The BRST transformations for gravity with torsion including Weyl symmetry are discussed by using the so-called Maurer-Cartan horizontality conditions. Also the coupling of scalar matter fields to gravity is incorporated in this analysis. With the help of an operator δ which allows to decompose the exterior space-time derivative as a BRST commutator we solve the Wess-Zumino consistency condition...

In 1990 Allen Bell presented a suucient condition for the primeness of the universal enveloping algebra of a Lie superal-gebra. Let Q be a nonsingular bilinear form on a nite-dimensional vector space over a eld of characteristic zero. In this paper we show that Bell's criterion applies to the Hamiltonian Cartan type superalgebras determined by Q, and hence obtain some new prime noetherian rings.

It is shown that the projectivised tangent bundle of Finsler spaces with the Chern connection has a contact metric structure under a conformal transformation with certain condition of the Finsler function and moreover it is locally isometric to E × Sm−1(4) for m > 2 and flat for m = 2 if and only if the Cartan tensor vanishes, i.e., the Finsler space is a Riemannian manifold. M.S.C. 2000: 53C60...

A new notion of Cartan pairs as a substitute of notion of vector fields in the noncommutative geometry is proposed. The correspondence between Cartan pairs and differential calculi is established.

A manifestly gauge invariant formulation of the coupling of the Maxwell theory with an Einstein Cartan geometry is given, where the space time torsion originates from a massless Kalb-Ramond field augmented by suitable U(1) Chern Simons terms. We focus on the situation where the torsion violates parity, and relate it to earlier proposals for gravitational parity violation. Electronic address: pa...

A limiting diagram for the Segre classification of the energy-momentum tensor is obtained and discussed in connection with a Penrose specialization diagram for the Segre types. A generalization of the coordinate-free approach to limits of Paiva et al. to include non-vacuum space-times is made. Geroch’s work on limits of space-times is also extended. The same argument also justifies part of the ...

The notion of phase plays an essential role in both semiclassical and quantum mechanics. But what is exactly a phase, and how does it change with time? It turns out that the most universal definition of a phase can be given in terms of Lagrangian manifolds by exploiting the properties of the Poincaré–Cartan form. Such a phase is defined, not in configuration space, but rather in phase space and...

In many engineering applications that use tensor analysis, such as tensor imaging, the underlying tensors have the characteristic of being positive definite. It might therefore be more appropriate to use techniques specially adapted to such tensors. We will describe the geometry and calculus on the Riemannian symmetric space of positive-definite tensors. First, we will explain why the geometry,...

We give a geometric realization of space-time spinors and associated representations, using the Jordan triple structure associated with the Cartan factors of type 4, the so-called spin factors. We construct certain representations of the Lorentz group, which at the same time realize bosonic spin-1 and fermionic spin2 wave equations of relativistic field theory, showing some unexpected relations...