17 research outputs found
Nilpotent classical mechanics: s-geometry
We introduce specific type of hyperbolic spaces. It is not a general linear
covariant object, but of use in constructing nilpotent systems. In the present
work necessary definitions and relevant properties of configuration and phase
spaces are indicated. As a working example we use a D=2 isotropic harmonic
oscillator.Comment: 8 pages, presented at QGIS, June 2006, Pragu
Extension of the Shirafuji model for Massive Particles with Spin
We extend the Shirafuji model for massless particles with primary spacetime
coordinates and composite four-momenta to a model for massive particles with
spin and electric charge. The primary variables in the model are the spacetime
four-vector, four scalars describing spin and charge degrees of freedom as well
as a pair of Weyl spinors. The geometric description proposed in this paper
provides an intermediate step between the free purely twistorial model in
two-twistor space in which both spacetime and four-momenta vectors are
composite, and the standard particle model, where both spacetime and
four-momenta vectors are elementary. We quantize the model and find explicitly
the first-quantized wavefunctions describing relativistic particles with mass,
spin and electric charge. The spacetime coordinates in the model are not
commutative; this leads to a wavefunction that depends only on one covariant
projection of the spacetime four-vector (covariantized time coordinate)
defining plane wave solutions.Comment: Latex, 27 pages, appendix.sty, newlfont.sty (attached
Massive relativistic particle model with spin from free two-twistor dynamics and its quantization
We consider a relativistic particle model in an enlarged relativistic phase
space M^{18} = (X_\mu, P_\mu, \eta_\alpha, \oeta_\dalpha, \sigma_\alpha,
\osigma_\dalpha, e, \phi), which is derived from the free two-twistor dynamics.
The spin sector variables (\eta_\alpha, \oeta_\dalpha, \sigma_\alpha,\
osigma_\dalpha) satisfy two second class constraints and account for the
relativistic spin structure, and the pair (e,\phi) describes the electric
charge sector. After introducing the Liouville one-form on M^{18}, derived by a
non-linear transformation of the canonical Liouville one-form on the
two-twistor space, we analyze the dynamics described by the first and second
class constraints. We use a composite orthogonal basis in four-momentum space
to obtain the scalars defining the invariant spin projections. The
first-quantized theory provides a consistent set of wave equations, determining
the mass, spin, invariant spin projection and electric charge of the
relativistic particle. The wavefunction provides a generating functional for
free, massive higher spin fields.Comment: FTUV-05-0919, IFIC-05-46, IFT UWr 0110/05. Plain latex file, no
macros, 22 pages. A comment and references added. To appear in PRD1