Dr Pok Man Lo (IFT)

CANCELLED: S-matrix approach to quantum virial expansion

THIS SEMINAR IS POSTPONED ON A LATER TIME In this talk, we discuss the application of S-mat rix formalism to study higher virial coefficients for a quantum-mechanical system of hadrons. The virial expansion provides a convenient way to parametrize the equation of state of a many-body system. It expresses the partition function and various thermodynamic functions as a power series in the particle density. For a classical system (e.g. the van der Waals non-ideal gas), the coefficients of the expansion can be computed directly from the Hamiltonian using the standard Mayer cluster expansion. The quantum version of such expansion has been formulated by Dashen, Ma and Bernstein within the framework of S-matrix. This allows the exact calculation of the 2nd virial coefficient from the knowledge of phase shift. We shall review briefly how this formalism can be applied to describe system of hadrons in heavy ion collisions. Using the input of empirical phase shifts from hadron scattering experiments, the important physics of resonance widths, coupling strengths and unitary constraints are naturally incorporated, beyond the capability of the standard Breit-Wigner formulation. The extension to third (and higher) virial coefficients is more challenging. Here, we attempt a generalization of two-body phase shift and define an analogous physical quantity suitable for discussing N-body scatterings. We shall examine such generalized phase shift in details for a gas of pions.