 Author

B.J. Nauta
 Title
 Dynamics of Gauge Fields at High Temperature
 Supervisors
 Award date
 8 November 2000
 Number of pages
 128
 Document type
 PhD thesis
 Faculty
 Faculty of Science (FNWI)
 Institute
 Institute for Theoretical Physics Amsterdam (ITFA)
 Abstract

An effective description of dynamical Bose fields is provided by the classical (hightemperature) limit of thermal field theory. The main subject of this thesis is to improve the ensuing classical field theory, that is, to include the dominant quantum corrections and to add counter terms for the RayleighJeans divergences. The dominant quantum corrections are the wellknown hard thermal loops. After a diagrammatic calculation of the HTL photon selfenergy in QED, a kinetic formulation of HTL's is given, following the work of Blaizot and Iancu. It is shown that the classical HTL equation of motion is consistent with the classical statistical theory, provided a random noise term is added.
For both SU(N) gauge theory and scalar field theory with a lambda^4 interaction term, it is demonstrated that the the RayleighJeans divergences are restricted to one and twoloop (sub)diagrams. This implies that the proof of Aarts and Smit that local mass counter terms render classical \lambda^4theory finite up to two loops, may be extended to any number of loops. It will be shown that classical oneloop diagrams that correspond to HTL's in the quantum theory lead to linear divergences; all other oneloop diagrams are finite in the classical theory. A general argument is presented that twoloop diagrams can at most give logarithmic divergences. This is explicitly verified for twoloop selfenergy corrections in SU(N) and scalar theories. We also use the Ward identities to show that the logarithmic divergence in the SU(N) selfenergy is transverse. It has been surmised that subtraction in the plasmon frequency is sufficient to render the theory free of linear divergences at one loop. This is confirmed and also that beyond oneloop linear divergences are absent. Furthermore the introduction of counter terms for classical lattice theories is investigated. It is found that to match a classical to a quantum theory is less complicated then to match a lattice theory to a continuum one. Nevertheless, in the latter case approximate counter terms can be given. In the final chapter, a different topic is approached, namely the problem of explaining the baryon asymmetry in the early universe. Usually the required CPviolation is induced in a model by an effective dimensionsix operator. In the thesis the effect of dimensioneight CPviolating operators on sphaleron transitions is studied. It is argued that in a pure gauge theory in equilibrium the distribution function of the ChernSimons number (that is related to the baryon number) will develop an asymmetry. Also a scenario for baryogenesis is presented where this effect is utilized.  Note
 Research conducted at: Universiteit van Amsterdam
 Permalink
 http://hdl.handle.net/11245/1.175165
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Thesis

Cover

Titlepage

Contents

1 Introduction

2 Classical field theory

03 Hard thermal loops

3 Hard thermal loops

4 Divergence structure of hot, realtime classical field theory

5 Counterterms for linear divergences

6 Baryonnumber generation in the broken phase

Bibliography

Samenvatting

Dankwoord

Cover

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