We propose an alternative axiomatic description for non-commutative field theories (NCFT) based on some ideas by Soloviev to nonlocal quantum fields. The local commutativity axiom is replaced by the weaker condition that the fields commute at sufficiently large spatial separations, called asymptotic commutativity, formulated in terms of the theory of analytic functionals. The question of a poss...

It is known that the solution to a Cauchy problem of linear differential equations: x′(t) = A(t)x(t), with x(t0) = x0, can be presented by the matrix exponential as exp( ∫ t t0 A(s) ds)x0, if the commutativity condition for the coefficient matrix A(t) holds: [ ∫ t t0 A(s) ds, A(t) ] = 0. A natural question is whether this is true without the commutativity condition. To give a definite answer to...