Renormalisation II: Improving perturbation theory

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Perturbation Theory ◽  
Critical Phenomena ◽  
Renormalisation Group ◽  
Green Functions ◽  
Ward Identities ◽  
Generating Functional ◽  
Vacuum Polarisation ◽  
Quantum Action ◽  
Effective Theories

This chapter introduces the quantum action as the generating functional of 1PI Green functions. The Ward identities of QED are derived and the vacuum polarisation is calculated. The renormalisation group equations are introduced. Critical phenomena and Wilsonian effective theories are discussed.

scholarly journals Aspects on Effective Theories and the QCD Transition

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 945
Author(s):  
Angel Gómez Nicola
Keyword(s):  
Phase Diagram ◽  
Perturbation Theory ◽  
Quantum Chromodynamics ◽  
Chiral Symmetry ◽  
Current Knowledge ◽  
Chiral Symmetry Restoration ◽  
Chiral Perturbation ◽  
Ward Identities ◽  
Hadron Gas ◽  
Effective Theories

We review recent advances in the understanding of the Quantum Chromodynamics (QCD) transition and its nature, paying special attention to the analysis of chiral symmetry restoration within different approaches based on effective theories. After presenting some of the main aspects of the current knowledge of the phase diagram from the theoretical, experimental and lattice sides, we discuss some recent problems where approaches relying on effective theories have been particularly useful. In particular, the combination of ideas such as Chiral Perturbation Theory, unitarity and Ward Identities allows us to describe successfully several observables of interest. This is particularly relevant for quantities expected to be dominated by the light meson components of the hadron gas such as the scalar and topological susceptibilities. In addition, ward identities and effective Lagrangians provide systematic results regarding chiral and U ( 1 ) A partner degeneration properties which are of great importance for the interplay between those two transitions and the nature of chiral symmetry restoration. Special attention is paid to the connection of this theoretical framework with lattice simulations.

scholarly journals Supersymmetric invariant theories

2014 ◽  
Vol 29 (11n12) ◽  
pp. 1450065 ◽  
Author(s):  
S. R. Esipova ◽  
P. M. Lavrov ◽  
O. V. Radchenko
Keyword(s):  
Ward Identity ◽  
Direct Consequence ◽  
Functional Integral ◽  
Field Theories ◽  
Green Functions ◽  
Exact Form ◽  
Generating Functional ◽  
Quantum Description ◽  
Change Of Variables ◽  
Quantum Action

We study field models for which a quantum action (i.e. the action appearing in the generating functional of Green functions) is invariant under supersymmetric transformations. We derive the Ward identity which is a direct consequence of this invariance. We consider a change of variables in functional integral connected with supersymmetric transformations when its parameter is replaced by a nilpotent functional of fields. Exact form of the corresponding Jacobian is found. We find restrictions on generators of supersymmetric transformations when a consistent quantum description of given field theories exists.

scholarly journals Contribution of QCD condensates to the OPE of Green functions of chiral currents

2019 ◽  
Vol 199 ◽  
pp. 05025
Author(s):  
Tomáš Kadavý ◽  
Karol Kampf ◽  
Jiří Novotný
Keyword(s):  
Perturbation Theory ◽  
Operator Product Expansion ◽  
High Energy ◽  
Operator Product ◽  
Green Functions ◽  
Chiral Perturbation ◽  
Unknown Parameters ◽  
Energy Behaviour ◽  
Intrinsic Parity ◽  
Effective Theories

A framework of operator product expansion (OPE) allows us to study high-energy behaviour of Green functions. A calculation of such Green functions within chiral perturbation theory (χPT) or resonance chiral theory (RχT) and subsequent matching of the result to the OPE enables us to determine constraints for unknown parameters of the effective theories. We present such procedure for Green functions in the odd-intrinsic parity sector of QCD.

Quantum Field Theory at Higher Orders

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Power Counting ◽  
Renormalisation Group ◽  
Green Functions ◽  
Quantum Field

Perturbation theory calculations at higher orders. Power counting. General regularisation schemes. Dimensional regularisation. Explicit 1-loop renormalisation for ϕ‎4 and QED. Discussion of higher orders. Renormalisation of Green functions with composite operators. The renormalisation group.

scholarly journals Fitting the lattice vacuum polarisation function to perturbation theory

2014 ◽  
Author(s):  
Gregorio Herdoiza ◽  
Hanno Horch ◽  
Benjamin Jaeger ◽  
Hartmut Wittig
Keyword(s):  
Perturbation Theory ◽  
Vacuum Polarisation
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