Star Products and Geometric Algebra

The formalism of geometric algebra can be described as deformed super analysis. The deformation is done with a fermionic star product, that arises from deformation quantization of pseudoclassical mechanics. If one then extends the deformation to the bosonic coefficient part of superanalysis one obtains quantum mechanics for systems with spin. This approach clarifies on the one hand the relation between Grassmann and Clifford structures in geometric algebra and on the other hand the relation between classical mechanics and quantum mechanics. Moreover it gives a formalism that allows to handle classical and quantum mechanics in a consistent manner.Comment: 21 page

Theory of Electric Transport in the Pseudogap State of High-Tc Cuprates

We theoretically investigate the electric transport in the pseudogap state of High-Tc cuprates. Starting from the repulsive Hubbard model, we perform the microscopic calculation to describe the pseudogap phenomena which are induced by the superconducting fluctuations. The single particle Green function, spin susceptibility and superconducting fluctuations are self-consistently determined by the SC-FLEX+T-matrix approximation. The longitudinal and transverse conductivities are calculated by using the Eliashberg and Kohno-Yamada formalism. The effects of the spin fluctuations and superconducting fluctuations are estimated, respectively. The vertex corrections arising from the two fluctuations are also calculated. The additional contribution from the Aslamazov-Larkin term is also estimated beyond the Eliashberg formalism. It is shown that the main effect of the superconducting fluctuations is the feedback effect through the spin fluctuations. The correct results are obtained by considering the superconducting fluctuations and the spin fluctuations simultaneously. The temperature and doping dependences of the resistivity and the Hall coefficient are well explained. We point out that the characteristic momentum dependence of the systems plays an essential role in this explanation.Comment: To appear in J. Phys. Soc. Jpn. Vol.71 No.1 (2002

Cooper pairing above the critical temperature in a unitary Fermi gas

We present an ab initio determination of spin responses of the unitary Fermi gas, based on finite temperature quantum Monte Carlo calculations and the Kubo linear-response formalism. We determine the temperature dependence of the spin susceptibility and the spin conductivity. We show that both quantities exhibit suppression above the critical temperature of the superfluid to normal phase transition due to presence of the Cooper pairs. The spin diffusion transport coefficient does not display the existence of a minimum in the vicinity of the critical temperature and it drops to very low values D_s approx 0.8hbar/m in the superfluid phase. All these spin observables show a smooth and monotonic behavior with temperature when crossing the critical temperature T_c, until the Fermi liquid regime is attained at the temperature T*, where the pseudogap regime disappears.Comment: 9 pages, 8 figures; supplemental materials included; published versio

Keldysh approach to the renormalization group analysis of the disordered electron liquid

We present a Keldysh nonlinear sigma-model approach to the renormalization group analysis of the disordered electron liquid. We include both the Coulomb interaction and Fermi-liquid type interactions in the singlet and triplet channels into the formalism. Based on this model, we reproduce the coupled renormalization group equations for the diffusion coefficient, the frequency, and interaction constants previously derived with the replica model in the imaginary time technique. With the help of source fields coupling to the particle-number and spin densities, we study the density-density and spin density-spin density correlation functions in the diffusive regime. This allows us to obtain results for the electric conductivity and the spin susceptibility and thereby to re-derive the main results of the one-loop renormalization group analysis of the disordered electron liquid in the Keldysh formalism.Comment: 29 pages, 15 figure

Equations of Motion of Spinning Relativistic Particle in Electromagnetic and Gravitational Fields

We consider the motion of a spinning relativistic particle in external electromagnetic and gravitational fields, to first order in the external field, but to an arbitrary order in spin. The noncovariant spin formalism is crucial for the correct description of the influence of the spin on the particle trajectory. We show that the true coordinate of a relativistic spinning particle is its naive, common coordinate \r. Concrete calculations are performed up to second order in spin included. A simple derivation is presented for the gravitational spin-orbit and spin-spin interactions of a relativistic particle. We discuss the gravimagnetic moment (GM), a specific spin effect in general relativity. It is shown that for the Kerr black hole the gravimagnetic ratio, i.e., the coefficient at the GM, equals unity (just as for the charged Kerr hole the gyromagnetic ratio equals two). The equations of motion obtained for relativistic spinning particle in external gravitational field differ essentially from the Papapetrou equations.Comment: 32 pages, latex, Plenary talk at the Fairbank Meeting on the Lense--Thirring Effect, Rome-Pescara, 29/6-4/7 199