Abstract
The search for unifying principles of quantum mechanics with special theory of relativity began at the end of the 1920s. However, it had been realized from the beginning that relativistic quantum field theory was plagued by the insuperable difficulty of the ultraviolet (UV) divergences. As is now well known, the search for a solution to the problem of subtraction of UV divergences, lasting from the 1940s to the 1970s, led to the establishment of a consistent theoretical and mathematical formulation called the renormalization group (RG).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
E.C.G. Stueckelberg, A. Petermann, La normalization des constantes dans la theorie des quanta. Helv. Phys. Acta 26, 499 (1953)
M. Gell-Mann, F.E. Low, Quantum electrodynamics at small distances. Phys. Rev. 95, 1300 (1954)
W.E. Lamb, R.C. Retherford, Fine structure of the hydrogen atom by a microwave method. Phys. Rev. 72(3), 241–243 (1947)
N.N. Bogoliubov, O.S. Parasyuk, A theory of multiplication of causative singular functions. Dokl. Akad. Nauk BSSR 100, 25–28 (1955)
D.J. Gross, F. Wilczek, Ultraviolet behavior of non-abelian gauge theories. Phys. Rev. Lett. 30, 1343–1346 (1973)
D.J. Gross, F. Wilczek, Asymptotically free gauge theories. I. Phys. Rev. D 8, 3633–3652 (1973)
D.J. Gross, F. Wilczek, Asymptotically free gauge theories. II. Phys. Rev. D 9, 980–993 (1974)
L.P. Kadanoff, Scaling laws for ising model near \(T_{c}\). Physics 2, 263 (1966)
K.G. Wilson, Renormalization group and critical phenomena. I. Renormalization group and the kadanoff scaling picture. Phys. Rev. B 4, 3174 (1971)
K.G. Wilson, Renormalization group and critical phenomena. II. Phase-space cell analysis of critical behavior. Phys. Rev. B 4, 3184–3205 (1971)
K.G. Wilson, The renormalization group: critical phenomena and the Kondo problem. Rev. Mod. Phys. 47, 773–840 (1975)
K.G. Wilson, The renormalization group and critical phenomena. Rev. Mod. Phys. 55, 583–600 (1983)
S. Ma, Introduction to the renormalization group. Rev. Mod. Phys. 45, 589–614 (1973)
G.L. Eyink, The renormalization group method in statistical hydrodynamics. Phys. Fluids 6, 3063 (1994)
P.C. Martin, E.D. Siggia, H.A. Rose, Statistical dynamics of classical systems. Phys. Rev. A 8, 423 (1973)
D.J. Amit, Field Theory, the Renormalization Group, and Critical Phenomena (McGraw-Hill Inc., New York, 1978)
M. Le Bellac, Quantum and Statistical Field Theory (Oxford University Press, New York, 1991)
E.V. Teodorovich, The renormalization-group method in problems of mechanics. J. Appl. Math. Mech. 68, 299–326 (2004)
E.V. Teodorovich, The renormalization-group approach to solving the equation of nonlinear transfer. J. Phys. A: Math. Theor. 42, 155202 (2009)
V.F. Kovalev, D.V. Shirkov, Functional self-similarity and renormalization group symmetry in mathematical physics. Theor. Math. Phys. 121, 1315–1332 (1999)
D.V. Shirkov, Renormalization group, invariance principle and functional self-similarity. Sov. Phys. Dokl. 27, 197–200 (1982)
C.G. Callan Jr, Broken scale invariance in scalar field theory. Phys. Rev. D 2, 1541–1547 (1970)
K. Symanzik, Small distance behaviour in field theory and power counting. Commun. Math. Phys. 18, 227 (1970)
K. Symanzik, Small-distance-behaviour analysis and wilson expansions. Commun. Math. Phys. 23, 49 (1971)
L.V. Ovsyannikov, Group properties of the equation of heat conductivity. Sov. Phys. Dokl. 125, 492 (1959)
L.V. Ovsyannikov, Group Analysis of Differential Equations (Academic, New York, 1982)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Barkhudarov, E. (2014). Introduction. In: Renormalization Group Analysis of Equilibrium and Non-equilibrium Charged Systems. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-06154-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-06154-2_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06153-5
Online ISBN: 978-3-319-06154-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)