A quantum causal topology is presented. This is modeled after a non-commutative scheme type of theory for the curved finitary spacetime sheaves of the non-abelian incidence Rota algebras that represent ‘gravitational quantum causal sets’. The finitary spacetime primitive algebra scheme structures for quantum causal sets proposed here are interpreted as the kinematics of a curved and reticular l...

We find the deformed Heisenberg algebra and the Laplace-Beltrami operator on the extended h-deformed quantum plane and solve the Schrödinger equations explicitly for simple systems on the quantum plane. In the commutative limit the behavior of a quantum particle on the quantum plane becomes that of the quantum particle on the Poincaré half-plane, a surface of constant negative Gaussian curvature.

Effectuses have recently been introduced as categorical models for quantum computation, with probabilistic and Boolean (classical) computation as special cases. These ‘probabilistic’ models are called commutative effectuses. All known examples of such commutative effectuses are Kleisli categories of a monad. This paper answers the open question what properties a monad should satisfy so that its...

In this paper, we present a non-commutative version of some portions of finance theory, including theory of arbitrage, asset princing, and optional decomposition in financial markets based on finite dimensional quantum probability spaces. The binomial model (or, the CRR-model) is studied in the non-commutative setting, and in particular, we prove that a single-step model in non-commutative sett...

We give a general formula relating self cup products in cohomology to connecting maps in nonabelian cohomology, and apply it to obtain a formula for the self cup product associated to the Weil pairing.

By using a complex eld with a symmetric combination of electric and magnetic elds, a rstorder covariant Lagrangian for Maxwell's equations is obtained, similar to the Lagrangian for the Dirac equation. This leads to a dual-symmetric quantum electrodynamic theory with an in nite set of local conservation laws. The dual symmetry is shown to correspond to a helical phase, conjugate to the conserve...

Generalizing the ’t Hooft and Veltman method of unitary regulators, we demonstrate for the first time the existence of local, Lorentz-invariant, physically motivated Lagrangians of quantum-electrodynamic phenomena such that: (i) Feynman diagrams are finite and equal the diagrams of QED but with regularized propagators. (ii) N-point Green functions are causal. (iii) Smatrix relates only electron...

In this paper, we will introduce Quantum Toric Varieties which are (non-commutative) generalizations of ordinary toric varieties where all the tori classical theory replaced by quantum tori. geometry is non-commutative version theory; it generalizes non-trivially most theorems and properties geometry. By considering as (non-algebraic) stacks, show that their category equivalent to a certain fan...