Game comonads provide a categorical syntax-free approach to finite model theory, and their Eilenberg-Moore coalgebras typically encode important combinatorial parameters of structures. In this paper, we develop framework whereby the essential properties these categories are captured in purely axiomatic fashion. To end, introduce arboreal categories, which have an intrinsic process structure, al...

A realistic physical axiomatic approach of the relativistic quantum field theory is presented. Following the action principle of Schwinger, a covariant and general formulation is obtained. The correspondence principle is not invoked and the commutation relations are not postulated but deduced. The most important theorems such as spin-statistics, and CPT are proved. The theory is constructed for...

The causal approach to perturbative quantum field theory is presented in detail, which goes back to a seminal work by Henri Epstein and Vladimir Jurko Glaser in 1973. Causal perturbation theory is a mathematically rigorous approach to renormalization theory, which makes it possible to put the theoretical setup of perturbative quantum field theory on a sound mathematical basis. Epstein and Glase...

Pragmatist approaches to relativistic quantum field theories (RQFTs) trade mathematical rigor for the ability to derive predictions from realistic interacting theories. Examples include the Lagrangian approach found in most textbooks, and Weinberg’s approach. Purist approaches to RQFTs trade the ability to formulate realistic interacting theories for mathematical rigor. Examples include the axi...