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 ...

In this letter we propose a possible mechanism of leftand right-handed neutrino couplings to photons, which arises quite naturally in non-commutative gauge field theory. We estimate the predicted additional energy-loss in stars induced by space-time non-commutativity. The usual requirement that any new energy-loss mechanism in globular stellar clusters should not excessively exceed the standard...

In this paper we prove that a finite partial commutative (idempotent commutative) Latin square can be embedded in a finite commutative (idempotent commutative) Latin square. These results are then used to show that the loop varieties defined by any non-empty subset of the identities {x(xy) = y, (yx)x = y} and the quasi-group varieties defined by any non-empty subset of {x” = x, x(xy) = y, (yx)x...

In [Ans08a, Ans08b], we investigated monic multivariate non-commutative orthogonal polynomials, their recursions, states of orthogonality, and corresponding continued fraction expansions. In this note, we collect a number of examples, demonstrating what these general results look like for the most important states on non-commutative polynomials, namely for various product states. In particular,...

Let R be a commutative ring with identity and T (R) its total quotient ring. We extend the notion of well-centered overring of an integral domain to an arbitrary commutative ring and we investigate the transfer of this property to different extensions of commutative rings in both integral and non-integral cases. Namely in pullbacks and trivial extensions. Our aim is to provide new classes of co...

We deal with the following question: What is the proper way to introduce symmetric difference in orthomodular lattices? Imposing two natural conditions on this operation, six possibilities remain: the two (commutative) normal forms of the symmetric difference in Boolean algebras and four noncommutative terms. It turns out that in many respects the non-commutative forms, though more complex with...

The Maxwell theory on non-commutative spaces has been considered. The non-linear equations of electromagnetic fields on non-commutative spaces were obtained in the compact spin-tensor (quater-nion) form. It was shown that the plane electromagnetic wave is the solution of the system of non-linear wave equations of the second order for the electric and magnetic induction fields. We have found the...

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/...

By a commutative term we mean an element of the free commutative groupoid F of infinite rank. For two commutative terms a, b write a ≤ b if b contains a subterm that is a substitution instance of a. With respect to this relation, F is a quasiordered set which becomes an ordered set after the appropriate factorization. We study definability in this ordered set. Among other thing, we prove that e...