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On the Bosonization of the Many Electron Problem
Author(s) -
Cabo A.
Publication year - 1986
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.19860341003
Subject(s) - bosonization , pauli exclusion principle , saddle point , limit (mathematics) , physics , trace (psycholinguistics) , path integral formulation , hamiltonian (control theory) , electron , operator (biology) , saddle , lattice (music) , representation (politics) , mathematics , statistical physics , theoretical physics , quantum mechanics , mathematical analysis , fermion , quantum , mathematical optimization , geometry , philosophy , repressor , law , linguistics , chemistry , acoustics , biochemistry , political science , transcription factor , politics , gene
The Garbaczewski bosonization procedure is applied to the many‐electron problem. It leads to a non‐local c‐number path integral representation for the trace of the evolution operator which also depends on a mapping of the lattice points in the natural numbers. This mapping is needed for the implementation of the bosonization. We argue that the non‐local interactions and the dependence on the mapping can be disregarded in the limit of small electron c ‐number field. We can then discuss the physics of the saddle point contribution. In the discussion the effects of the Pauli exclusion principle are introduced phenomenologically.