Multisymplectic formulation of vielbein gravity. De Donder-Weyl formulation, Hamiltonian (n-1)-forms

We consider the De Donder-Weyl (DW) Hamiltonian formulation of the Palatini action of vielbein gravity formulated in terms of the solder form and spin connection, which are treated as independent variables. The basic geometrical constructions necessary for the DW Hamiltonian theory of vielbein gravity are presented. We reproduce the DW Hamilton equations in the multisymplectic and pre-multisymplectic formulations. We also give basic examples of Hamiltonian (n-1)-forms and related Poisson brackets.Comment: 47 pages, 0 figure v4 Minor corrections. (notations more light

Torsion formulation of gravity

We make it precise what it means to have a connection with torsion as solution of the Einstein equations. While locally the theory remains the same, the new formulation allows for topologies that would have been excluded in the standard formulation of gravity. In this formulation it is possible to couple arbitrary torsion to gauge fields without breaking the gauge invariance.Comment: AMS-LaTeX, 25 pages. Appendices have been eliminated and the necessary concepts have been inroduced in the text. We have added some reference

BRST Formulation of 4-Monopoles

A supersymmetric gauge invariant action is constructed over any 4-dimensional Riemannian manifold describing Witten's theory of 4-monopoles. The topological supersymmetric algebra closes off-shell. The multiplets include the auxiliary fields and the Wess-Zumino fields in an unusual way, arising naturally from BRST gauge fixing. A new canonical approach over Riemann manifolds is followed, using a Morse function as an euclidean time and taking into account the BRST boundary conditions that come from the BFV formulation. This allows a construction of the effective action starting from gauge principles.Comment: 18 pages, Amste

An anisotropic hybrid non-perturbative formulation for 4D N = 2 supersymmetric Yang-Mills theories

We provide a simple non-perturbative formulation for non-commutative four-dimensional N = 2 supersymmetric Yang-Mills theories. The formulation is constructed by a combination of deconstruction (orbifold projection), momentum cut-off and matrix model techniques. We also propose a moduli fixing term that preserves lattice supersymmetry on the deconstruction formulation. Although the analogous formulation for four-dimensional N = 2 supersymmetric Yang-Mills theories is proposed also in Nucl.Phys.B857(2012), our action is simpler and better suited for computer simulations. Moreover, not only for the non-commutative theories, our formulation has a potential to be a non-perturbative tool also for the commutative four-dimensional N = 2 supersymmetric Yang-Mills theories.Comment: 32 pages, final version accepted in JHE

Improved-Accuracy Source Reconstructionon Arbitrary 3-D Surfaces

This paper presents a novel formulation of the source reconstruction problem on arbitrary three-dimensional (3-D) surfaces based on integral equations. Rigorous boundary integral field identities are employed to enforce that the two unknown currents are Maxwellian on the reconstruction surface; this leads to a dual integral-equation formulation, in contrast to the single-equation formulation found in literature. Numerical tests against reference currents allow a quantitative assessment of the improvements in accuracy afforded by the novel formulation, with important benefits in diagnostic application