From Classical Mechanics to Quantum Field Theory, A Tutorial

10.1142/11556 ◽  
2020 ◽  
Author(s):  
Manuel Asorey ◽  
Elisa Ercolessi ◽  
Valter Moretti
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Classical Mechanics ◽  
Quantum Field

scholarly journals METHODS FOR THE ANALYSIS OF THE LINDSTEDT SERIES FOR KAM TORI AND RENORMALIZABILITY IN CLASSICAL MECHANICS: A review with Some Applications

1996 ◽  
Vol 08 (03) ◽  
pp. 393-444 ◽  
Author(s):  
G. GENTILE ◽  
V. MASTROPIETRO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Formal Solution ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Hamiltonian Function ◽  
Quantum Field ◽  
Kam Theorem ◽  
Renormalization Group Approach ◽  
Lindstedt Series

This paper consists in a unified exposition of methods and techniques of the renormalization group approach to quantum field theory applied to classical mechanics, and in a review of results: (1) a proof of the KAM theorem, by studying the perturbative expansion (Lindstedt series) for the formal solution of the equations of motion; (2) a proof of a conjecture by Gallavotti about the renormalizability of isochronous hamiltonians, i.e. the possibility to add a term depending only on the actions in a hamiltonian function not verifying the anisochrony condition so that the resulting hamiltonian is integrable. Such results were obtained first by Eliasson; however the difficulties arising in the study of the perturbative series are very similar to the problems which one has to deal with in quantum field theory, so that the use of the methods which have been envisaged and developed in the last twenty years precisely in order to solve them allows us to obtain unified proofs, both conceptually and technically. In the final part of the review, the original work of Eliasson is analyzed and exposed in detail; its connection with other proofs of the KAM theorem based on his method is elucidated.

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

Sign in / Sign up

Export Citation Format

Share Document