortar (CVM) presents physical characteristics similar to those of wood. The experiment was carried out at Seropédica, RJ, Brazil, for eight months. The cement-vermiculite mortar was compared with a control material (pinewood), in the construction of Langstroth boxes and boards, in a completely randomized design, with respect to thermal control, thermal conductivity and its capacity to absorb and lose water. The production cost for a CVM box was estimated. There were no internal temperature differences between CVM and wooden boxes. Thermal conductivity values for CVM and pinewood were similar. CVM absorbed more water and lost water faster than pinewood. Since CVM boxes can be easily constructed, at a low cost and with similar characteristics as traditional boxes, made of wood, the material can be recommended for use in non-migratory beekeeping

Higher spin quaternion waves in the Klein-Gordon theory

Electromagnetic interactions are discussed in the context of the Klein-Gordon fermion equation. The Mott scattering amplitude is derived in leading order perturbation theory and the result of the Dirac theory is reproduced except for an overall factor of sixteen. The discrepancy is not resolved as the study points into another direction. The vertex structures involved in the scattering calculations indicate the relevance of a modified Klein-Gordon equation, which takes into account the number of polarization states of the considered quantum field. In this equation the d'Alembertian is acting on quaternion-like plane waves, which can be generalized to representations of arbitrary spin. The method provides the same relation between mass and spin that has been found previously by Majorana, Gelfand, and Yaglom in infinite spin theories