Related papers: Polydimensional Supersymmetric Principles
The most general 2+1 dimensional spinning particle model is considered. The action functional may involve all the possible first order Poincare invariants of world lines, and the particular class of actions is specified thus the…
In three space dimensions, when a physical system possesses spherical symmetry, the dynamical equations automatically lead to the Legendre and the associated Legendre equations, with the respective orthogonal polynomials as their standard…
The space-time geometry is considered to be a physical geometry, i.e. a geometry described completely by the world function. All geometrical concepts and geometric objects are taken from the proper Euclidean geometry. They are expressed via…
The Clifford action on superspaces is analyzed with a view on generalized Dirac fields taking values in some Clifford supermodule. the stress is here on two principles: complexification and polarisation. For applications in field theory,…
The classical motion of spinning particles can be described without employing Grassmann variables or Clifford algebras, but simply by generalizing the usual spinless theory. We only assume the invariance with respect to the Poincare' group;…
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
We show that Wigner's infinite spin particle classically is described by a reparametrization invariant higher order geometrical Lagrangian. The model exhibit unconventional features like tachyonic behaviour and momenta proportional to…
Geometric Algebra and Calculus are mathematical languages encoding fundamental geometric relations that theories of physics seem to respect. We propose criteria given which statistics of expressions in geometric algebra are computable in…
This paper challenges some of the common assumptions underlying the mathematics used to describe the physical world. We start by reviewing many of the assumptions underlying the concepts of real, physical, rigid bodies and the translational…
The equations defining pure spinors are interpreted as equations of motion formulated on the lightcone of a ten-dimensional, lorentzian, momentum space. Most of the equations for fermion multiplets, usually adopted by particle physics, are…
The propagator of a spinning particle in external Abelian field and in arbitrary dimensions is presented by means of a path integral. The problem has different solutions in even and odd dimensions. In even dimensions the representation is…
Considering an extension of the principle of covarience to the action along a path in relativistic Lagrangian mechanics, we motivate the use of geometric -- i.e. covariant and parameter invariant -- Lagrangian functions. We then study some…
From the simple Lagrangian the equations of motion for the particle with spin are derived. The spin is shown to be conserved on the particle world-line. In the absence of a spin the equation coincides with that of a geodesic. The equations…
The E. Cartan's equations defining "simple" spinors (renamed "pure" by C. Chevalley) are interpreted as equations of motions for fermion multiplets in momentum spaces which, in a constructive approach based bilinearly on those spinors,…
We present a simple method to derive the semiclassical equations of motion for a spinning particle in a gravitational field. We investigate the cases of classical, rotating particles (pole-dipole particles), as well as particles with…
Lagrangian contact supersymmetries (depending on derivatives of arbitrary order) are treated in very general setting. The cohomology of the variational bicomplex on an arbitrary graded manifold and the iterated cohomology of a generic…
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic…
The superspace Lagrangian formulation of N=1 supersymmetric quantum mechanics is presented. The general Lagrangian constructed out of chiral and antichiral supercoordinates containing up to two derivatives and with a canonically normalized…
Many difficulties of interpretation met by contemporary researchers attempting to recast or generalize Dirac's, Proca's, or Maxwell's theories using biquaternions or Clifford numbers have been encountered long ago by a number of physicists…
We propose a graded classification of the entire field of multivector physics, including all alternative points of view. The (often tacit) postulates of different types of formulations are contrasted, summarizing their consequences.…