Related papers: Geometric Structure of Two Self-dual Fields with C…

Following the approach of Grignani and Nardelli [1], we show how to cast the two-dimensional model $L \sim curv^2 + torsion^2 + cosm.const$ -- and in fact any theory of gravity -- into the form of a Poincare gauge theory. By means of the…

Recently it has been argued, that Poincar\'{e} supersymmetric field theories admit an underlying loop space hamiltonian (symplectic) structure. Here shall establish this at the level of a general $N=1$ supermultiplet. In particular, we…

We develop an electromagnetic symplectic structure on the space-time manifold by defining a Poisson bracket in terms of an invertible electromagnetic tensor F_{\mu\nu}. Moreover, we define electromagnetic symplectic diffeomorphisms by…

We investigate the gauging of a two-dimensional deformation of the Poincare algebra, which accounts for the existence of an invariant energy scale. The model describes 2D dilaton gravity with torsion. We obtain explicit solutions of the…

In the (2+2) formulation of general relativity spacetime is foliated by a two-parameter family of spacelike 2-surfaces (instead of the more usual one-parameter family of spacelike 3-surfaces). In a partially gauge-fixed setting (double-null…

We review a construction, using the harmonic space method, of solutions to the superfield equations of motion for N-extended self-dual supergravity theories. A superspace gauge condition suitable for the performance of a component analysis…

We briefly review the structure and properties of self-dual field actions.

A gauge invariant quantization in a closed integral form is developed over a linear phase space endowed with an inhomogeneous Faraday electromagnetic tensor. An analog of the Groenewold product formula (corresponding to Weyl ordering) is…

We investigate symmetries of the scalar field theory with harmonic term on the Moyal space with euclidean scalar product and general symplectic form. The classical action is invariant under the orthogonal group if this group acts also on…

We develop a geometric approach to Poisson electrodynamics, that is, the semi-classical limit of noncommutative $U(1)$ gauge theory. Our framework is based on an integrating symplectic groupoid for the underlying Poisson brackets, which we…

Pandres has developed a theory in which the geometrical structure of a real four-dimensional space-time is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group called the conservation group.…

We study the geometry of a family of Lie groups, which contained the classical affine Lie groups, endowed with an exact left invariant symplectic form. We show that this family is closed by symplectic reduction and symplectic double…

The effect of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The analysis is most easily performed in a space of constant curvature the…

We consider compact K\"ahlerian manifolds $X$ of even dimension 4 or more, endowed with a log-symplectic structure $\Phi$, a generically nondegenerate closed 2-form with simple poles on a divisor $D$ with local normal crossings. A simple…

We present a new multisymplectic framework for second-order classical field theories which is based on an extension of the unified Lagrangian-Hamiltonian formalism to these kinds of systems. This model provides a straightforward and simple…

We study the general form of the possible kinetic terms for 2-form fields in four dimensions, under the restriction that they have a semibounded energy density. This is done by using covariant symplectic techniques and generalizes previous…

The following work demonstrates the viability of Poincar\'e symmetry in a discrete universe. We develop the technology of the discrete principal Poincar\'e bundle to describe the pairing of (1) a hypercubic lattice `base manifold' labeled…

We formulate a geometric measurement theory of dynamical classical systems possessing both continuous and discrete degrees of freedom. The approach is covariant with respect to choices of clocks and canonically incorporates laboratories.…

In the present paper we consider a generic perturbation of a nearly integrable system of $n$ and a half degrees of freedom $ H_\epsilon(\theta,p,t)=H_0(p)+\epsilon H_1(\theta,p,t)$, with a strictly convex $H_0$. For $n=2$ we show that at a…

Let $G$ be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary…