In this work, we give a general class of solutions of the spinning cosmic string in Einstein’s theory of gravity. After treating same problem in Einstein Cartan (EC) theory of gravity, the exact solution satisfying both exterior and interior space-times representing a spin fluid moving along the symmetry axis is presented in the EC theory. The existence of closed timelike curves in this spaceti...

We investigate the relations between spinors and null vectors in Clifford algebra of any dimension with particular emphasis on the conditions that a spinor must satisfy to be simple (also: pure). In particular we prove: i) a new property for null vectors: each of them bisects spinor space into two subspaces of equal size; ii) that simple spinors form one-dimensional subspaces of spinor space; i...

Let G=H be an irreducible globally hyperbolic semisimple symmetric space, and let S G be a subsemigroup containing H not isolated in S. We show that if S o 6 = then there are H-invariant minimal and maximal cones C min C max in the tangent space at the origin such that H exp C min S HZ K (a) exp C max. A double coset decomposition of the group G in terms of Cartan subspaces and the group H is p...

In this paper we review the recently proposed path-integral counterpart of the Koopman-von Neumann operatorial approach to classical Hamiltonian mechanics. We identify in particular the geometrical variables entering this tbrmulation and show that they are essentially a basis of the cotangent bundle to the tangent bundle to phase-space. In this space we introduce an extended Poisson brackets st...

Complex simple Lie algebras were classified by Cartan and Killing 100 years ago. Their proof proceeds by reducing the question to a combinatorical problem: the classification of irreducible root systems, and then performing the classification. We present a new proof of the classification via the projective geometry of homogeneous varieties. Our proof is constructive: we build a homogeneous spac...

In this paper we review the recently proposed path-integral counterpart of the Koopman-von Neumann operatorial approach to classical Hamiltonian mechanics. We identify in particular the geometrical variables entering this formulation and show that they are essentially a basis of the cotangent bundle to the tangent bundle to phase-space. In this space we introduce an extended Poisson brackets st...

It is shown that for the generalized rigid body certain Cartan subalgebras (called of coordinate type) of so(n) are equilibrium points for the rigid body dynamics. In the case of so(4) there are three coordinate type Cartan subalgebras which form the set of all the regular equilibria. These coordinate type Cartan subalgebras are the analogues of the three axes of equilibria for the classical ri...

We perform the non-linear realisation or the coset formulation of the pure N = 4, D = 5 supergravity. We derive the Lie superalgebra which parameterizes a coset map whose induced Cartan-Maurer form produces the bosonic field equations of the pure N = 4, D = 5 supergravity by canonically satisfying the Cartan-Maurer equation. We also obtain the first-order field equations of the theory as a twis...

We prove a two-sided transference theorem between $$L^{p}$$ spherical multipliers on the compact symmetric space U/K and vector $$i{\mathfrak {p}},$$ where Lie algebra of U has Cartan decomposition $$\mathfrak {k\oplus }i{\mathfrak {p}}$$ . This generalizes classic deLeeuw relating $$ L^{p}(\mathbb {T)}$$ $$L^{p}(\mathbb {R)}$$

In this work, we investigate the effects of torsion–fermionic interaction on energy levels fermions within a Riemann–Cartan geometry using model-independent approach. We consider case minimally coupled to background torsion as well non-minimal extensions via additional couplings with vector and axial fermionic currents which include parity-breaking interactions. limit zero-curvature, for cases ...