Quantum dynamical manifolds 5. Hydrogen mass-spacetime

Abstract

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

Quantum dynamical manifolds: Pair states in high‐temperature superconductivity

“…At this point, we want to record the complete solution for the Dirac pair where the secular problem associated with Eqs. (20) and (21) or Eq. (22), including a polarization field, can be written as det 21 Ϫk…”

“…The connection-modifying gauge potentials can be computed in a self-consistent manner for evolving manifolds as shown in Refs. [8] and [20]. Thus, by using the equations for the dynamical formation of manifolds discussed next one can form quantum dynamical manifold fields with specified internal and external symmetry.…”

“…The solutions to these equations have, of course, their own geometry, the geometry of an underlying quantum dynamical manifold. These equations are subject to the Cartan structure equations and both curvature and torsion can be computed from their frame field solutions [8,9,20]. The physics described is that of a particle field located in some region of a (n ϩ 1)-D space-time manifold.…”

“…The existence of the Pauli principle, in fact, indicates that pair states are prevalent and important. The straightforward generalization of the QDMEs above to many-particle systems introduces quasiparticle moving frames whose evolution can be used to directly define a many-body quantum geometry [9,20].…”

“…In this reformulation of quantum mechanics, the famous Yang-Mills equations become topological constraints similar in spirit to the Bianchi constraints employed in Einstein's GRT. In our approach the physical, quasiparticle wave functions that are elements of a (possibly) nonorthonormal moving frame field and the differential connection, involving the so-called gauge potentials (called nonlocal interactions in physics and quantum chemistry), are both self-consistently determined [8,9,20]. Because the evolution equations of the moving frame field are partial differential equations, the evolution of initial conditions defines a mass spacetime or geometric frame field that can be treated using nonperturbative numerical methods of quantum chemistry.…”