Quantum fields in toroidal topology

►C∗-algebra is used to describe fields in compactified space-time dimensions. ► The space-time is characterized by toroidal topologies. ► Representations of the Poincaré group are studied by using the modular operator. ► We derive non-abelian gauge theories in compactified regions of space-time. ► We show the compactification effect in the decay of particles using the S-matrix.