The bundles of algebraic and Dirac-Hestenes spinor fields

Our main objective in this paper is to clarify the ontology of Dirac-Hestenes spinor fields (DHSF) and its relationship with even multivector fields, on a Riemann-Cartan spacetime (RCST) M=(M,g,del,tau(g),up arrow) admitting a spin structure, and to give a mathematically rigorous derivation of the so-called Dirac-Hestenes equation (DHE) in the case where M is a Lorentzian spacetime (the general case when M is a RCST will be discussed in another publication). To this aim we introduce the Clifford bundle of multivector fields (Cl(M,g)) and the left (Cl-Spin1,3(el)(M)) and right (Cl-Spin1,3(er)(M)) spin-Clifford bundles on the spin manifold (M,g). The relation between left ideal algebraic spinor fields (LIASF) and Dirac-Hestenes spinor fields (both fields are sections of Cl-Spin1,3(el)(M)) is clarified. We study in detail the theory of covariant derivatives of Clifford fields as well as that of left and right spin-Clifford fields. A consistent Dirac equation for a DHSF Psiis an element ofsec Cl-Spin1,3(el)(M) (denoted DECll) on a Lorentzian spacetime is found. We also obtain a representation of the DECll in the Clifford bundle Cl(M,g). It is such equation that we call the DHE and it is satisfied by Clifford fields psi(Xi)is an element ofsec Cl(M,g). This means that to each DHSF Psiis an element ofsec Cl-Spin1,3(el)(M) and spin frame Xiis an element ofsec P-Spin1,3(e)(M), there is a well-defined sum of even multivector fields psi(Xi)is an element ofsec Cl(M,g) (EMFS) associated with Psi. Such an EMFS is called a representative of the DHSF on the given spin frame. And, of course, such a EMFS (the representative of the DHSF) is not a spinor field. With this crucial distinction between a DHSF and its representatives on the Clifford bundle, we provide a consistent theory for the covariant derivatives of Clifford and spinor fields of all kinds. We emphasize that the DECll and the DHE, although related, are equations of different mathematical natures. We study also the local Lorentz invariance and the electromagnetic gauge invariance and show that only for the DHE such transformations are of the same mathematical nature, thus suggesting a possible link between them. (C) 2004 American Institute of Physics.4572945296

Evolution of populations expanding on curved surfaces

This is the author accepted manuscript. The final version is available from EPL Association via the DOI in this recordThe expansion of a population into new habitat is a transient process that leaves its footprints in the genetic composition of the expanding population. How the structure of the environment shapes the population front and the evolutionary dynamics during such a range expansion is little understood. Here, we investigate the evolutionary dynamics of populations consisting of many selectively neutral genotypes expanding on curved surfaces. Using a combination of individual-based off-lattice simulations, geometrical arguments, and lattice-based stepping-stone simulations, we characterise the effect of individual bumps on an otherwise flat surface. Compared to the case of a range expansion on a flat surface, we observe a transient relative increase, followed by a decrease, in neutral genetic diversity at the population front. In addition, we find that individuals at the sides of the bump have a dramatically increased expected number of descendants, while their neighbours closer to the bump's centre are far less lucky. Both observations can be explained using an analytical description of straight paths (geodesics) on the curved surface. Complementing previous studies of heterogeneous flat environments, the findings here build our understanding of how complex environments shape the evolutionary dynamics of expanding populations.Nederlandse Organisatie voor Wetenschappelijk Onderzoek I (NWO-I)American Physical SocietySociedade Brasileira de FísicaFAPESPCenter for Computation and Visualization, Brown Universit

Classical kinetic energy, quantum fluctuation terms and kinetic-energy functionals

We employ a recently formulated dequantization procedure to obtain an exact expression for the kinetic energy which is applicable to all kinetic-energy functionals. We express the kinetic energy of an N-electron system as the sum of an N-electron classical kinetic energy and an N-electron purely quantum kinetic energy arising from the quantum fluctuations that turn the classical momentum into the quantum momentum. This leads to an interesting analogy with Nelson's stochastic approach to quantum mechanics, which we use to conceptually clarify the physical nature of part of the kinetic-energy functional in terms of statistical fluctuations and in direct correspondence with Fisher Information Theory. We show that the N-electron purely quantum kinetic energy can be written as the sum of the (one-electron) Weizsacker term and an (N-1)-electron kinetic correlation term. We further show that the Weizsacker term results from local fluctuations while the kinetic correlation term results from the nonlocal fluctuations. For one-electron orbitals (where kinetic correlation is neglected) we obtain an exact (albeit impractical) expression for the noninteracting kinetic energy as the sum of the classical kinetic energy and the Weizsacker term. The classical kinetic energy is seen to be explicitly dependent on the electron phase and this has implications for the development of accurate orbital-free kinetic-energy functionals. Also, there is a direct connection between the classical kinetic energy and the angular momentum and, across a row of the periodic table, the classical kinetic energy component of the noninteracting kinetic energy generally increases as Z increases.Comment: 10 pages, 1 figure. To appear in Theor Chem Ac

Some remarks on the coupling prescription of teleparallel gravity

By using a nonholonomic moving frame version of the general covariance principle, an active version of the equivalence principle, an analysis of the gravitational coupling prescription of teleparallel gravity is made. It is shown that the coupling prescription determined by this principle is always equivalent with the corresponding prescription of general relativity, even in the presence of fermions. An application to the case of a Dirac spinor is made.36112525253

Multivector Dirac equation and Z(2)-gradings of Clifford algebras

We generalize certain aspects of Hestenes's approach to Dirac theory to obtain multivector Dirac equations associated to a large class of representations of the gamma matrices. This is done by replacing the usual even/odd decomposition of the space-time algebra with more general Z(2)-gradings. Some examples are given and the chiral case, which is not addressed by the usual approach, is considered in detail. A Lagrangian formulation is briefly discussed. A relationship between this work and certain quaternionic models of the (usual) quantum mechanics is obtained. Finally, we discuss under what conditions the Hestenes's form can be recovered and we suggest a geometrical interpretation for the corresponding situation.4191651167

The transient regime in Frohlich's condensation phenomenon in biosystems

We consider the emergence of the so-called Frohlich's effect in a biosystem, a phenomenon consisting of the condensation of excitations in the polar vibrational modes lying at the bottom of these modes' frequency spectrum. This complex behavior of the system, which seems to have relevance in bioenergetics, may arise in open biomaterial, which is governed by nonlinear kinetic equations, and when under the action of a pumping source of metabolic energy. We analyze here in detail the dynamics of (i) the transient stage before the establishment of a steady state and (ii) the relaxation to the original thermodynamic equilibrium state after the pumping source is turned off. (C) 1997 John Wiley & Sons, Inc.62436337

Quantum-classical correspondence via a deformed kinetic operator

We propose an approach to quantum-classical correspondence based on a deformation of the momentum and kinetic operators of quantum mechanics. Making use of the factorization method, we construct classical versions of the momentum and kinetic operators which, in addition to the standard quantum expressions, contain terms that are functionals of the N-particle density. We show that this implementation of quantum-classical correspondence is related to Witten's deformation of the exterior derivative and Laplacian, introduced in the context of supersymmetric quantum mechanics. The corresponding deformed action is also shown to be related to the Fisher information. Finally, we briefly consider the possible relevance of our approach to the construction of kinetic-energy density functionals.38173869387