We show that the notions of space and time in algebraic quantum field theory arise from translation symmetry if we assume asymptotic commutativity. We argue that this construction can be applied to string theory. The goal of the present paper is to understand better the foundations of string theory. I will start with the question ”What is quantum field theory?” I hope to explain that in quantum...

A general mechanism for "breaking" commutativity in algebras is proposed: if the underlying set taken to be not a crisp set, but rather an obscure/fuzzy membership function, reflecting degree of truth that element belongs can incorporated into commutation relations. The special "deformations" and $\varepsilon $-commutativity are introduced such way equal degrees result "nondeformed" case. We al...

in this paper we study the structure and the commutativity of a ring r, in which for each x,y ? r, there exist two integers depending on x,y such that [x,y]k equals x n or y n.

We study the non-commutative supersymmetric Yang-Mills theory at strong coupling using the AdS/CFT correspondence. The supergravity description and the UV/IR relation confirms the expectation that the non-commutativity affects the ultra-violet but not the infra-red of the Yang-Mills dynamics. We show that the supergravity solution dual to the non-commutative N = 4 SYM in four dimensions has no ...

Theorem 1. The convolution ∗ admits a commutativity constraint making Sph into a rigid tensor category. There exists a faithful, exact tensor “fiber” functor Sat : Sph → Vect inducing an equivalence (modulo a sign in the commutativity constraint) of Sph with Rep(G) as tensor categories, where G is the Langlands dual group of the reductive group G, whose weights are the coweights of G and vice v...

Two types of robust cycle bases are defined via recursively nice arrangements; complete and bipartite complete graphs are shown to have such bases. It is shown that a diagram in a groupoid is commutative up to natural equivalence (cutne) if for each cycle in a robust basis of the graph underlying the diagram, the composition of the morphisms is naturally equivalent to the identity. For a hyperc...

Commutativity of subsystems in cascade connected forms to form larger systems gets worthy to improve noise disturbance properties, stability, robustness and many other properties in system design. In this paper, another benefit of commutativity property is indicated, as far as the author knowledge for the first time, and illustrated by examples. This benefit is the gain of a new and original me...