相关论文: Quantisation on general spaces

In the context of (2+1)--dimensional quantum gravity with negative cosmological constant and topology R x T^2, constant matrix--valued connections generate a q--deformed representation of the fundamental group, and signed area phases relate…

The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…

We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…

The variance of observables of quantum states of the Laplacian on the modular surface is calculated in the semiclassical limit. It is shown that this hermitian form is diagonalized by the irreducible representations of the modular quotient…

The phenomenology for the deep spatial geometry of loop quantum gravity is discussed. In the context of a simple model of an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used…

This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…

Several physical systems (two identical particles in two dimensions, isotropic oscillator and Kepler system in a 2-dim curved space) and mathematical structures (quadratic algebra QH(3), finite W algebra $\bar {\rm W}_0$) are shown to…

Quantum estimation of the operators of a system is investigated by analyzing its Liouville space of operators. In this way it is possible to easily derive some general characterization for the sets of observables (i.e. the possible quorums)…

We develop a new method to compute the homology groups of finite topological spaces (or equivalently of finite partially ordered sets) by means of spectral sequences giving a complete and simple description of the corresponding…

We quantize the Hamilton equations instead of the Hamilton condition. The resulting equation has the simple form $-\D u=0$ in a fiber bundle, where the Laplacian is the Laplacian of the Wheeler-DeWitt metric provided $n\not=4$. Using then…

The convenient setting for smooth mappings, holomorphic mappings, and real analytic mappings in infinite dimension is sketched. Infinite dimensional manifolds are discussed with special emphasis on smooth partitions of unity and tangent…

In this article we propose a new construction of the spatial scalar curvature operator in (1+3)-dimensional LQG based on the twisted geometry. The starting point of the construction is to express the holonomy of the spin connection on a…

The Hamiltoinian analysis of the vector-tensor theory of gravity is performed. The resulting geometrical dynamics is reformulated into the connection dynamics, with the real SU(2)-connection serving as one of the configuration variables.…

We propose a quantum mechanics of extended objects that accounts for the finite extent of a particle defined via its Compton wavelength. The Hilbert space representation theory of such a quantum mechanics is presented and this…

This paper investigates homogenization problems for the nonlocal operators with rapidly oscillating coefficients in the cases of periodic and random statistically homogeneous micro-structures. These operators involve the fractional…

We describe the quantum theory of massless (p,0)-forms that satisfy a suitable holomorphic generalization of the free Maxwell equations on Kaehler spaces. These equations arise by first-quantizing a spinning particle with a U(1)-extended…

The coadjoint orbits for the series $B_l,\ C_l$ and $D_l$ are considered in the case when the base point is a multiple of a fundamental weight. A quantization of the big cell is suggested by means of introducing a $\ast$-algebra generated…

Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…

A general deformation of the Heisenberg algebra is introduced with two deformed operators instead of just one. This is generalised to many variables, and permits the simultaneous existence of coherent states, and the transposition of…

It is shown that four-dimensional generalized symmetric spaces can be naturally equipped with some additional structures defined by means of their curvature operators. As an application, those structures are used to characterize generalized…