Related papers: A Spacetime for SU(N)
We discuss non-Lorentzian Lagrangian field theories in $2n-1$ dimensions that admit an $SU(1,n)$ spacetime symmetry which includes a scaling transformation. These can be obtained by a conformal compactification of a $2n$-dimensional…
Let $N$ be a Riemannian, neutral or Lorentzian $4$-dimensional space form. In this paper, the expressions of the equations of Gauss, Codazzi and Ricci of a space-like or time-like surface in $N$ given in [7] are naturally understood in…
We shall here discuss a new spacetime gauge-covariant Lagrangian formulation of General Relativity by means of the Barbero-Immirzi SU(2)-connection on spacetime. To the best of our knowledge the Lagrangian based on SU(2) spacetime fields…
This work is focused on searching a geodesic interpretation of the dynamics of a particle under the effects of a Snyder like deformation in the background of the Kepler problem. In order to accomplish that task, a newtonian spacetime is…
Noncommutativity of the spacetime coordinates has been explored in several contexts, mostly associated to phenomena at the Planck length scale. However, approaching this question through deformation theory and the principle of stability of…
We show the existence of a noncommutative spacetime structure in the context of a complete discussion on the underlying spacetime symmetries for the physical system of a free massless relativistic particle. The above spacetime symmetry…
Commuting and noncommuting space-time coordinates in a class of deformed special relativity theories are investigated. Their momentum space representation, transformation behaviour, space-time algebra, invariants and the corresponding field…
We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific…
Dynamics with noncommutative coordinates invariant under three dimensional rotations or, if time is included, under Lorentz transformations is developed. These coordinates turn out to be the boost operators in SO(1,3) or in SO(2,3)…
Spacetime is modelled by binary relations - by the classes of the automorphisms $\GL(\C^2)$ of a complex 2-dimensional vector space with respect to the definite unitary subgroup $\U(2)$. In extension of Feynman propagators for particle…
Type II supergravity on backgrounds admitting SU(3) x SU(3) structure and general fluxes is considered. Using the generalized geometry formalism, we study dimensional reductions leading to N=2 gauged supergravity in four dimensions,…
Authors derive the Lorentz-Einstein transformation for the space-time coordinates starting with a one-space dimension approach. They add to the results the invariance of the space coordinates measured perpendicular to the direction of…
The necessity of rejecting the numerical model of geometrical extension is postulated on the basis of the idea of identity of space-time and physical vacuum. An attempt is made to define space-time not via the concept of manifold, but via…
The paper contains the derivation of a general set of recurrence formulas for the calculus of the SU(3) Clebsch-Gordan coefficients. The first six sections are introductory, presenting the notations and placing SU(3) in the framework of the…
A set of compatible formulas for the Clebsch-Gordan coefficients of the quantum algebra $U_{q}({\rm su}_2)$ is given in this paper. These formulas are $q$-deformations of known formulas, as for instance: Wigner, van der Waerden, and Racah…
The Schr\"odinger equation is shown to be equivalent to a constrained Liouville equation under the assumption that phase space is extended to Grassmann algebra valued variables. For onedimensional systems, the underlying Hamiltonian…
In Parts I and II we showed that e, $\nu$ propagators can be derived from rotation invariant projection operators, thereby providing examples of how quantities with spacetime symmetry can be obtained by constraining rotationally symmetric…
We determine the coefficients of the terms multiplying the gauge fields, gravitational field and cosmological term in a scheme whereby properties are characterized by $N$ anticommuting scalar Grassmann variables. We do this for general $N$,…
We present a numerical study of the time-dependent SN equations in 3 dimensions with 3 different kinds of symmetry: spherically symmetric, axially symmetric and translationally symmetric. We find that the solutions manifest the competing…
We study S-duality transformations that mix the Riemann tensor with the field strength of a 3-form field. The dual of an (A)dS space time - with arbitrary curvature - is seen to be flat Minkowski space time, if the 3-form field has…