Related papers: Quantum Dynamics on the Worldvolume from Classical…
We present an explicit matrix algebra quantization of the algebra of volume-preserving diffeomorphisms of the $n$-torus. That is, we approximate the corresponding classical Nambu brackets using…
M-branes are related to theories on function spaces $\cal{A}$ involving M-linear non-commutative maps from $\cal{A} \times \cdots \times \cal{A}$ to $\cal{A}$. While the Lie-symmetry-algebra of volume preserving diffeomorphisms of $T^M$…
We give a representation of the volume preserving diffeomorphism of $\bR^p$ in terms of the noncommutative (p-2)-branes whose kinetic term is described by the Hopf term. In the static gauge, the (p-2)-brane can be described by the free…
The dynamics of a classical branelike object in a curved background is derived from the covariant stress-energy conservation of the brane matter. The world sheet equations and boundary conditions are obtained in the pole-dipole…
We briefly introduce the conception on Euler-Lagrange cohomology groups on a symplectic manifold $(\mathcal{M}^{2n}, \omega)$ and systematically present the general form of volume-preserving equations on the manifold from the cohomological…
In canonical gravity, covariance is implemented by brackets of hypersurface-deformation generators forming a Lie algebroid. Lie algebroid morphisms therefore allow one to relate different versions of the brackets that correspond to the same…
We present a geometrical inspired study of the dynamics of $Dp$-branes. We focus on the usual nonpolynomial Dirac-Born-Infeld action for the worldvolume swept out by the brane in its evolution in general background spacetimes. We emphasize…
In this paper we discuss the relation between the unimodularity of a Lie algebroid $\tau_{A}: A\to Q$ and the existence of invariant volume forms for the hamiltonian dynamics on the dual bundle $A^{*}$. The results obtained in this…
Several quantum mechanical wave equations for $p$-branes are proposed based on the role that the volume-preserving diffeomorphisms group has on the physics of extended objects. The $p$-brane quantum mechanical wave equations determine the…
A model for 2D-quantum gravity from the Virasoro symmetry is studied. The notion of space-time naturally arises as a homogeneous space associated with the kinematical (non-dynamical) SL(2,R) symmetry in the kernel of the Lie-algebra central…
The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…
Moser proved in 1965 in his seminal paper that two volume forms on a compact manifold can be conjugated by a diffeomorphism, that is to say they are equivalent, if and only if their associated cohomology classes in the top cohomology group…
Phase Space is the framework best suited for quantizing superintegrable systems--systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of the hamiltonian invariants are preserved…
We consider Nambu-Poisson 3-algebras on three dimensional manifolds $ {\cal M}_{3} $, such as the Euclidean 3-space $R^{3}$, the 3-sphere $S^{3}$ as well as the 3-torus $T^{3}$. We demonstrate that in the Clebsch-Monge gauge, the Lie…
It is shown that a relativistic (i.e. a Poincar{\' e} invariant) theory of extended objects (called p-branes) is not necessarily invariant under reparametrizations of corresponding $p$-dimensional worldsheets (including worldlines for $p =…
We prove that the group of area-preserving diffeomorphisms of the 2-sphere admits a non-trivial homogeneous quasimorphism to the real numbers with the following property. Its value on any diffeomorphism supported in a sufficiently small…
We present here a cohomological analysis of the new spacetime superalgebras that arise in the context of superbrane theory. They lead to enlarged superspaces that allow us to write D-brane actions in terms of fields associated with the…
We formulate world-volume actions that describe the dynamics of Dirichlet p-branes in a flat 10d background. The fields in these theories consist of the 10d superspace coordinates and an abelian world-volume gauge field. The global…
We consider a recently proposed setup where a codimension one brane is embedded in the background of a smooth domain wall interpolating between AdS and Minkowski minima. Since the volume of the transverse dimension is infinite, bulk…