相关论文: The Full Laplace-Beltrami operator on U(N) and SU(…
In this paper, we construct Laplace-Beltrami operators associated with arbitrary Riemannian metrics on noncommutative tori of any dimension. These operators enjoy the main properties of the Laplace-Beltrami operators on ordinary Riemannian…
The Lie algebroids are generalization of the Lie algebras. They arise, in particular, as a mathematical tool in investigations of dynamical systems with the first class constraints. Here we consider canonical symmetries of Hamiltonian…
The SU(3) chiral lagrangian for the lightest octets of mesons and baryons is constructed on a spacetime lattice. The lattice spacing acts as an ultraviolet momentum cutoff which appears directly in the Lagrangian so chiral symmetry remains…
The higher spin Laplace operator has been constructed recently as the generalization of the Laplacian in higher spin theory. This acts on functions taking values in arbitrary irreducible representations of the Spin group. In this paper, we…
We show that the resolvent of the Laplacian on SL(3,$\mathbb{R}$)/SO(3) can be lifted to a meromorphic function on a Riemann surface which is a branched covering of $\mathbb{C}$. The poles of this function are called the resonances of the…
Laplacian gauge fixing was introduced to find a unique representative of the gauge orbit, which on the lattice could be implemented by a ``finite'' algorithm. What was still lacking was a perturbative formulation of this gauge, which will…
We have discovered that the gauge invariant observables of matrix models invariant under U($N$) form a Lie algebra, in the planar large-N limit. These models include Quantum Chromodynamics and the M(atrix)-Theory of strings. We study here…
We review some recent results on the theory of Lagrangian systems on Lie algebroids. In particular we consider the symplectic and variational formalism and we study reduction. Finally we also consider optimal control systems on Lie…
We develop an analytical approach for studying lattice gauge theories within the plaquette representation where the plaquette matrices play the role of the fundamental degrees of freedom. We start from the original Batrouni formulation and…
A general, consistent and complete framework for geometrical formulation of mechanical systems is proposed, based on certain structures on affine bundles (affgebroids) that generalize Lie algebras and Lie algebroids. This scheme covers and…
We describe Laplacian operators on the quantum group SUq (2) equipped with the four dimensional bicovariant differential calculus of Woronowicz as well as on the quantum homogeneous space S2q with the restricted left covariant three…
It is showed how the Hamiltonian lattice $loop$ $representation$ can be cast straightforwardly in the Lagrangian formalism. The procedure is general and here we present the simplest case: pure compact QED. This connection has been shaded by…
Spaces of differential forms over configuration spaces with Poisson measures are constructed. The corresponding Laplacians (of Bochner and de Rham type) on 1-forms and associated semigroups are considered. Their probabilistic interpretation…
Lattice $SU(N)\times SU(N)$ chiral models are analyzed by strong and weak coupling expansions and by numerical simulations. $12^{th}$ order strong coupling series for the free and internal energy are obtained for all $N\geq 6$. Three loop…
We deal with a real valued integral operator L of Laplace transformation type acting between Lebesgue spaces on the semi-axis. Sufficient conditions for belonging L to Schatten type classes are obtained. Some upper asymptotic estimates for…
The spectrum of the Laplace-Beltrami operator, computed on the spatial slices of Causal Dynamical Triangulations, is a powerful probe of the geometrical properties of the configurations sampled in the various phases of the lattice theory.…
We construct a manifestly gauge invariant Lagrangian in 3+1 dimensions for N Kaluza-Klein modes of an SU(m) gauge theory in the bulk. For example, if the bulk is 4+1, the effective theory is \Pi_{i=1}^{N+1} SU(m)_i with N chiral (\bar{m},m)…
A simple Lagrangian is proposed that by the choice of the representation of SU(2), gives rise to field equations for arbitrary spin. In explicit examples it is shown, how the Klein-Gordon, the Dirac, and the Proca equation can be obtained…
We introduce the notion of a family of convolution operators associated with a given elliptic partial differential operator. Such a convolution structure is shown to exist for a general class of Laplace-Beltrami operators on two-dimensional…
For bicovariant differential calculi on quantum matrix groups a generalisation of classical notions such as metric tensor, Hodge operator, codifferential and Laplace-Beltrami operator for arbitrary k-forms is given. Under some technical…