Abstract. New applications of the renormalization group method in physics: A brief introduction. 1 Introduction Quantum theory, and equilibrium statistical mechanics have traditionally been the areas most influenced by renormalization group theory and phase transitions. Abstract The stability or lack thereof of nonrelativistic fermionic systems to interactions is studied within the Renormalization Group (RG) framework, in close analogy with the study of critical phenomena using φ4 scalar field theory. The methods of the real-space renormalization group, and their application to critical and chaotic phenomena are reviewed. The article consists of two parts: the first part deals with phase transitions and critical phenomena; the second part, bifurcations and transitions to chaos. But equilibrium statistical mechanics and quantum theory are only convenient descriptions for a fairly limited subset of interesting systems in nature. Bringing together several fields of research which have used the renormalization group method, this book acts as an introduction to more specialized monographs. We begin with an introduction to the phenomenology of phase transitions and critical phenomena. physicists believed that fundamental principles of physics had to be changed to elim-inate the divergences. In the late 1940’s Bethe, Feynman, Schwinger, Tomonaga, and Dyson, and others proposed a program of ‘renormalization’ that gave finite and physically sensible results by absorbing the divergences into redefinitions of physi-cal quantities. Juli 2014 Andreas Wipf (FSU Jena) The Functional Renormalization Group Method – An Introduction 21. Sloan Laboratory of Physics Yale University New Haven CT 06520 REVISED AND EXPANDED JUNE 1993 FOR REV.MOD.PHYS. Juli 2014 1 / 60. review path integral methods, the relationship between early renormalization theory and renormalization group methods, and conceptual shifts in thinking about quantum field theory spurred by the development of renormalization group methods. Starting with fractals, the concepts of self-similarity, scaling and homogeneous functions are introduced. The renormalization group methods for partial differential equations such as the Barenblatt equation @12,15,16#, and front propagation problems in reaction-diffusion equations @11# are, in retrospect, examples of the general approach dis-cussed in this paper. Renormalization Group Methods Porter Williams It is a truism, in physics if not in philosophy, that in order to study phys-ical behavior at a particular scale one is best served by using degrees of free- dom de ned at (or suitably near) that scale. This is an introduction to renormalization group methods in quantum field theory aimed at philosophers of science. The Functional Renormalization Group Method – An Introduction A. Wipf Theoretisch-Physikalisches Institut, FSU Jena La Plata 21.

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