No abstract

Fluid dynamical analogs of the electrodynamical Lorentz force law and Poynting theorem are derived and their implications analyzed. The companion paper by Scofield and Huq 2014 Fluid. Dyn. Res. 46 055513 gives a heuristic introduction to the present results. The fluid dynamical analogs are consequences of a new causal, covariant, geometrodynamical theory of fluids (GTF). Compared to the Navier-Stokes theory, GTF shows the existence of new causal channels of stress-energy propagation and dissipation due to the action of transverse modes of flow. These channels describe energy-dissipation and transport along curved stream tubes common in turbulent flows.

A self‐consistent, non‐Abelian gauge theory is developed for high‐temperature superconductors (HTSCs). As a physical example, a spontaneously broken (SO(4)⊃SO(3)×U(1))×3 gauge theory is described that includes excitonic and antiferromagnetic boson exchange pairing forces for the interacting superconducting and antiferromagnetic phases of the soft superconductor YBa2Cu3O7−x. A new differential geometric approach for generating quantum dynamical manifolds, called quantum dynamical manifold theory (QDMT) is used to compute the quantum geometry of these systems. It is shown how geometric conditions applied to the quasi‐particle system can be used to determine self‐consistent, self‐gauge fields (SC‐SGFs) and fix the coupling constants to reduce the calculational number of degrees of freedom of such many‐body systems. The resulting theory is formulated in a way that real crystal quasi‐particle basis sets are used. This work raises the hope that ab initio property calculation and systematic exploration of different mechanisms for HTSCs will become possible. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 341–368, 2000

ABSTRACT:The physical rationale supporting the introduction of many-body differential geometric methods for self-consistently calculating the properties of quantum systems is given. The methods are then used to determine new self-consistent, self-gauge field quantum dynamical manifold equations describing a high temperature superconductor. This includes itinerant electron screening of Coulomb repulsion and local electron, exciton-mediated attraction. The article includes new quantum geometric equations for the paired electrons or holes (potential cooperons) of a superconductor. It is shown how other mechanisms can easily be incorporated into the calculation of the quasi-particle geometry of the quantum dynamical manifold.

The newly developed methods of quantum dynamical manifold theory (QDMT) are used to determine a theory of the differential geometry and topology of the quantum dynamical manifold of the hydrogen nuclear‐electron system. This provides an ab initio theory of the structure of nuclear‐atomic system including the quarks, gluons, and (W+,Z0,W−) in the proton and the atomic orbital electron in a way that treats the strong, electromagnetic, weak, and gravitational forces from a unified QDMT viewpoint. The calculations proposed resemble self‐consistent Green's function ones in Fourier space. The quasi‐particles provide the basis for computing the globally defined connection needed for determining the self‐consistent gauge potentials. This approach allows the simultaneous determination of coupling constants and masses along with the quasi‐particle amplitudes. All integrals needed can be analytically computed using a Gaussian‐type orbital basis. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 369–393, 2000