We introduce a family of hypergroups, called weakly complete, generalizing the construction complete hypergroups. Starting from given group G, our prescribes β-classes hypergroups and allows some hyperproducts not to be parts, based on suitably defined relation over G. The commutativity degree can related that underlying group. Furthermore, in analogy commutativity, we completeness finite analy...

Considering operators defined using Structural Operational Semantics (SOS), commutativity axioms are intuitive properties that hold for many of them. Proving this intuition is usually a laborious task, requiring several pages of boring and standard proof. To save this effort, we propose a syntactic SOS format which guarantees commutativity for a set of composition operators.

We consider scalar field theory with space and space-time-dependent non-commutativity. In perturbation theory, we find that the structure of the UV/IR mixing is quite different from cases with constant non-commutativity. In particular, UV/IR mixing becomes intertwined in an interesting way with violations of momentum conservation. email: [email protected] email: [email protected]