Super boson-fermion correspondence

Victor G. Kac; J. W. Van de Leur

Annales de l'institut Fourier (1987)

  • Volume: 37, Issue: 4, page 99-137
  • ISSN: 0373-0956

Abstract

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We establish a super boson-fermion correspondence, generalizing the classical boson-fermion correspondence in 2-dimensional quantum field theory. A new feature of the theory is the essential non-commutativity of bosonic fields. The superbosonic fields obtained by the super bosonization procedure from super fermionic fields form the affine superalgebra g ˜ l 1 | 1 . The converse, super fermionization procedure, requires introduction of the super vertex operators. As applications, we give vertex operator constructions of all degenerate highest weight representations of g ˜ l 1 | 1 and of some interesting representations of g ˜ l ∞ | ∞ ( C ) , and also derive some new combinatorial identities. We hope that this construction will provide representation theoretical framework for hierarchies of super soliton equations.

How to cite

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Kac, Victor G., and Van de Leur, J. W.. "Super boson-fermion correspondence." Annales de l'institut Fourier 37.4 (1987): 99-137. <http://eudml.org/doc/74784>.

@article{Kac1987,
abstract = {We establish a super boson-fermion correspondence, generalizing the classical boson-fermion correspondence in 2-dimensional quantum field theory. A new feature of the theory is the essential non-commutativity of bosonic fields. The superbosonic fields obtained by the super bosonization procedure from super fermionic fields form the affine superalgebra $\tilde\{g\} l_\{1\vert 1\}$. The converse, super fermionization procedure, requires introduction of the super vertex operators. As applications, we give vertex operator constructions of all degenerate highest weight representations of $\tilde\{g\} l_\{1\vert 1\}$ and of some interesting representations of $\tilde\{g\} l_\{\infty \vert \infty \}(\{\bf C\})$, and also derive some new combinatorial identities. We hope that this construction will provide representation theoretical framework for hierarchies of super soliton equations.},
author = {Kac, Victor G., Van de Leur, J. W.},
journal = {Annales de l'institut Fourier},
keywords = {super boson-fermion correspondence; quantum field theory; bosonic fields; superbosonic fields; affine superalgebra; super fermionization procedure; super vertex operators; highest weight representations; combinatorial identities},
language = {eng},
number = {4},
pages = {99-137},
publisher = {Association des Annales de l'Institut Fourier},
title = {Super boson-fermion correspondence},
url = {http://eudml.org/doc/74784},
volume = {37},
year = {1987},
}

TY - JOUR
AU - Kac, Victor G.
AU - Van de Leur, J. W.
TI - Super boson-fermion correspondence
JO - Annales de l'institut Fourier
PY - 1987
PB - Association des Annales de l'Institut Fourier
VL - 37
IS - 4
SP - 99
EP - 137
AB - We establish a super boson-fermion correspondence, generalizing the classical boson-fermion correspondence in 2-dimensional quantum field theory. A new feature of the theory is the essential non-commutativity of bosonic fields. The superbosonic fields obtained by the super bosonization procedure from super fermionic fields form the affine superalgebra $\tilde{g} l_{1\vert 1}$. The converse, super fermionization procedure, requires introduction of the super vertex operators. As applications, we give vertex operator constructions of all degenerate highest weight representations of $\tilde{g} l_{1\vert 1}$ and of some interesting representations of $\tilde{g} l_{\infty \vert \infty }({\bf C})$, and also derive some new combinatorial identities. We hope that this construction will provide representation theoretical framework for hierarchies of super soliton equations.
LA - eng
KW - super boson-fermion correspondence; quantum field theory; bosonic fields; superbosonic fields; affine superalgebra; super fermionization procedure; super vertex operators; highest weight representations; combinatorial identities
UR - http://eudml.org/doc/74784
ER -

References

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