Petr Jizba

Quantum Field Theory of Topological Defects as Inhomogeneous Condensates

Topological defects play an important role in many physical systems ranging from cosmology to condensed matter. Thus they link apparently unrelated areas characterized by very different energy and time scales. The issue of spontaneous defect formation during symmetry breaking phase transitions has recently attracted much attention [1]. As originally pointed out by Kibble [2] and more recently by Zurek [3], different regions of a system may be unable to correlate during the quench time which characterizes the transition and, as a result, some parts of space may remain trapped in the original (symmetric) phase, giving rise to topological defects. Although the Kibble–Zurek mechanism gives a reasonable estimate of the defect density as a function of the quench time (as confirmed, for instance, by recent experiments on superfluid Helium [4]), this picture is essentially phenomenological. It is clear that a full understanding of the process of defect formation requires a full quantum field theoretical formulation of the problem. There has recently been much progress in this direction [5], and here we give some novel results based on the approach which we are currently developing. A more systematic account will be presented in two forthcoming papers [6,7].

One particular approach to the non-equilibrium quantum dynamics

We present a particular approach to the non-equilibrium dynamics of quantum field theory. This approach is based on the Jaynes-Gibbs principle of the maximal entropy and its implementation, throughout the initial-value data, into the dynamical equations for Green’s functions. We use the φ4 theory in the large N limit to show how our method works by calculating the pressure for a system which is invariant under both spatial and temporal translations.

Hydrostatic pressure of the O(N) phi**4 theory in the large N limit

With non-equilibrium applications in mind we present in this paper a self-contained calculation of the hydrostatic pressure of the O(N)\lambda \phi^4 theory at finite temperature. By combining the Keldysh-Schwinger closed-time path formalism with thermal Dyson-Schwinger equations we compute in the large N limit the hydrostatic pressure in a fully resumed form. We also calculate the high-temperature expansion for the pressure (in D=4) using the Mellin transform technique. The result obtained extends the results found by Drummond et al. [hep-ph/9708426] and Amelino-Camelia and Pi [hep-ph/9211211]. The latter are reproduced in the limits m_r(0)\to 0, T \to \infty and T \to \infty, respectively. Important issues of renormalizibility of composite operators at finite temperature are addressed and the improved energy-momentum tensor is constructed. The utility of the hydrostatic pressure in the non-equilibrium quantum systems is discussed.