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Field Theories of Condensed Matter Systems (Advanced Books Classics) (v. 82): Fradkin

Condensed Matter Physics is a very rich and diverse field. If we are to define it as being "whatever gets published in the Condensed Matter section of a physics journal", we would conclude that it ranges from problems typical of material science to subjects which are as fundamental as particle physics or cosmology. Because of its diversity, it is sometimes hard to figure out where the field is going, particularly if you do not work in this field. Unfortunately, this is the case for people who have to make decisions about funding, grants, tenure and other unpleasant aspects in the life of a physicist. They have a hard time figuring-out where to put this subject which is neither applied science nor dealing with the smallest length scales or the highest energies. However, the richness of the field comes precisely from its diversity.

The past two decades have witnessed the development of two areas of Condensed Matter Physics which best illustrate the strengths of this field: Critical Phenomena and the Quantum Hall Effect. In both cases, it was the ability to produce extremely pure samples which allowed the discovery and the experimental study of the phenomenon. Its physical explanation required the use of concepts and the development of new theoretical tools, such as the renormalization group, conformal invariance and fractional statistics.

While the concept of conformal invariance was well known in field theory before Critical Phenomena was recognized as a field, its importance to the complete structure of the field theory was not understood. The situation changed with the development of the Renormalization Group (RG). For Condensed Matter Physics, the RG is the main tool for the interpretation of the experimental data, the conceptual framework and the computational algorithm which has allowed the theory to make powerful predictions. In Particle Physics, the RG is also a tool for the interpretation of the data. But, more importantly, the concept of infrared unstable fixed point has become the defindon of the field theory itself.

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