R-matrix

The term R-matrix has several meanings, depending on the field of study.

The term R-matrix is used in connection with the Yang–Baxter equation, first introduced in the field of statistical mechanics in the works of J. B. McGuire in 1964[1] and C. N. Yang in 1967[2] and in the group algebra of the symmetric group in the work of A. A. Jucys in 1966.[3]

The classical R-matrix arises in the definition of the classical Yang–Baxter equation.[4]

In quasitriangular Hopf algebra, the R-matrix is a solution of the Yang–Baxter equation.

The numerical modeling of diffraction gratings in optical science can be performed using the R-matrix propagation algorithm.[5]

  1. ^ McGuire, J. B. (1964-05-01). "Study of Exactly Soluble One-Dimensional N-Body Problems". Journal of Mathematical Physics. 5 (5). The American Institute of Physics (AIP): 622–636. Bibcode:1964JMP.....5..622M. doi:10.1063/1.1704156. ISSN 0022-2488.
  2. ^ Yang, C. N. (1967-12-04). "Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction". Physical Review Letters. 19 (23). American Physical Society (APS): 1312–1315. Bibcode:1967PhRvL..19.1312Y. doi:10.1103/PhysRevLett.19.1312. ISSN 0031-9007.
  3. ^ Jucys, A. A. (1966). "On the Young operators of the symmetric group" (PDF). Lietuvos Fizikos Rinkinys. 11 (23). Gos. Izd-vo Polit. i Nauch. literatury.: 163–180.
  4. ^ Kupershmidt, Boris A. (1999). "What a Classical r-Matrix Really Is". Journal of Nonlinear Mathematical Physics. 6 (4). Informa UK Limited: 448–488. arXiv:math/9910188. Bibcode:1999JNMP....6..448K. doi:10.2991/jnmp.1999.6.4.5. ISSN 1402-9251.
  5. ^ Li, Lifeng (1994-11-01). "Bremmer series, R-matrix propagation algorithm, and numerical modeling of diffraction gratings". Journal of the Optical Society of America A. 11 (11). The Optical Society: 2829–2836. Bibcode:1994JOSAA..11.2829L. doi:10.1364/josaa.11.002829. ISSN 1084-7529.