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barcode in vb.net 2008 L X in Java
L X Read QR Code JIS X 0510 In Java Using Barcode Control SDK for Java Control to generate, create, read, scan barcode image in Java applications. Creating QR Code JIS X 0510 In Java Using Barcode creation for Java Control to generate, create QR Code 2d barcode image in Java applications. = 0 , QR Code Reader In Java Using Barcode decoder for Java Control to read, scan read, scan image in Java applications. Bar Code Generator In Java Using Barcode generator for Java Control to generate, create barcode image in Java applications. X Bar Code Scanner In Java Using Barcode decoder for Java Control to read, scan read, scan image in Java applications. QR Code Generator In Visual C#.NET Using Barcode maker for Visual Studio .NET Control to generate, create QR Code image in VS .NET applications. = 0 , Make QR Code JIS X 0510 In Visual Studio .NET Using Barcode encoder for ASP.NET Control to generate, create QR Code JIS X 0510 image in ASP.NET applications. Encoding QR Code JIS X 0510 In .NET Using Barcode maker for .NET Control to generate, create QR Code image in .NET framework applications. (Dirichlet) Quick Response Code Creator In Visual Basic .NET Using Barcode encoder for VS .NET Control to generate, create QR image in .NET applications. USS128 Printer In Java Using Barcode drawer for Java Control to generate, create USS128 image in Java applications. (2.22) Code 128B Generator In Java Using Barcode generation for Java Control to generate, create Code 128A image in Java applications. Printing Linear 1D Barcode In Java Using Barcode drawer for Java Control to generate, create Linear Barcode image in Java applications. A closed string is a little loop moving through spacetime. In this case, the worldsheet is a cylinder or a tube. The boundary conditions are periodic, described by X ( , ) = X ( , + ) (2.23) Make RoyalMail4SCC In Java Using Barcode creator for Java Control to generate, create British Royal Mail 4State Customer Barcode image in Java applications. Making Universal Product Code Version A In None Using Barcode creation for Microsoft Excel Control to generate, create UPCA image in Microsoft Excel applications. Now let s write down the conjugate momenta for the string. First recall the lagrangian L = T ( X X ) 2 ( X ) 2 ( X ) 2 The conjugate momentum corresponding to the coordinate s is P = L = T ( X X ) 2 ( X ) 2 ( X ) 2 X X Recognizing GTIN  12 In Visual Basic .NET Using Barcode decoder for VS .NET Control to read, scan read, scan image in .NET applications. EAN / UCC  14 Encoder In None Using Barcode printer for Font Control to generate, create EAN / UCC  14 image in Font applications. (2.24) Drawing Code 128A In ObjectiveC Using Barcode creator for iPhone Control to generate, create Code 128 Code Set A image in iPhone applications. Create Code128 In ObjectiveC Using Barcode printer for iPad Control to generate, create Code 128 Code Set B image in iPad applications. 1/ 2 T ( X X ) 2 ( X ) 2 ( X ) 2 2 ( X X ) X 2 X 2 X 2
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and we also have a conjugate momentum corresponding to the coordinate : L = T ( X X ) 2 ( X ) 2 ( X ) 2 X X P = (2.25) 1/ 2 T ( X X ) 2 ( X ) 2 ( X ) 2 2 ( X X ) X 2 X 2 X 2
= T ( X X ) X X 2 X ( X X )2 ( X )2 ( X )2 Now, let s vary the action to obtain the equations of motion for the string. First, if it s been awhile since you ve had eld theory, convince yourself that X = ( X ) X = X X = = ( X ) Then, we can vary the action, and using the conjugate momenta we get f L L S = T d d ( X ) + ( X ) i 0 X X f = T d d ( X ) + ( X ) 0 i We can rewrite this expression so that we can get terms multiplied by X by using the product rule from calculus. For example, P X + X P X = P P P X = P X X
CHAPTER 2 Equations of Motion
Similarly, P X = P P X X
This means that the variation of the action can be written as P S = T d d P X X i 0 P f T d d P X X i 0 Recall from classical mechanics that a variation is de ned such that variation at the endpoints is 0, that is, at the initial and nal times X = 0. In the case of the endpoints of the string, we can apply either Neumann or Dirichlet boundary conditions so we will have to handle each case differently (more on this as we go along). For now, let s take X = 0 for simplicity. This means that we can throw away the terms in the above expression which are integrals of total derivatives: P X = 0
P X = 0
This leaves us with P P f f 0 = S = T d d X + T d d X i 0 i 0 P P f + = T d d X 0 i This gives us the equation of motion for the string, derived from the NambuGoto action: P + P =0 (2.26) String Theory Demysti ed
The Polyakov Action
Quantization using the NambuGoto action is not convenient due to the presence of the square root in the lagrangian. It is possible to write down an equivalent action, equivalent in the sense that it leads to the same equations of motion that does not have the cumbersome square root. This action goes by the name of the Polyakov action or by the more modern term the string sigma model action. Look back to the start of the chapter when we considered the point particle. There too, we ran into a situation where the action had a square root and we dealt with it by introducing an auxiliary eld a( ). We can use the same procedure here, to rewrite the action for the string in a more convenient form. This is done by introducing an intrinsic metric h ( , ), which acts like the auxiliary eld. We use the notation h because the metric can be written as a matrix. We use the indices to denote rows and columns in this matrix. Then, using the notation h = det h , the Polyakov action can be written as SP = T d 2 h h X X 2 (2.27) A historical aside: While Polyakov did important work with this action, it was actually proposed by Brink, Di Vecchia, and Howe and independently by Desser and Zumino. Polyakov got his name attached to it by using it in a path integral quantization of the string. It is also called the string sigma action.

