Related papers: Geometry of Quantum Spheres
In this paper, we prove some foundational results on the deformation theory of E-infinity ring spectra.
Optical spectroscopy and quantum control of semiconductor quantum dots has become a vivid field of research. The recent progress in both theory and experiment is reviewed, with emphasis on theoretical and computational concepts.
Geometrical form of the one-loop divergences induced by conical singularities of background manifolds is studied. To this aim the heat kernel asymptotic expansion on spaces having the structure $C_{\alpha}\times \Sigma$ near singular…
The geodesic total curvature of rectifiable spherical curves is analyzed. We extend to the case of high dimension spheres the explicit formula that holds true for curves supported into the 2-sphere. For this purpose, we take advantage of…
A quantum deformation of 4-dimensional superconformal algebra realized on quantum superspace is investigated. We study the differential calculus and the action of the quantum generators corresponding to $sl_q(1|4)$ which act on the quantum…
We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum…
The quantum group structure of the Liouville theory is reviewd and shown to be an important tool for solving the theory.
After a review of the results in arXiv:1203.3184 [math-ph] about Pythagorean inequalities for products of spectral triples, I will present some new results and discuss classes of spectral triples and states for which equality holds.
The deformation quantization of Moyal-Weyl star product of functions of quaternions is investigated.
Studies of the effective regime of loop quantum gravity (LQG) revealed that, in the limit of Planckian curvature scales, spacetime may undergo a transition from the Lorentzian to Euclidean signature. This effect is a consequence of quantum…
The triple point numbers and the triple point spectrum of a closed 3-manifold were defined in (R. Vigara, Representaci\'on de 3-variedades por esferas de Dehn rellenantes, PhD Thesis, UNED 2006). They are topological invariants that give a…
We compare the geometrical and physical properties of the maths-type coherent states for $q>1$ with those of the same for $0 < q < 1$.
The spherometer used for measuring radius of curvature of spherical surfaces is explicitly based on a geometric relation unique to circles and spheres. We present an alternate approach using coordinate geometry, which reproduces the…
Differential calculus on the quantum quaternionic group GL(1,H$_q$) is introduced.
A regular spectral triple is proposed for a two-dimensional $\kappa$-deformation. It is based on the naturally associated affine group $G$, a smooth subalgebra of $C^*(G)$, and an operator $\caD$ defined by two derivations on this…
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
The quantum deformation concept is applied to a study of isovector pairing correlations in nuclei of the mass 40<A<100 region. While the non-deformed (q -> 1) limit of the theory provides a reasonable global estimate for strength parameters…
We investigate both theoretical and computational aspects of using wavelet bases to decouple physics on different scales in quantum field theory.
We study the q-deformed fuzzy sphere, which is related to D-branes on SU(2) WZW models, for both real q and q a root of unity. We construct for both cases a differential calculus which is compatible with the star structure, study the…
Geometric and topological bounds are obtained for the first energy level gap of a particle constrained to move on a compact surface in 3-space. Moreover, geometric properties are found which allows for stationary and uniformly distributed…