Statistical mechanical evaluation of phase-space integrals

Numerical evaluation of phase space integrals by sector decomposition

In a series of papers we have developed the method of iterated sector decomposition for the calculation of infrared divergent multi-loop integrals. Here we apply it to phase space integrals to calculate a contribution to the double real emission part of the ee → 2 jets cross section at NNLO. The explicit cancellation of infrared poles upon summation over all possible cuts of a given topology is...

Semiclassical trace formulas in terms of phase space path integrals

Semiclassical trace formulas are examined using phase space path integrals. Our main concern in this paper is the Maslov index of the periodic orbit, which seems not fully understood in previous works. We show that the calculation of the Maslov index is reduced to a classification of connections on a vector bundle over S with structure group Sp(2n,R). We derive a formula for the index of the n-...

Feynman path integrals on phase space and the metaplectic representation

A quantum mechanical representation in phase space

A quantum mechanical representation suitable for studying the time evolution of quantum densities in phase space is proposed and examined in detail. This representation on 2'2 (2) phase space is based on definitions of the operators P and Q in phase space that satisfy various correspondences for the Liouville equation in classical and quantum phase space, as well as quantum position and momentu...

Quantum–Mechanical Dualities from Classical Phase Space

The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum with respect to an observer on C. We illustrate this property explicitly in the case when classical phase space is complex n–dimensional projective space CPn. ...