On Clifford Subalgebras, Spacetime Splittings and Applications

Z2-gradings of Clifford algebras are reviewed and we shall be concerned with an alpha-grading based on the structure of inner automorphisms, which is closely related to the spacetime splitting, if we consider the standard conjugation map automorphism by an arbitrary, but fixed, splitting vector. After briefly sketching the orthogonal and parallel components of products of differential forms, where we introduce the parallel [orthogonal] part as the space [time] component, we provide a detailed exposition of the Dirac operator splitting and we show how the differential operator parallel and orthogonal components are related to the Lie derivative along the splitting vector and the angular momentum splitting bivector. We also introduce multivectorial-induced alpha-gradings and present the Dirac equation in terms of the spacetime splitting, where the Dirac spinor field is shown to be a direct sum of two quaternions. We point out some possible physical applications of the formalism developed.Comment: 22 pages, accepted for publication in International Journal of Geometric Methods in Modern Physics 3 (8) (2006

Maximally Causal Quantum Mechanics

We present a new causal quantum mechanics in one and two dimensions developed recently at TIFR by this author and V. Singh. In this theory both position and momentum for a system point have Hamiltonian evolution in such a way that the ensemble of system points leads to position and momentum probability densities agreeing exactly with ordinary quantum mechanics.Comment: 7 pages,latex,no figures,to appear in Praman

Thermodynamic Gravity and the Schrodinger Equation

We adopt a 'thermodynamical' formulation of Mach's principle that the rest mass of a particle in the Universe is a measure of its long-range collective interactions with all other particles inside the horizon. We consider all particles in the Universe as a 'gravitationally entangled' statistical ensemble and apply the approach of classical statistical mechanics to it. It is shown that both the Schrodinger equation and the Planck constant can be derived within this Machian model of the universe. The appearance of probabilities, complex wave functions, and quantization conditions is related to the discreetness and finiteness of the Machian ensemble.Comment: Minor corrections, the version accepted by Int. J. Theor. Phy

Stationary Flows of the Parabolic Potential Barrier in Two Dimensions

In the two-dimensional isotropic parabolic potential barrier $V(x, y)=V_0 -m\gamma^2 (x^2+y^2)/2$, though it is a model of an unstable system in quantum mechanics, we can obtain the stationary states corresponding to the real energy eigenvalue $V_0$. Further, they are infinitely degenerate. For the first few eigenstates, we will find the stationary flows round a right angle that are expressed by the complex velocity potentials $W=\pm\gamma z^2/2$.Comment: 12 pages, AmS-LaTeX, 4 figure

Time-like flows of energy-momentum and particle trajectories for the Klein-Gordon equation

The Klein-Gordon equation is interpreted in the de Broglie-Bohm manner as a single-particle relativistic quantum mechanical equation that defines unique time-like particle trajectories. The particle trajectories are determined by the conserved flow of the intrinsic energy density which can be derived from the specification of the Klein-Gordon energy-momentum tensor in an Einstein-Riemann space. The approach is illustrated by application to the simple single-particle phenomena associated with square potentials.Comment: 14 pages, 11 figure

Justification of the symmetric damping model of the dynamical Casimir effect in a cavity with a semiconductor mirror

A "microscopic" justification of the "symmetric damping" model of a quantum oscillator with time-dependent frequency and time-dependent damping is given. This model is used to predict results of experiments on simulating the dynamical Casimir effect in a cavity with a photo-excited semiconductor mirror. It is shown that the most general bilinear time-dependent coupling of a selected oscillator (field mode) to a bath of harmonic oscillators results in two equal friction coefficients for the both quadratures, provided all the coupling coefficients are proportional to a single arbitrary function of time whose duration is much shorter than the periods of all oscillators. The choice of coupling in the rotating wave approximation form leads to the "mimimum noise" model of the quantum damped oscillator, introduced earlier in a pure phenomenological way.Comment: 9 pages, typos corrected, corresponds to the published version, except for the reference styl