This paper is an expanded version of [28] and [30] where there is presented an introduction to a point of view for discrete foundations of physics. In taking a discrete stance, we find that the initial expression of physical observation naturally occurs in a context of non-commutative algebra. In this way a formalism similar to quantum mechanics occurs first, but not necessarily with the usual ...

We compute the shear viscosity of the non-commutative N=4 super Yang-Mills quantum field theory at strong coupling using the dual supergravity background. Special interest derives from the fact that the background presents an intrinsic anisotropy in space through the distinction of commutative and non-commutative directions. Despite this anisotropy the analysis exhibits the ubiquitous result η/...

We lay down the categorical foundations for the study of super, quantum and non-commutative combinatorics.

We develop a GL qp (2) invariant differential calculus on a two-dimensional noncommutative quantum space. Here the coordinate space for the exterior quantum plane is spanned by the differentials that are commutative (bosonic) in nature.

We present the mathematical setting of an algebraic approach to quantum theory, including the Tomita–Takesaki theory, liouvilleans and quantum dynamical systems, and non-commutative integration up to the Falcone–Takesaki theory.

We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on SUq(2) . The construction is presented within the setting of a general theory of quantum principal bundles with quantum group (Hopf algebra) fiber, associated quantum vector...

We compute the Grothendieck group K0 of non-commutative analogues of projective space bundles. Our results specialize to give the K0-groups of non-commutative analogues of projective spaces, and specialize to recover the K0-group of a usual projective space bundle over a regular noetherian separated scheme. As an application, we develop an intersection theory for quantum ruled surfaces.

Strongly confined photonic modes can couple to quantum emitters and mechanical excitations. To harness the full potential in quantum photonic circuits, interactions between different constituents have to be precisely and dynamically controlled. Here, a prototypical coupled element, a photonic molecule defined in a photonic crystal membrane, is controlled by a radio frequency surface acoustic wa...

The typical values of R = quantum energy/potential amplitude in electron energy of an incident radiation treated in quantum electrodynamics, an electric wiggler, and a magnetic wiggler are 108, 10–4 and 10–10, respectively. Therefore, the interaction of a free electron with these fields cannot be described with the same principle. The wave-function phase of the final state through a transition ...