Semi-classical periodic-orbit theory for chaotic Hamiltonians with discrete symmetries

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We generalize an idea applied recently to the case of identical particles and present a group-theoretical analysis of the periodic-orbit structure of a chaotic dynamical system with a discrete symmetry. The class structure of the group provides the key for the classification of periodic orbits. This structure perfectly fits the quantum-mechanical trace formula which is the starting point for the Balian-Bloch-Gutzwiller semi-classical approximation. For a specific irreducible representation of the symmetry group, we derive a modified form of the periodic-orbit sum.