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Quantum Physics in One Dimension$
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Thierry Giamarchi

Print publication date: 2003

Print ISBN-13: 9780198525004

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198525004.001.0001

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PECULIARITIES OF D = 1

PECULIARITIES OF D = 1

Chapter:
(p.1) 1 PECULIARITIES OF D = 1
Source:
Quantum Physics in One Dimension
Author(s):

Thierry Giamarchi

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198525004.003.0001

This chapter provides an overview of the basic ideas of interacting electrons and the peculiarities of one dimension. Interactions among particles are what endows the one-dimensional world with its special properties. Indeed, there are little differences between, for example, one-dimensional free electrons and their higher-dimensional counterparts. Before discussing one-dimensional systems, the effects of interactions in higher dimensions are briefly reviewed. The basic concepts and ideas of Fermi liquids are then explained, along with why one-dimensional systems are so different. This chapter also looks at the fermionic techniques used to tackle one dimension.

Keywords:   one-dimensional systems, fermions, Fermi liquids, perturbation theory, Dzyaloshinskii-Larkin solution, renormalized solution

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