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Quantum Field Theory of Crystals and Dislocations
Author(s) -
Wadati M.,
Matsumoto H.,
Takahashi Y.,
Umezawa H.
Publication year - 1978
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.19780260602
Subject(s) - physics , quantum field theory , transformation (genetics) , dislocation , quantum , boson , burgers vector , field (mathematics) , field theory (psychology) , translation (biology) , theoretical physics , quantum mechanics , mathematical physics , mathematics , condensed matter physics , pure mathematics , biochemistry , chemistry , gene , messenger rna
We present a quantum field theoretical treatment of crystals from the view point of the spontaneous breakdown of the spatial translation invariance. It is proved that at least three massless Goldstone particles exist and they are identified as the acoustic phonons. We carry out the boson transformation to show that the classical phenomenological theory of crystals can be derived. The classical momentum and stress tensor are expressed in terms of the classical displacement field. The method is extended to a microscopic derivation of the theory of crystal dislocations. It is shown that the Burgers vector is quantized and is a special case of the so‐called topological quantum number. An explicit expression of a general solution of the dislocation is obtained.