Abstract
We reformulate the string classical mechanics by substituting the standard Lagrangian by a non-standard exponential Lagrangian where higher-order derivative terms occur naturally in the equations of motion. Our motivation is based on the accumulating evidence that higher-order derivatives play a leading role in string field theories. Since non-standard Lagrangians generate higher-order derivatives in a usual way, it will be of interest to explore their roles in classical string field mechanics. It was observed that replacing standard by non-standard Lagrangians gives another possibility to obtain new aspects which may have interesting physical effects.
Highlights
String theory is a quantum theory of one-dimensional objects called strings which come in two different types: open and closed
The follow-on modified Euler–Lagrange equation that results from the standard calculus of variations leads to equations of motion that correspond to physically interesting nonlinear dynamical systems
The objective of this work was to discuss the impacts of exponentially non-standard Lagrangians in string classical mechanics
Summary
String theory is a quantum theory of one-dimensional objects called strings which come in two different types: open and closed. We can use this to define the transverse component of the string velocity v? Corollary 2.1 Consider the boundary condition in this parameterization, together with our pre-gauge fixed expression for oL=oXr, the equations of motion are given by:. Proof The proof follows directly from Eq (3) after considering a rotating string with constant angular velocity and assuming a general solution of the motion describing left and right motion of the form [26]: Xðs; rÞ 1⁄4 bðA cos v ðc À ctÞþ B cos vðc þ ctÞÞx^ þ bðC sin vðc À ctÞ þ D sin vðc þ ctÞÞy^, b; c; v 2 R, where ðA; B; C; DÞ are constants to be determined from boundary conditions and ðx^; y^Þ are unit vectors.
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