ITAP2009_Part_I - Advanced Condensed Matter Field Theory Part I Introduction Review of Second Quantization Techniques PART I Introduction Overview

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Advanced Condensed Matter Part I: Introduction & Review of Second Quantization Techniques Field Theory Nai-Chang Yeh ITAP (July 2009) 1 PART I. Introduction & Overview of Modern Condensed Matter Physics Condensed matter physics is a branch of physics that investigates the physical phenomena associated with the many-body interaction of materials in their “condensed” (i.e. liquid and solid) states. The objective of this course is to apply quantum field theory to various modern topics of condensed matter physics. Typically most condensed matter physics topics may be described in terms of non-relativistic quantum field theory. However, for topics involving gauge theory ( e.g. spin liquids, high-temperature superconductivity) and topological field theory ( e.g. fractional quantum-Hall states), knowledge of relativistic quantum field theory becomes necessary. In the interest of time, we shall first focus on non-relativistic descriptions of the many-body interactions in fermions and bosons, although the basics of relativistic quantum field theory will be briefly reviewed before taking the relativistic quantum field theory to the non-relativistic limit. The necessary relativistic quantum field concepts for gauge theory, fractional statistics and topological field theory will be covered in the context of high-temperature superconductivity and fractional quantum Hall states later in this course. Throughout this course we shall mostly use natural units in which the Dirac symbol = (which is the Planck constant h divided by 2 π ) and the speed of light c are both set to 1, although at times we’ll restore them for quantitative comparison with experiments. Thus, in natural units both time and space are treated on the same footing, and mass is inversely proportional to length. I.1. Overview of Modern Condensed Matter Physics The scope of condensed matter physics has evolved and expanded significantly in recently years, from traditional “solid state physics” that largely focuses on effective single-particle pictures in solids and Landau symmetry-breaking theory of phase transitions, to a new arena encompassing a broad range of topics from highly interdisciplinary research such as nano- and biophysical sciences, optical lattices and Bose- Einstein condensation in laser-cooled atoms, quantum computation, to fundamental subjects such as gauge theory, quantum orders and quantum phase transitions, strongly correlated electronic systems, fractional statistics, spin liquids, topological field theory, string-net condensate for unification of fermions and bosons, etc. In the development of modern condensed matter physics, quantum field theory (QFT) and group theory have played essential roles in the description of many-body interactions, symmetries and symmetry-breaking.
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This note was uploaded on 07/15/2009 for the course PHYSIC condessed taught by Professor Alitozar during the Spring '09 term at Selçuk Üniversitesi.

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ITAP2009_Part_I - Advanced Condensed Matter Field Theory Part I Introduction Review of Second Quantization Techniques PART I Introduction Overview

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