An action for a classical string, the equation of motion and group invariant classical solutions

• Autorzy: Paul Bracken
• Języki publikacji: EN

Abstrakty

EN

A string action which is essentially a Willmore functional is presented and studied. This action determines the physics of a surface in Euclidean three space which can be used to model classical string configurations. By varying this action an equation of motion for the mean curvature of the surface is obtained which is shown to govern certain classical string configurations. Several classes of classical solutions for this equation are discussed from the symmetry group point of view and an application is presented.

Słowa kluczowe

EN

classical strings; Gaussian curvature; mean curvature; Weierstrass representation; Euler-Lagrange equation

• Czasopismo: Open Physics
• Rocznik: 2008
• Tom: 6
• Numer: 3
• Strony: 662-670

Daty

wydano

2008-09-01

online

2008-07-17

Twórcy

autor

Paul Bracken

• Department of Mathematics, University of Texas, Edinburg, TX, 78539, USA,

Bibliografia

• [1] B. Konopelchenko, I. Taimanov, J. Phys. A 29, 1261 (1986) http://dx.doi.org/10.1088/0305-4470/29/6/012[Crossref]
• [2] D.G. Gross, C.N. Pope, S. Weinberg, Two-dimensional Quantum Gravity and Random Surfaces (World Scientific, Singapore, 1992)
• [3] K.S. Viswanathan, R. Parthasarathy, Phys. Rev. D 55, 3800 (1997) http://dx.doi.org/10.1103/PhysRevD.55.3800[Crossref]
• [4] P. Bracken, Phys. Lett. B 541, 166 (2002) http://dx.doi.org/10.1016/S0370-2693(02)02191-3[Crossref]
• [5] A.M. Poyakov, Nucl. Phys. B 268, 406 (1986) http://dx.doi.org/10.1016/0550-3213(86)90162-8[Crossref]
• [6] H. Kleinert, Phys. Lett. B 174, 335 (1986) http://dx.doi.org/10.1016/0370-2693(86)91111-1[Crossref]
• [7] P. Bracken, A.M. Grundland, L. Martina, J. Math. Phys. 40, 3379 (1999) http://dx.doi.org/10.1063/1.532894[Crossref]
• [8] S.N. Behera, A. Khare, Pramana 15, 245 (1980) http://dx.doi.org/10.1007/BF02847222[Crossref]
• [9] R. Jackiw, Rev. Mod. Phys. 49, 681 (1977) http://dx.doi.org/10.1103/RevModPhys.49.681[Crossref]
• [10] R.M. White, T.H. Geballe, Long Range Order in Solids (Academic, New York, 1979)
• [11] B.G. Konopelchenko, Phys. Lett. B 459, 522 (1999) http://dx.doi.org/10.1016/S0370-2693(99)00699-1[Crossref]
• [12] P.J. Olver, Applications of Lie Groups to Differential Equations (Graduate Texts in Mathematics, Springer, New York, 1993), vol 107
• [13] E.L. Ince, Ordinary Differential Equations (Dover, New York, 1956)
• [14] P. Winternitz, A.M. Grundland, J.A. Tuszynski, J. Phys. C 21, 4931 (1988) http://dx.doi.org/10.1088/0022-3719/21/28/008[Crossref]
• [15] P.F. Byrd, M.D. Friedman, Handbook of Elliptic Integrals for Engineers and Scientists (Springer, Berlin, 1971)
• [16] P. Bracken, Acta Appl. Math. 92, 63 (2006) http://dx.doi.org/10.1007/s10440-006-9059-9[Crossref]
• [17] P. Bracken, A.M. Grundland, Czech. J. Phys. 51, 293 (2001) http://dx.doi.org/10.1023/A:1017529203946[Crossref]

Identyfikatory

DOI

10.2478/s11534-008-0092-3