Shiva diagrams for composite-boson many-body effects:
how they work |
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Authors: | M Combescot O Betbeder-Matibet |
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Institution: | (1) Institut des NanoSciences de Paris, Université Pierre et Marie Curie-Paris 6, Université Denis Diderot-Paris 7, CNRS, UMR 7588, Campus Boucicaut, 140 rue de Lourmel, 75015 Paris, France |
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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. |
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Keywords: | 71 35 -y Excitons and related phenomena 05 30 Ch Quantum ensemble theory 05 30 Jp Boson systems |
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