Resummation and Renormalization in Effective Theories of Particle Physics (Paperback, 1st ed. 2016)

Effective models of strong and electroweak interactions are extensively applied in particle physics phenomenology, and in many instances can compete with large-scale numerical simulations of Standard Model physics. These contexts include but are not limited to providing indications for phase transitions and the nature of elementary excitations of strong and electroweak matter. A precondition for obtaining high-precision predictions is the application of some advanced functional techniques to the effective models, where the sensitivity of the results to the accurate choice of the input parameters is under control and the insensitivity to the actual choice of ultraviolet regulators is ensured. The credibility of such attempts ultimately requires a clean renormalization procedure and an error estimation due to a necessary truncation in the resummation procedure. In this concise primer we discuss systematically and in sufficient technical depth the features of a number of approximate methods, as applied to various effective models of chiral symmetry breaking in strong interactions and the BEH-mechanism of symmetry breaking in the electroweak theory. After introducing the basics of the functional integral formulation of quantum field theories and the derivation of different variants of the equations which determine the n-point functions, the text elaborates on the formulation of the optimized perturbation theory and the large-N expansion, as applied to the solution of these underlying equations in vacuum. The optimisation aspects of the 2PI approximation is discussed. Each of them is presented as a specific reorganisation of the weak coupling perturbation theory. The dimensional reduction of high temperature field theories is discussed from the same viewpoint. The renormalization program is described for each approach in detail and particular attention is paid to the appropriate interpretation of the notion of renormalization in the presence of the Landau singularity. Finally, results which emerge from the application of these techniques to the thermodynamics of strong and electroweak interactions are reviewed in detail.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	Lecture Notes in Physics, 912
Release date:	November 2015
First published:	2016
Authors:	Antal Jakovac • Andras Patkos
Dimensions:	235 x 155 x 14mm (L x W x T)
Format:	Paperback
Pages:	223
Edition:	1st ed. 2016
ISBN-13:	978-3-319-22619-4
Categories:	Books > Science & Mathematics > Physics > Particle & high-energy physics Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematical modelling Books > Science & Mathematics > Physics > Thermodynamics & statistical physics > Statistical physics Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics) > General
LSN:	3-319-22619-3
Barcode:	9783319226194

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