Abstract
We apply a phase space expansion scheme to incorporate the N-body scattering processes in the S-matrix formulation of statistical mechanics. A generalized phase shift function suitable for studying the thermal contribution of N rightarrow N processes is motivated and examined in various models. Using the expansion scheme, we revisit how the hadron resonance gas model emerges from the S-matrix framework, and consider an example of structureless scattering in which the phase shift function can be exactly worked out. Finally we analyze the influence of dynamics on the phase shift function in a simple example of 3- and 4-body scattering.
Highlights
The S-matrix formulation of statistical mechanics by Dashen et al [1] allows the computation of the grand canonical potential in terms of scattering matrix elements
Relying on the empirical data of the scattering phase shifts, the contributions from both the low-lying resonances and the purely repulsive channels are consistently included in the description of thermodynamics
The need for the systematic inclusion of the N -body interactions in describing the thermodynamics is common for many theoretical approaches
Summary
The S-matrix formulation of statistical mechanics by Dashen et al [1] allows the computation of the grand canonical potential in terms of scattering matrix elements. We shall discuss the latter issue and make some efforts to elucidate the expansion of the N -body trace in terms of the Lorentz invariant phase space. This offers important insights into how the N -body scattering processes enter the thermodynamics. We work towards applying the S-matrix approach beyond the 2-body setting within some simplified model amplitudes. A phase space expansion scheme for handling the 2-body trace is introduced and the definition of a generalized phase shift function, suitable for describing an N → N scattering process, is motivated.
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