arXiv subjects
Publications and source records attributed to Bert-Jan Nauta.
We show that CP-violation can lead to an asymmetric diffusion of the Chern-Simons number in thermal equilibrium. This asymmetry leads to a linearly growing expectation value of the third power of the Chern-Simons number. In the long-time limit all expectation values of powers of Chern-Simon numbers are determined by their appropriate disconnected parts.
We study Chern-Simons number diffusion in a SU(2)-Higgs model with CP-odd dimension-eight operators. We find that the thermal average of the magnitude of the velocity of the Chern-Simons number depends on the direction of the velocity. This implies that the distribution function of the Chern-Simons number will develop an asymmetry. It is argued that this asymmetry manifests itself through a linear growth of the expectation value of the third power of the Chern-Simons number. This linear behavior of the third power of a coordinate of a periodic direction is verified by a numerical solution of a one-dimensional Langevin equation. Further, we make some general remarks on thermal averages and on the possibility of the generation of the baryon asymmetry in a non-equilibrium situation due to asymmetric diffusion of the Chern-Simons number.
We calculate the effect of two CP-violating (dimension-eight) operators of the SU(2)-Higgs model on the motion along a particular path from the vacuum to the sphaleron. It turns out that CP-violation may introduce a difference between the sphaleron rate towards larger Chern-Simons number and the rate towards smaller Chern-Simons number. Such a difference induces a non-zero baryon-number without a first order phase transition.
The classical approximation provides a non-perturbative approach to time-dependent problems in finite temperature field theory. We study the divergences in hot classical field theory perturbatively. At one-loop, we show that the linear divergences are completely determined by the classical equivalent of the hard thermal loops in hot quantum field theories, and that logarithmic divergences are absent. To deal with higher-loop diagrams, we present a general argument that the superficial degree of divergence of classical vertex functions decreases by one with each additional loop: one-loop contributions are superficially linearly divergent, two-loop contributions are superficially logarithmically divergent, and three- and higher-loop contributions are superficially finite. We verify this for two-loop SU(N) self-energy diagrams in Feynman and Coulomb gauges. We argue that hot, classical scalar field theory may be completely renormalized by local (mass) counterterms, and discuss renormalization of SU(N) gauge theories.
We consider the extension of static dimensional reduction to real-time. For a scalar field theory it is shown that in the high-temperature limit this leads to an effective classical theory. Quantum corrections to the leading classical behavior are determined by an effective action which can be calculated perturbatively in the background of the classical fields. Feynman rules for (λϕ^4)-theory are given and the extension to SU($N$) gauge theories is outlined.