scholarly journals Continuous Renormalization Group Analysis of Spectral Problems in Quantum Field Theory

2015 ◽  
Vol 268 (4) ◽  
pp. 749-823 ◽  
Author(s):  
Volker Bach ◽  
Miguel Ballesteros ◽  
Jürg Fröhlich
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Group Analysis ◽  
Quantum Field ◽  
Renormalization Group Analysis ◽  
Spectral Problems

scholarly journals DIRAC EQUATION FOR QUASI-PARTICLES IN GRAPHENE AND QUANTUM FIELD THEORY OF THEIR COULOMB INTERACTION

2012 ◽  
Vol 26 (21) ◽  
pp. 1242005 ◽  
Author(s):  
RIAZUDDIN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Dirac Equation ◽  
Coulomb Interaction ◽  
Group Analysis ◽  
Fermi Velocity ◽  
Quantum Field ◽  
Renormalization Group Analysis ◽  
Self Energy ◽  
Conserved Currents

There is evidence for existence of massless Dirac quasiparticles in graphene, which satisfy Dirac equation in (1+2) dimensions near the so called Dirac points which lie at the corners at the graphene's brilluoin zone. We revisit the derivation of Dirac equation in (1+2) dimensions obeyed by quasiparticles in graphene near the Dirac points. It is shown that parity operator in (1+2) dimensions play an interesting role and can be used for defining "conserved" currents resulting from the underlying Lagrangian for Dirac quasiparticles in graphene which is shown to have UA(1) × UB(1) symmetry. Further the quantum field theory (QFT) of Coulomb interaction of 2D graphene is developed and applied to vacuum polarization and electron self-energy and the renormalization of the effective coupling g of this interaction and Fermi velocity vf which has important implications in the renormalization group analysis of g and vf.

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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