Combinatorics for computing relativistic several complex variable domains

Examples are given of combinatorics involved in computing analytic extensions of several complex variable domains. These domains discussed arise in the relativistic quantum theory of fields. The results are in the form of exact symbolic computation over continuous spaces, namely several complex variable domains Cn. Underlying symmetries, which involve the discrete permutation group on n symbols and the continuous Poincaré group, are utilized in the computation. Some insight is obtained regarding factoring out translational and Lorentz invariances even though a semidirect product between them is involved. Extensions of four-point Wightman function domains are obtained explicitly beyond what was previously known. It is also thus illustrated, in a practical sense, that computation over the continuum can involve discrete combinatorial techniques.