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Resummation and Renormalization in Effective Theories of Particle Physics (Paperback, 1st ed. 2016)
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Resummation and Renormalization in Effective Theories of Particle Physics (Paperback, 1st ed. 2016)
Series: Lecture Notes in Physics, 912
Expected to ship within 10 - 15 working days
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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.
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