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Báo cáo " On equations of motion, boundary conditions and conserved energy-momentum of the rigid string "

The correct forms of the equations of motion, of the boundary conditions and of the reconserved energy - momentum for the a classical rigid string are given. Certain consequences of the equations of motion are presented. We also point out that in Hamilton description of ˙ the rigid string the usual time evolution equation F = {F, H} is modified by some boundary terms | VNU Journal of Science Mathematics - Physics 24 2008 111-118 On equations of motion boundary conditions and conserved energy-momentum of the rigid string Nguyen Suan Han Department of Physics College of Science VNU 334 Nguyen Trai Thanh Xuan Hanoi Vietnam Received 28 June 2008 Abstract. The correct forms of the equations of motion of the boundary conditions and of the reconserved energy - momentum for the a classical rigid string are given. Certain consequences of the equations of motion are presented. We also point out that in Hamilton description of the rigid string the usual time evolution equation F F H is modified by some boundary terms 1. Introduction The modified string model so-called rigid or smooth strings has been discussed 1 11 . The action functional in this model contains in addition to the usual Nambu-Gato the term proportional to the external curvature of the world sheet of the string.These models are expected to have many different applications in string interpretation of QCD in a statistical theory of random surfaces in connection with two dimensional quantized gravity 12 . Our main goal in this paper is to re-derive the classical equations of motion boundary conditions and conserved energy - momentum of the rigid string obtained by 4 6 . The first reason to discuss in detail such basis is that rigid model is an example of a Lagrangian field theory with higher order derivatives. In such case the seemingly standard derivations contain many interesting points which in our opinion have not been sufficient emphasized. The second reason is that one can find in the literature many misleading or even erroneous statements concerning in equations of motion the boundary conditions and the energy-momentum. The plan of our paper is the following. In Section 2 we present the derivation of the Euler -Lagrange equations of motion of the boundary conditions and of the conserved energy-momentum in the case of genetic Lagrangian with second order derivatives . In .