Representation of spectral functions and thermodynamics

Abstract

In this paper we study the question of effective field assignment to measured or nonperturbatively calculated spectral functions. The straightforward procedure is to approximate it by a sum of independent Breit-Wigner resonances, and assign an independent field to each of these resonances. The problem with this idea is that it introduces new conserved quantities in the free model (the new particle numbers), therefore it changes the symmetry of the system. We avoid this inconsistency by representing each quantum channel with a single effective field, no matter how complicated the spectral function is. Thermodynamical characterization of the system will be computed with this representation method, and its relation to the independent resonance approximation will be discussed.Comment: 15 pages, 9 figures, revtex

Nuclear and quark matter at high temperature

“…This observation leads to the explanation of the Gibbs paradox in interacting systems [90]. The original paradox, valid in free systems is that if the molecules of two gases differ only in a tiny, continuously disappearing thing (e.g.…”

“…In field theory we can describe this process by observing the hadronic spectral functions [90,91,17]. A mathematically similar description can be obtained using the Mott transition analogy [92][93][94][95][96][97][98].…”

“…(46) Finally, we renormalize the expressions and express pressure through thermodynamical relations. The result reads as [90,91,17]…”

QCD aboveTc: Hadrons, partons, and the continuum

“…This procedure has already been worked out in [35] and applied in [31], but in order to be self-contained, we repeat the main arguments here. We assume that the most important nonperturbative change in the system is the modification of the particle spectra, while the interaction remains weak in the complete temperature regime.…”

“…For the mathematical details we examine typical spectral functions as inputs and build effective quadratic models which are compatible with the given spectral functions. Using the formulas of [31,35] we determine the thermodynamics based on these spectral functions. The model spectral functions contain several peaks and one continuum, thermal-mass and spatial-momentum dependence.…”