Conserved charges from self-duality
Abstract
Given a simple self-dual quantum Hamiltonian H = KB+GAMMAB, where K and GAMMA are coupling constants, and the condition the (B,(B,(B,B))) = 16(B,B), then we construct an infinite set of conserved charges Q/sub 2n/; (H,Q/sub 2n/) = 0. In simple models, like the two-dimensional Ising or Baxter eight-vertex, these charges appear in the associated quantum theories and are equivalent to those which result from the transfer-matrix formulation and exact quantum integrability of the system. The power of our result is that it is an operator statement and does not refer to the number of dimensions or the nature of the space-time manifold: lattice, continuum, or loop space. It is suggested how the establishment of this link between duality and integrability could be used to exploit the Kramers-Wannier-type self-duality of the four-dimensional SU (N) gauge theory to find hidden symmetry.
- Authors:
- Publication Date:
- Research Org.:
- Rockefeller University, New York, New York 10021
- OSTI Identifier:
- 5422287
- DOE Contract Number:
- AC02-81ER40033-B000
- Resource Type:
- Journal Article
- Journal Name:
- Phys. Rev. D; (United States)
- Additional Journal Information:
- Journal Volume: 25:6
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; GAUGE INVARIANCE; DUALITY; CLASSICAL MECHANICS; COUPLING CONSTANTS; HAMILTONIANS; QUANTUM FIELD THEORY; SPACE-TIME; SU GROUPS; FIELD THEORIES; INVARIANCE PRINCIPLES; LIE GROUPS; MATHEMATICAL OPERATORS; MECHANICS; QUANTUM OPERATORS; SYMMETRY GROUPS; 645400* - High Energy Physics- Field Theory; 645201 - High Energy Physics- Particle Interactions & Properties-Theoretical- General & Scattering Theory
Citation Formats
Dolan, L, and Grady, M. Conserved charges from self-duality. United States: N. p., 1982.
Web. doi:10.1103/PhysRevD.25.1587.
Dolan, L, & Grady, M. Conserved charges from self-duality. United States. https://doi.org/10.1103/PhysRevD.25.1587
Dolan, L, and Grady, M. 1982.
"Conserved charges from self-duality". United States. https://doi.org/10.1103/PhysRevD.25.1587.
@article{osti_5422287,
title = {Conserved charges from self-duality},
author = {Dolan, L and Grady, M},
abstractNote = {Given a simple self-dual quantum Hamiltonian H = KB+GAMMAB, where K and GAMMA are coupling constants, and the condition the (B,(B,(B,B))) = 16(B,B), then we construct an infinite set of conserved charges Q/sub 2n/; (H,Q/sub 2n/) = 0. In simple models, like the two-dimensional Ising or Baxter eight-vertex, these charges appear in the associated quantum theories and are equivalent to those which result from the transfer-matrix formulation and exact quantum integrability of the system. The power of our result is that it is an operator statement and does not refer to the number of dimensions or the nature of the space-time manifold: lattice, continuum, or loop space. It is suggested how the establishment of this link between duality and integrability could be used to exploit the Kramers-Wannier-type self-duality of the four-dimensional SU (N) gauge theory to find hidden symmetry.},
doi = {10.1103/PhysRevD.25.1587},
url = {https://www.osti.gov/biblio/5422287},
journal = {Phys. Rev. D; (United States)},
number = ,
volume = 25:6,
place = {United States},
year = {Mon Mar 15 00:00:00 EST 1982},
month = {Mon Mar 15 00:00:00 EST 1982}
}