Infrared properties of scalar field theories

Marchais, Edouard (2013) Infrared properties of scalar field theories. Doctoral thesis (PhD), University of Sussex.

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Phase transitions and critical phenomena are of central importance in quantum field theory and statistical physics. We investigate the low energy properties of O(N) symmetric
scalar field theories using functional renormalisation group methods for all N. This modern formulation of Wilson's renormalisation group allows a continuous interpolation between short and long distance physics without resorting to a weak coupling expansion. To leading order in the derivative expansion, we study the phase transition and the approach to convexity in the deep infrared limit. In the limit of infinite N, the fluctuations of the Goldstone modes dominate allowing for a complete analytical discussion of the effective potential. For finite N, the radial fluctuations become important and we resort to systematic series expansions. In both cases a systematic and thorough analysis of the diverse fixed point solutions is carried out. This leads to a comprehensive picture of the scaling potential for a large number of universality classes. We also study the dependence of our results on the regularisation scheme. Finally, we establish that the infrared completion of the effective potential in the broken phase is driven by a fixed point that leads to the flattening of the non-convex part of the potential.

Item Type: Thesis (Doctoral)
Schools and Departments: School of Mathematical and Physical Sciences > Physics and Astronomy
Subjects: Q Science > QC Physics > QC0770 Nuclear and particle physics. Atomic energy. Radioactivity
Depositing User: Library Cataloguing
Date Deposited: 28 Jun 2013 05:13
Last Modified: 10 Sep 2015 15:24

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