# visual basic print barcode label The Fourier expansion can be used to derive Poisson brackets for the modes. These are in Java Printer QR Code 2d barcode in Java The Fourier expansion can be used to derive Poisson brackets for the modes. These are

The Fourier expansion can be used to derive Poisson brackets for the modes. These are
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The Poisson brackets will be the starting point to quantize the theory.
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1. Consider the lagrangian given in the Eq. (2.10) which includes the auxiliary eld. Use the Euler-Lagrange equations to derive the equation of motion. 2. Start with the Nambu-Goto lagrangian L = X 2 X 2 ( X X 2 ) and consider the gauge choice which gives the at metric h . Using the constraints X 2 + X 2 = 0, X X = 0, nd the equations of motion. 3. Consider the Polyakov action. A Weyl transformation is one of the form h e ( , ) h and X = 0. Determine the form of the Polyakov action ( , ) h ]. under a Weyl transformation [hint: h e 4. Using the Polyakov action, de ne the energy-momentum tensor on the worldsheet by varying the action with respect to the intrinsic metric T = 2 T
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Using the fact that h = 1 h h h nd an expression for the 2 induced metric so that it can be eliminated from the action. This should allow you to recover the Nambu-Goto action.
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5. Consider an open string with free endpoints. Find the variation of the center of mass position of the string with by calculating 1
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6. Find the conserved momentum of the open string with free endpoints by calculating P = T d X ( , )
where the dot represents differentiation with respect to .
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 energy-momentum 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.