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QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA
International Journal of Modern Physics A, Volume: "A8", Issue: 05, Pages: 947 - 982
Swansea University Author:
Timothy Hollowood
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DOI (Published version): 10.1142/S0217751X93000370
Abstract
The problem of quantizing a class of two-dimensional integrable quantum field theories is considered. The classical equations of the theory are the complex $sl(n)$ affine Toda equations which admit soliton solutions with real masses. The classical scattering theory of the solitons is developed using...
Published in: | International Journal of Modern Physics A |
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ISSN: | 0217-751X 1793-656X |
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1992
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URI: | https://cronfa.swan.ac.uk/Record/cronfa28594 |
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2016-06-03T14:37:07.7223941 v2 28594 2016-06-03 QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA ea9ca59fc948276ff2ab547e91bdf0c2 0000-0002-3258-320X Timothy Hollowood Timothy Hollowood true false 2016-06-03 SPH The problem of quantizing a class of two-dimensional integrable quantum field theories is considered. The classical equations of the theory are the complex $sl(n)$ affine Toda equations which admit soliton solutions with real masses. The classical scattering theory of the solitons is developed using Hirota's solution techniques. A form for the soliton $S$-matrix is proposed based on the constraints of $S$-matrix theory, integrability and the requirement that the semi-classical limit is consistent with the semi-classical WKB quantization of the classical scattering theory. The proposed $S$-matrix is an intertwiner of the quantum group associated to $sl(n)$, where the deformation parameter is a function of the coupling constant. It is further shown that the $S$-matrix describes a non-unitary theory, which reflects the fact that the classical Hamiltonian is complex. The spectrum of the theory is found to consist of the basic solitons, scalar states (or breathers) and excited (or `breathing') solitons. It is also noted that the construction of the $S$-matrix is valid for any representation of the Hecke algebra, allowing the definition of restricted $S$-matrices, in which case the theory is Journal Article International Journal of Modern Physics A "A8" 05 947 982 0217-751X 1793-656X 31 3 1992 1992-03-31 10.1142/S0217751X93000370 http://inspirehep.net/record/333204 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University 2016-06-03T14:37:07.7223941 2016-06-03T14:37:07.5351929 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Timothy Hollowood 0000-0002-3258-320X 1 |
title |
QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA |
spellingShingle |
QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA Timothy Hollowood |
title_short |
QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA |
title_full |
QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA |
title_fullStr |
QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA |
title_full_unstemmed |
QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA |
title_sort |
QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA |
author_id_str_mv |
ea9ca59fc948276ff2ab547e91bdf0c2 |
author_id_fullname_str_mv |
ea9ca59fc948276ff2ab547e91bdf0c2_***_Timothy Hollowood |
author |
Timothy Hollowood |
author2 |
Timothy Hollowood |
format |
Journal article |
container_title |
International Journal of Modern Physics A |
container_volume |
"A8" |
container_issue |
05 |
container_start_page |
947 |
publishDate |
1992 |
institution |
Swansea University |
issn |
0217-751X 1793-656X |
doi_str_mv |
10.1142/S0217751X93000370 |
college_str |
Faculty of Science and Engineering |
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|
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facultyofscienceandengineering |
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Faculty of Science and Engineering |
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facultyofscienceandengineering |
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Faculty of Science and Engineering |
department_str |
School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics |
url |
http://inspirehep.net/record/333204 |
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description |
The problem of quantizing a class of two-dimensional integrable quantum field theories is considered. The classical equations of the theory are the complex $sl(n)$ affine Toda equations which admit soliton solutions with real masses. The classical scattering theory of the solitons is developed using Hirota's solution techniques. A form for the soliton $S$-matrix is proposed based on the constraints of $S$-matrix theory, integrability and the requirement that the semi-classical limit is consistent with the semi-classical WKB quantization of the classical scattering theory. The proposed $S$-matrix is an intertwiner of the quantum group associated to $sl(n)$, where the deformation parameter is a function of the coupling constant. It is further shown that the $S$-matrix describes a non-unitary theory, which reflects the fact that the classical Hamiltonian is complex. The spectrum of the theory is found to consist of the basic solitons, scalar states (or breathers) and excited (or `breathing') solitons. It is also noted that the construction of the $S$-matrix is valid for any representation of the Hecke algebra, allowing the definition of restricted $S$-matrices, in which case the theory is |
published_date |
1992-03-31T03:34:51Z |
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1763751484262973440 |
score |
11.022936 |