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Advanced Condensed Matter
Part I:
Introduction & Review of Second Quantization Techniques
Field Theory
NaiChang 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 manybody 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 nonrelativistic quantum field
theory. However, for topics involving gauge theory (
e.g.
spin liquids, hightemperature superconductivity)
and topological field theory (
e.g.
fractional quantumHall states), knowledge of relativistic quantum field
theory becomes necessary. In the interest of time, we shall first focus on nonrelativistic descriptions of the
manybody 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 nonrelativistic limit. The
necessary relativistic quantum field concepts for gauge theory, fractional statistics and topological field
theory will be covered in the context of hightemperature 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 singleparticle pictures in solids and
Landau symmetrybreaking 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 lasercooled 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, stringnet 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 manybody interactions, symmetries and symmetrybreaking.
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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.
 Spring '09
 alitozar
 Physics, Phases Of Matter

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