Shiva diagrams for composite-boson many-body effects: how they work

M. Combescot () and O. Betbeder-Matibet

The European Physical Journal B: Condensed Matter and Complex Systems, 2007, vol. 55, issue 1, 63-76

Abstract: The purpose of this paper is to show how the diagrammatic expansion in fermion exchanges of scalar products of N-composite-boson (“coboson”) states can be obtained in a practical way. The hard algebra on which this expansion is based, will be given in an independent publication. Due to the composite nature of the particles, the scalar products of N-coboson states do not reduce to a set of Kronecker symbols, as for elementary bosons, but contain subtle exchange terms between two or more cobosons. These terms originate from Pauli exclusion between the fermionic components of the particles. While our many-body theory for composite bosons leads to write these scalar products as complicated sums of products of “Pauli scatterings” between two cobosons, they in fact correspond to fermion exchanges between any number P of quantum particles, with 2 ≤P≤N. These P-body exchanges are nicely represented by the so-called “Shiva diagrams”, which are topologically different from Feynman diagrams, due to the intrinsic many-body nature of the Pauli exclusion from which they originate. These Shiva diagrams in fact constitute the novel part of our composite-exciton many-body theory which was up to now missing to get its full diagrammatic representation. Using them, we can now “see” through diagrams the physics of any quantity in which enters N interacting excitons — or more generally N composite bosons —, with fermion exchanges included in an exact — and transparent — way. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Keywords: 71.35.-y Excitons and related phenomena; 05.30.Ch Quantum ensemble theory; 05.30.Jp Boson systems (search for similar items in EconPapers)
Date: 2007
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1140/epjb/e2007-00048-0 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurphb:v:55:y:2007:i:1:p:63-76

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/10051

DOI: 10.1140/epjb/e2007-00048-0

Access Statistics for this article

The European Physical Journal B: Condensed Matter and Complex Systems is currently edited by P. Hänggi and Angel Rubio

More articles in The European Physical Journal B: Condensed Matter and Complex Systems from Springer, EDP Sciences
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().