We study separability of the Hamilton-Jacobi and massive Klein-Gordon equations in the general Kerr-de Sitter spacetime in all dimensions. Complete separation of both equations is carried out in 2n+1 spacetime dimensions with all n rotation parameters equal, in which case the rotational symmetry group is enlarged from (U(1)) to U(n). We explicitly construct the additional Killing vectors associ...

We consider the automorphism groups of various Lorentzian lattices over the Eisenstein, Gaussian, and Hurwitz integers, and in some of them we find reflection groups of finite index. These provide new finitecovolume reflection groups acting on complex and quaternionic hyperbolic spaces. Specifically, we provide groups acting on CH for all n < 6 and n = 7, and on HH for n = 1, 2, 3, and 5. We co...

A ne Invariant Deformation Curves A Tool for Shape Characterization Rein van den Boomgaard Dept. of Computer Science University of Amsterdam The Netherlands In this paper we describe a combination of two well-known concepts: morphological deformation curves and a ne invariant evolution processes. A morphological deformation curve is a shape descriptor obtained by continuously deforming the shap...

We propose a geometric setting for the Hamiltonian description of mechanical systems with a nonholonomic constraint, which may be used for constraints of general type (non-linear in the velocities, and such that the constraint forces may not obey Chetaev's rule). Such constraints may be realized by servomechanisms; therefore, the corresponding mechanical system may be nonconservative. In that s...

Relative equilibria of Lagrangian and Hamiltonian systems with symmetry are critical points of appropriate scalar functions parametrized by the Lie algebra (or its dual) of the symmetry group. Setting aside the structures – symplectic, Poisson, or variational – generating dynamical systems from such functions highlights the common features of their construction and analysis, and supports the co...

We investigate the canonical quantization of gravity coupled to pointlike matter in 2+1 dimensions, starting from the usual point particle action, and working in the rst order formalism. By introducing an auxiliary variable, we make the theory locally Poincar e invariant. The enlarged symmetry group simpliies the analysis of diieomorphism invariance. In the passage to the quantum theory, a non-...

The anomalous dimensions of local single trace gauge invariant operators in N = 4 supersymmetric Yang-Mills theory can be computed by diagonalizing a long range integrable Hamiltonian by means of a perturbative asymptotic Bethe ansatz. This formalism breaks down when the number of fields of the composite operator is smaller than the range of the Hamiltonian which coincides with the order in per...

Abstract Following the paradigm on the sphere, we begin the study of irrational conformal field theory (ICFT) on the torus. In particular, we find that the affine-Virasoro characters of ICFT satisfy heat-like differential equations with flat connections. As a first example, we solve the system for the general g/h coset construction, obtaining an integral representation for the general coset cha...

The fundamental structure of the universe is posited to be a network of causal relationships. Coordinate systems are interpreted as a regular structure of causal links. The discrete nature of such coordinate systems and the associated aliasing gives rise to the existence of a phase factor. This in turn leads to an interpretation of the probabilistic nature of observation and the path integral a...

The conservation of helicity in ideal barotropic fluids is discussed from a group theoretical point of view. A new symmetry group is introduced i.e. the alpha group of translations. It is proven via the Noether theorem that this group generates helicity conservation.