Related papers: On quantization of Regge links
The quantum measure in area tensor Regge calculus can be constructed in such the way that it reduces to the Feynman path integral describing canonical quantisation if the continuous limit along any of the coordinates is taken. This…
For a finite dimensional semisimple Lie algebra ${\frak{g}}$ and a root $q$ of unity in a field $k,$ we associate to these data a double quiver $\bar{\cal{Q}}.$ It is shown that a restricted version of the quantized enveloping algebras…
Simplicial lattices provide an elegant framework for discrete spacetimes. The inherent orthogonality between a simplicial lattice and its circumcentric dual yields an austere representation of spacetime which provides a conceptually simple…
We study the ground state wave function for a universe which is topologically a lens space within the Regge calculus approach. By restricting the four dimensional simplicial complex to be a cone over the boundary lens space, described by a…
If nature is described by string theory, and if the compactification radius is large (as suggested by the unification of couplings), then the theory is in a regime best described by the low energy limit of $M$-theory. We discuss some…
This paper is devoted to study of differential calculi over quadratic algebras, which arise in the theory of quantum bounded symmetric domains. We prove that in the quantum case dimensions of the homogeneous components of the graded vector…
Simplicial approximation and the ideas associated with the Regge calculus.provide a concrete way of implementing a sum over histories formulation ofquantum gravity. A four-dimensional simplicial geometry is made up of flat four-simplices…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
The convergence properties of numerical Regge calculus as an approximation to continuum vacuum General Relativity is studied, both analytically and numerically. The Regge equations are evaluated on continuum spacetimes by assigning squared…
We examine the dependence of quantization on global properties of a classical system. Quantization based on local properties may lead to ambiguities and inconsistency between local and global symmetries of a quantum system. Our quantization…
Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which…
We employ the methods of discrete (Lorentzian) Regge calculus for analysing Lorentzian quantum cosmology models with a special focus on discrete analogues of the no-boundary proposal for the early universe. We use a simple 4-polytope, a…
We extend the result in J. Reine Angew. Math. 664, 29-53, to the non-compact case. Namely, we prove that the canonical connection on a simply connected and irreducible naturally reductive space is unique, provided the space is not a sphere,…
A scalar quantum field theory defined on a discrete spatial coordinate is examined. The renormalization of the lattice propagator is discussed with an emphasis on the periodic nature of the associated momentum coordinate. The analytic…
We show that R-matricies of all simple quantum groups have the properties which permit to present quantum group twists as transitions to other coordinate frames on quantum spaces. This implies physical equivalence of field theories…
We define a simplified version of Regge quantum gravity where the link lengths can take on only two possible values, both always compatible with the triangle inequalities. This is therefore equivalent to a model of Ising spins living on the…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for…
A time-dependent completely integrable Hamiltonian system is quantized with respect to time-dependent action-angle variables near an instantly compact regular invariant manifold. Its Hamiltonian depends only on action variables, and has a…
The continuous limit of one dimensional discrete-time quantum walks with time- and space-dependent coefficients is investigated. A given quantum walk does not generally admit a continuous limit but some families (1-jets) of quantum walks…
The discrete spectrum of complex Jacobi matrices that are compact perturbations of the discrete laplacian is under consideration. The rate of stabilization for the the matrix entries which provides finiteness of the discrete spectrum and is…