Search results for "Null vector"
showing 4 items of 4 documents
Monte Carlo investigation of a model for a three-dimensional orientational glass with short-range gaussian interaction
1987
The analogue of the Edwards-Anderson model for isotropic vector spin glasses, but taking quadrupoles instead of unit vectors at each lattice site of the considered simple cubic lattice, is studied as a model for an orientational glass. We study both the case where the quadrupole moment can orient in a three-dimensional space (m=3) and the case where the orientation is restricted to a plane (m=2), but otherwise the Hamiltonian is fully isotropic. ℋ= $$ - \sum\limits_{\left\langle {i,j} \right\rangle } {J_{ij} } \left[ {\left( {\sum\limits_{\mu = 1}^m {S_i^\mu S_j^\mu } } \right)^2 - \frac{1}{m}} \right]$$ , whereJ ij is a random gaussian interaction between nearest neighbors, andS i μ the μ'…
Lorentzian Comments on Stokes Parameters
2003
The popular Stokes statements about polarized light are interpreted in a Minkowskian language using a Lorentzian representation for the Stokes parameters and the degree of polarization. The evolution equations for Stokes parameters on a curved space-time are obtained using the parallel transport of the polarization vector along a null geodesic. The interest of these equations in Astrophysics and Relativistic Cosmology is outlined.
Quantization on the Virasoro group
1990
The quantization of the Virasoro group is carried out by means of a previously established group approach to quantization. We explicitly work out the two-cocycles on the Virasoro group as a preliminary step. In our scheme the carrier space for all the Virasoro representations is made out of polarized functions on the group manifold. It is proved that this space does not contain null vector states, even forc≦1, although it is not irreducible. The full reduction is achieved in a striaghtforward way by just taking a well defined invariant subspace ℋ(c, h), the orbit of the enveloping algebra through the vacuum, which is irreducible for any value ofc andh. ℋ(c, h) is a proper subspace of the sp…
Subdivisions of Ring Dupin Cyclides Using Bézier Curves with Mass Points
2021
Dupin cyclides are algebraic surfaces introduced for the first time in 1822 by the French mathematician Pierre-Charles Dupin. A Dupin cyclide can be defined as the envelope of a one-parameter family of oriented spheres, in two different ways. R. Martin is the first author who thought to use these surfaces in CAD/CAM and geometric modeling. The Minkowski-Lorentz space is a generalization of the space-time used in Einstein’s theory, equipped of the non-degenerate indefinite quadratic form $$Q_{M} ( \vec{u} ) = x^{2} + y^{2} + z^{2} - c^{2} t^{2}$$ where (x, y, z) are the spacial components of the vector $$ \vec{u}$$ and t is the time component of $$ \vec{u}$$ and c is the constant of the spee…