A new approach for the vertical part of the contour in thermal field theories

A lot of work has been devoted in the past to understand the role of vertical branch of the time path in thermal field theories, and in particular to see how to deal with it in the real-time formalism. Unlike what is commonly believed, I emphasize on the fact that the vertical part of the path contributes to real-time Green's functions, and I prove that this contribution is taken into account simply by the substitution $n(\omega_{\boldsymbol k})\to n(|k_o|)$ in the real time Feynman rules. This new proof is based on very simple algebraic properties of the contour integration.Comment: LaTeX2e, 2 postscript figures (requires the package graphics), 14 page

Kinetic theory of a longitudinally expanding system

We use kinetic theory in order to study the role of quantum fluctuations in the isotropization of the pressure tensor in a system subject to fast longitudinal expansion, such as the matter produced in the early stages of a heavy ion collision.Comment: Proceedings of the POETIC 6 conference. 7 figures, 7 page

Cutting rules in the real time formalisms at finite temperature

In this paper, we review the set of rules specific to the calculation of the imaginary part of a Green's function at finite temperature in the real-time formalisms. Emphasis is put on the clarification of a recent controversy concerning these rules in the "1/2" formalism, more precisely on the issue related to the interpretation of these rules in terms of cut diagrams, like at T=0. On the second hand, new results are presented, enabling one to calculate the imaginary part of thermal Green's functions in other formulations of the real-time formalism, like the "retarded/advanced" formalism in which a lot of simplifications occur.Comment: 25 pages, LaTeX file with "article" style, 6 postscript figures included by \epsfbo

Fluctuations of the initial color fields in high energy heavy ion collisions

In the Color Glass Condensate approach to the description of high energy heavy ion collisions, one needs to superimpose small random Gaussian distributed fluctuations to the classical background field, in order to resum the leading secular terms that result from the Weibel instability, that would otherwise lead to pathological results beyond leading order. In practical numerical simulations, one needs to know this spectrum of fluctuations at a proper time $\tau \ll Q_s^{-1}$ shortly after the collision, in the Fock-Schwinger gauge $A^\tau=0$. In this paper, we derive these fluctuations from first principles, by solving the Yang-Mills equations linearized around the classical background, with plane wave initial conditions in the remote past. We perform the intermediate steps in light-cone gauge, and we convert the results to the Fock-Schwinger gauge at the end. We obtain simple and explicit formulas for the fluctuation modes.Comment: 36 pages, 5 figures (final version, includes a brief discussion of the numerical implementation