In this paper, the unitarization of the two–parameter deformed quantum group GLp,q (2) is studied. This results in a non-commutative phase associated with the unitarization of the quantum group. After the achievement of the quantum group Up,q (2) with pq real via a non–commutative phase, the representation of the algebra is built by means of the action of the operators constituting the Up,q (2)...

This paper is an introduction to discrete physics based on a non-commutative calculus of finite differences. This gives a context for the Feynman-Dyson derivation of non-commutative electromagnetism, and for generalizations of this result. The paper discusses these ideas and their relations with quantum groups and topological quantum field theory.

In recent years methods have been proposed to extend classical game theory into the quantum domain. In a previous publication the nature of several non-commutative games was briefly analyzed. Here we give an analysis of the simplest non-commutative quantum game, which is a gambling game much like simple heads or tails. The quantum game displays strategies which, though non direct-product strate...

Proposals that quantum gravity gives rise to non-commutative spacetime geometry and deformations of Poincaré symmetry are examined in the context of (2+1)dimensional quantum gravity. The results are expressed in five lessons, which summarise how the gravitational constant, Planck’s constant and the cosmological constant enter the non-commutative and non-cocommutative structures arising in (2+1)...

Quantum electrodynamic effects have been systematically tested in the progression of rotational quantum states in the X 1Σ(g)(+), v=0 vibronic ground state of molecular hydrogen. High-precision Doppler-free spectroscopy of the EF 1Σ(g)(+)-X 1Σ(g)(+) (0,0) band was performed with 0.005  cm(-1) accuracy on rotationally hot H2 (with rotational quantum states J up to 16). QED and relativistic contr...

We show that any quantum family of maps from a non commutative space to a compact quantum metric space has a canonical quantum semi metric structure.

The emerging field of plasmonics may lead to enhanced light–matter interactions at extremely nanoscale regions. Plasmonic (metallic) devices promise efficiently control classical and quantum properties light. waveguides are usually employed excite confined electromagnetic modes that can strongly interact with matter. Analysis shows nanowaveguides share similarities their low-frequency microwave...