We propose a novel BF-type formulation of real four-dimensional gravity, which generalizes previous models. In particular, it allows for an arbitrary Immirzi parameter. We also construct the analogue of the Urbantke metric for this model. PACS: 04.60.DsReal general relativity can be formulated as a constrained first-order BF-type theory of the form [1] (for an earlier alternative approach, seewhere. . = 0, 1, 2, 3 are raised and lowered with the Minkowski metric η IJ ). G(B, φ, µ) denotes a constraint quadratic in the 2-forms B IJ . Its role is to implement that, for some tetrad e I , the 2-forms take the form B IJ = * (e I ∧ e J ), with * the duality operator on Lorentz indices ( * 2 = −1). When the constraint is solved, substitution back in the action of this specific form would then recover general relativity in its first-order tetrad formulation. For Euclidean gravity, we have η IJ → δ IJ , the connection is valued in SO(4), and * 2 = +1. The constraint is of the formwith φ IJKL a Lagrange multiplier with obvious symmetries φ IJKL = −φ JIKL = −φ IJLK = φ KLIJ . It has 21 independent components. Since this is one too many, as the B IJ have 1

We present an alternative geometric inspired derivation of the quantum cosmology arising from a brane universe in the context of {\it geodetic gravity}. We set up the Regge-Teitelboim model to describe our universe, and we recover its original dynamics by thinking of such field theory as a second-order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. Our analysis highlights the second-order derivative nature of the RT model and the inherited geometrical aspect of the theory. A canonical transformation brings us to the internal physical geometry of the theory and induces its quantization straightforwardly. By using the Dirac canonical quantization method our approach comprises the management of both first- and second-class constraints where the counting of degrees of freedom follows accordingly. At the quantum level our Wheeler-De Witt Wheeler equation agrees with previous results recently found. On these lines, we also comment upon the compatibility of our approach with the Hamiltonian approach proposed by Davidson and coworkers.Comment: 11 pages, 2 figures, accepted for publication in Phys. Rev.

We consider a relativistic extended object described by a reparametrization invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behavior under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations shown to be consistent with the Euler-Lagrange equations.

The fuzzy supersphere S (2,2) F is a finite-dimensional matrix approximation to the supersphere S (2,2) incorporating supersymmetry exactly. Here the ⋆-product of functions on S (2,2) F is obtained by utilizing the OSp(2, 1) coherent states. We check its graded commutative limit to S (2,2) and extend it to fuzzy versions of sections of bundles using the methods of [1]. A brief discussion of the geometric structure of our ⋆-product completes our work.

The publishers would like to apologize for an error occurring in issue 5 (7 March 2001) of Classical and Quantum Gravity. The article by Capovilla et al was published as a Letter to the Editor, when it should have appeared as a Paper.