scholarly journals Applied Quantum Field Theory to General Diffusion-Reaction Phenomena

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Mabrouk Benhamou
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Large Time ◽  
Large Time Behavior ◽  
Diffusion Reaction ◽  
Time Behavior ◽  
Quantum Field ◽  
Parabolic Differential Equations ◽  
Sophisticated Method

Diffusion-reaction phenomena are generally described by parabolic differential equations (PDEs), and I am interested in those possessing solutions that fail at large time. A sophisticated method to study the large-time behavior is the Renormalization Group usually encountered in Particles-Physics and Critical Phenomena. In this paper, I review the application of such an approach. In particular, attention is paid to Quantum Field Theory techniques used for the extraction of the asymptotic solutions to PDEs. Finally, I extend discussion to the fractional-time PDEs and with noise.

scholarly journals The KAM theorem and renormalization group

2009 ◽  
Vol 29 (2) ◽  
pp. 419-431 ◽  
Author(s):  
E. DE SIMONE ◽  
A. KUPIAINEN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Elementary Proof ◽  
Renormalization Group Equation ◽  
Quadratic Nonlinearity ◽  
Picard Iteration ◽  
Group Equation ◽  
Quantum Field ◽  
Kam Theorem

AbstractWe give an elementary proof of the analytic KAM theorem by reducing it to a Picard iteration of a certain PDE with quadratic nonlinearity, the so-called Polchinski renormalization group equation studied in quantum field theory.

Renormalization Group

2020 ◽  
pp. 289-318
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Critical Phenomena ◽  
Degrees Of Freedom ◽  
Gaussian Model ◽  
Coupling Constants ◽  
Quantum Field ◽  
Important Notion ◽  
Effective Hamiltonians

Chapter 8 introduces the key ideas of the renormalization group, including how they provide a theoretical scheme and a proper language to face critical phenomena. It covers the scaling transformations of a system and their implementations in the space of the coupling constants and reducing the degrees of freedom. From this analysis, the reader is led to the important notion of relevant, irrelevant and marginal operators and then to the universality of the critical phenomena. Furthermore, the chapter also covers (as regards the RG) transformation laws, effective Hamiltonians, the Gaussian model, the Ising model, operators of quantum field theory, universal ratios, critical exponents and β‎-functions.

Charge renormalization group in quantum field theory

1956 ◽  
Vol 3 (5) ◽  
pp. 845-863 ◽  
Author(s):  
N. N. Bogoljubov ◽  
D. V. šiekov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Quantum Field ◽  
Charge Renormalization
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