相关论文: Quantum Curved Tetrahedron, Quantum Group Intertwi…

A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and…

It is shown that if H is a Hilbert space for a representation of a group G, then there are triplets of spaces F_H, H, F^H, in which F^H is a space of coherent state or vector coherent state wave functions and F_H is its dual relative to a…

The purpose of this paper is to introduce several basic theorems of coherent states and generalized coherent states based on Lie algebras su(2) and su(1,1), and to give some applications of them to quantum information theory for graduate…

We apply the recently suggested strategy to lift state spaces and operators for (2+1)-dimensional topological quantum field theories to state spaces and operators for a (3+1)-dimensional TQFT with defects. We start from the…

We derive an exact expression for the quantumness of a Hilbert space (defined in quant-ph/0302092), and show that in composite Hilbert spaces the signal states must contain at least some entangled states in order to achieve such a…

The Schr\"odinger cat states, constructed from Glauber coherent states and applied for description of qubits are generalized to the kaleidoscope of coherent states, related with regular n-polygon symmetry and the roots of unity. This…

Focus is on two parties with Hilbert spaces of dimension d, i.e. "qudits". In the state space of these two possibly entangled qudits an analogue to the well known tetrahedron with the four qubit Bell states at the vertices is presented. The…

Quantum mechanical phase factors can be related to dynamical effects or to the geometrical properties of a trajectory in a given space - either parameter space or Hilbert space. Here, we experimentally investigate a quantum mechanical phase…

We show how extended topological quantum field theories (TQFTs) can be used to obtain a kinematical setup for quantum gravity, i.e. a kinematical Hilbert space together with a representation of the observable algebra including operators of…

While causal perturbation theory and lattice regularisation allow treatment of the ultraviolet divergences in qed, they do not resolve the issues of constructive field theory, or show the validity of qed except as a perturbation theory. I…

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…

A quantum theory of gravity is described in the case of a positive cosmological constant in 3+1 dimensions. Both old and new results are described, which support the case that loop quantum gravity provides a satisfactory quantum theory of…

We analyse the quantum geometry of 3-dimensional deformed special relativity (DSR) and the notion of spacetime points in such a context, identified with coherent states that minimize the uncertainty relations among spacetime coordinates…

We study equivariant localization formulas for phase space path integrals when the phase space is a multiply connected compact Riemann surface. We consider the Hamiltonian systems to which the localization formulas are applicable and show…

A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…

We use boundary field theory to describe the phases accessible to a tetrahedral qubit coupled to Josephson junction chains acting as Tomonaga-Luttinger liquid leads. We prove that, in a pertinent range of the fabrication and control…

In the presence of spacetime boundaries, diffeomorphisms in gravitational theories can become physical and acquire non-vanishing Noether charges. These charges obey an algebra which, within the extended phase-space formalism, faithfully…

By applying loop quantum gravity techniques to 3D gravity with a positive cosmological constant $\Lambda$, we show how the local gauge symmetry of the theory, encoded in the constraint algebra, acquires the quantum group structure of…

We introduce a set of coherent states which are associated with quantum systems governed by a trilinear boson Hamiltonian. These states are produced by the action of a nonunitary displacement operator on a reference state and can be…

Within the generalized definition of coherent states as group orbits we study the orbit spaces and the orbit manifolds in the projective spaces constructed from linear representations. Invariant functions are suggested for arbitrary groups.…