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.