Upper Limits for Coupling Constants in Quantum Field Theory

1963 ◽  
Vol 11 (1) ◽  
pp. 55-58 ◽  
Author(s):  
B. V. Geshkenbein ◽  
B. L. Ioffe
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Coupling Constants ◽  
Quantum Field ◽  
Upper Limits

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.

scholarly journals BOGOLUBOV'S RECURSION AND INTEGRABILITY OF EFFECTIVE ACTIONS

2001 ◽  
Vol 16 (09) ◽  
pp. 1531-1558 ◽  
Author(s):  
A. GERASIMOV ◽  
A. MOROZOV ◽  
K. SELIVANOV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hopf Algebra ◽  
Moduli Space ◽  
Feynman Diagrams ◽  
Coupling Constants ◽  
Quantum Field ◽  
Integrable Structure ◽  
Standard Formalism

The Hopf algebra of Feynman diagrams, analyzed by A. Connes and D. Kreimer, is considered from the perspective of the theory of effective actions and generalized τ-functions, which describes the action of diffeomorphism and shift groups in the moduli space of coupling constants. These considerations provide additional evidence of the hidden group (integrable) structure behind the standard formalism of quantum field theory.

ORIGIN OF FERMION MASSES

1991 ◽  
Vol 06 (40) ◽  
pp. 3697-3704
Author(s):  
J. W. MOFFAT
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Integral Equations ◽  
Mass Spectra ◽  
Coupling Constants ◽  
Quantum Field ◽  
Fermion Masses ◽  
The Standard Model ◽  
Baryon Mass ◽  
Nonlocal Quantum

An eigenvalue equation for the spectrum of lepton and quark is obtained from a truncated set of Tamm-Dancoff integral equations, generated by a four-fermion interaction based on a finite nonlocal quantum field theory. Eigenvalue equations for the meson and baryon mass spectra are also derived and integral equations are proposed for the scattering amplitudes, which can be used to calculate coupling constants in the nonlocal version of the standard model.

QUANTUM FIELD THEORY RENORMALIZATION GROUP APPROACH TO SELF-ORGANIZED CRITICAL MODELS: THE CASE OF RANDOM BOUNDARIES

2002 ◽  
Vol 16 (08) ◽  
pp. 1171-1204 ◽  
Author(s):  
D. VOLCHENKOV ◽  
PH. BLANCHARD ◽  
B. CESSAC
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Asymptotic Behavior ◽  
Renormalization Group ◽  
Coupling Constants ◽  
Threshold Condition ◽  
Dimensional Manifold ◽  
Quantum Field ◽  
Stochastic Problem ◽  
Self Organized

The long time and large scale asymptotic behavior for a stochastic problem related to self-organized critical (SOC) models is studied in the framework of advanced quantum field theory renormalization group (RG) method. The threshold condition and time scale separation between the slow dynamics of energy injection and the fast dynamics of avalanches (relaxation) are taken into account in the model. Herewith, the reciprocal correlation time at wavenumber k scales as tc(k) ∝ k-2+2η with some phenomenological parameter η > 0 corresponding to the anomalous diffusion coefficient z = 2(1 - η). The quantum field theory corresponding to the nonlinear stochastic problem is multiplicatively renormalizable and has an infinite number of coupling constants. The RG equations have a two-dimensional manifold of fixed points. Some of them relate to the stable asymptotic solutions and stipulate a general scaling with the critical dimensions of time Δ[t] = -2 + 2η and the energy field Δ[E] = d/2 - 3(1 - η). Possible corrections to the leading asymptotic behavior are discussed.

scholarly journals REPRESENTATION DEPENDENCE OF SUPERFICIAL DEGREE OF DIVERGENCES IN QUANTUM FIELD THEORY

2011 ◽  
Vol 26 (17) ◽  
pp. 2913-2925 ◽  
Author(s):  
ABOUZEID M. SHALABY
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vacuum Energy ◽  
Space Time ◽  
Feynman Diagrams ◽  
Coupling Constants ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Metric Operator

In this work, we investigate a very important but unstressed result in the work of C. M. Bender, J.-H. Chen, and K. A. Milton, J. Phys. A39, 1657 (2006). These authors have calculated the vacuum energy of the iϕ3 scalar field theory and its Hermitian equivalent theory up to g4 order of calculations. While all the Feynman diagrams of the iϕ3 theory are finite in 0+1 space–time dimensions, some of the corresponding Feynman diagrams in the equivalent Hermitian theory are divergent. In this work, we show that the divergences in the Hermitian theory originate from superrenormalizable, renormalizable and nonrenormalizable terms in the interaction Hamiltonian even though the calculations are carried out in the 0+1 space–time dimensions. Relying on this interesting result, we raise a question: Is the superficial degree of divergence of a theory is representation dependent? To answer this question, we introduce and study a class of non-Hermitian quantum field theories characterized by a field derivative interaction Hamiltonian. We showed that the class is physically acceptable by finding the corresponding class of metric operators in a closed form. We realized that the obtained equivalent Hermitian and the introduced non-Hermitian representations have coupling constants of different mass dimensions which may be considered as a clue for the possibility of considering nonrenormalizability of a field theory as a nongenuine problem. Besides, the metric operator is supposed to disappear from path integral calculations which means that physical amplitudes can be fully obtained in the simpler non-Hermitian representation.

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".  

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