相关论文: Thomas precession angle and spinor algebra

Fundamentals of the local smooth loops due to Sabinin are concisely outlined together with the corresponding infinitesimal objects, so-called \nu-hyperalgebras, and the analogue of the Lie groups theory. We apply here this theory to to…

This is a review article of eleven dimensional supergravity in which we present all necessary calculations, namely the Noether procedure, the equations of motion (without neglecting the fermions), the Killing spinor equation, as well as…

An approximation result for the bilinear Hilbert transform is proved and used for the inversion of the bilinear Hilbert transform. Also, p-Lebesgue points $(p\geq 1)$ are analyzed.

We present a Mathematica package for doing computations with gamma matrices, spinors, tensors and other objects, in any dimension and signature. The approach we use is based on defining the commutation relations of the relevant matrices,…

The Bloch equations, which describe spin precession and relaxation in external magnetic fields, can be generalized to include the evolution of polarization tensors of various ranks in arbitrary multipole fields. The derivation of these…

We extend many theorems from the context of solid angle sums over rational polytopes to the context of solid angle sums over real polytopes. Moreover, we consider any real dilation parameter, as opposed to the traditional integer dilation…

We provide a simple topological derivation of a formula for the Reidemeister and the analityc torsion of spheres.

This preprint concerns a mathematically rigorous treatment of an interesting physical phenomenon in relativity theory. We would like to draw the reader's attention particularly to the abstract mathematical formalism of relativity (which was…

We determine the nonlinear transformations between coordinate systems which are mutually in a constant symmetrical accelerated motion. The maximal acceleration limit follows from the kinematical origin and it is an analogue of the maximal…

An exposition of the basic geometry of twistor integrals, intended for mathematicians.

For a spin-polarized plane wave passing through a spin-rotator containing uniform magnetic field, we provide a detailed analysis for solving the appropriate Schr\"{o}dinger equation. A modified expression for spin precession is obtained…

We consider the problem of a sphere rolling of a curved surface and solve it by mapping it to the precession of a spin 1/2 in a magnetic field of variable magnitude and direction. The mapping can be of pedagogical use in discussing both…

Reducing the NP-problems to the convex/linear analysis on the Birkhoff polytope.

In the first part of the paper we give a tensor version of the Dirac equation. In the second part we formulate and analyse a simple model equation which for weak external fields appears to have properties similar to those of the…

We define a certain abstract planar algebra by generators and relations, study various aspects of its structure, and then identify it with Jones' spin planar algebra.

This book is an introduction to the nascent field of Fourier analysis on polytopes, and cones. There is a rapidly growing number of applications of these methods, so it is appropriate to invite students, as well as professionals, to the…

We provide a complete structure theorem for involutory matrices. This yields a new approach to principal angles between subspaces and provide a series of nice formulae for these angles.

We study the apsidal precession of a Physical Symmetrical Pendulum (Allais' precession) as a generalization of the precession corresponding to the Ideal Spherical Pendulum (Airy's Precession). Based on the Hamilton-Jacobi formalism and…

Some unfortunate errors from our paper math/0505591 are corrected.

Discrete analogs of extrema of curvature and generalizations of the four-vertex theorem to the case of polygons and polyhedra are suggested and developed. For smooth curves and polygonal lines in the plane, a formula relating the number of…