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visual basic print barcode label The Fourier expansion can be used to derive Poisson brackets for the modes. These are in Java
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The Classical String II: Symmetries and Worldsheet Currents
In the last chapter we introduced some basic notions of classical string theory, including the equations of motion and boundary conditions. In this chapter we will expand our discussion of the classical string, discussing symmetries and introducing the energymomentum tensor and conserved currents. This will nish the groundwork we need for the classical string, and in the next chapter we will quantize the string. Copyright 2009 by The McGrawHill Companies, Inc. Click here for terms of use.
String Theory Demysti ed
The EnergyMomentum Tensor
Let s quickly review a few things before getting started. Recall that the intrinsic distance on the worldsheet can be determined using the induced metric h . This is given by ds 2 = h d d (3.1) where 0 = , 1 = are the coordinates which parameterize points on the worldsheet. A set of functions X ( , ) describe the shape of the worldsheet and the motion of the string with respect to the background spacetime, where = 0, 1, ..., D 1 for a Ddimensional spacetime. To nd the dynamics of the string, we can minimize the Polyakov action [Eq. (2.27)]: SP = T d 2 det(h ) h X X 2 (3.2) Minimizing SP (by minimizing the area of the worldsheet) gives us the equations of motion for the X ( , ), and hence the dynamics of the string. In the quiz at the end of Chap. 2 in Prob. 4, you were invited to show that the Polyakov and NambuGoto actions were equivalent by considering the energymomentum or stressenergy tensor T which is given by T = 2 T 1 SP h h (3.3) In this book we ll go mostly by the name energymomentum tensor. In a nutshell, the energymomentum tensor describes the density and ux of energy and momentum in spacetime. You should be familiar with the basics of what T is from some exposure to or study of quantum eld theory, so we re just going to go with that and describe how it works in string theory. When working out the solution to Prob. 4 in Chap. 2, you should have found that 1 T = X X h h X X 2 (3.4) The rst property that we will establish for the energymomentum tensor is that it has zero trace. We can calculate the trace using the induced metric: Tr (T ) = T = h T

