A SUPERSYMMETRIC POINT PARTICLE

Scanning QR Code In JavaUsing Barcode Control SDK for Java Control to generate, create, read, scan barcode image in Java applications.

Quick Response Code Drawer In JavaUsing Barcode creator for Java Control to generate, create QR-Code image in Java applications.

We introduce the formalism by going back to the simplest case we can describe a point particle. This will allow us to go over the main ideas without getting bogged down by the formalism. It turns out this approach actually has some direct relevance to string theory anyway. In modern parlance, a point particle is called a D0-brane. So the physics we will lay out here is known as the D0-brane action (this is a Dp-brane with p = 0 ). This type of object can be found in the type IIA superstring theory. The action for a relativistic point particle of mass m can be written as S= 1 1 2 2 d e x em 2 (9.4)

QR Code ISO/IEC18004 Scanner In JavaUsing Barcode recognizer for Java Control to read, scan read, scan image in Java applications.

Barcode Printer In JavaUsing Barcode creation for Java Control to generate, create bar code image in Java applications.

As noted in Chap. 2, e is called the auxiliary eld. The action written in this form is well suited to the study of massless particles. Letting m 0 gives S= 1 1 2 d e x 2 (9.5)

Recognizing Barcode In JavaUsing Barcode recognizer for Java Control to read, scan read, scan image in Java applications.

Painting Quick Response Code In Visual C#.NETUsing Barcode creator for .NET framework Control to generate, create Denso QR Bar Code image in Visual Studio .NET applications.

To make the jump to superspace, we consider the space de ned by the pair of coordinates: x , Aa (9.6)

QR Code Drawer In .NET FrameworkUsing Barcode generator for ASP.NET Control to generate, create QR Code JIS X 0510 image in ASP.NET applications.

Drawing QR Code 2d Barcode In .NETUsing Barcode creator for VS .NET Control to generate, create QR Code image in .NET applications.

CHAPTER 9 Superstring Theory Continued

Making QR Code In Visual Basic .NETUsing Barcode generation for .NET framework Control to generate, create QR Code JIS X 0510 image in .NET applications.

Generate Data Matrix 2d Barcode In JavaUsing Barcode generator for Java Control to generate, create DataMatrix image in Java applications.

where Aa is anticommuting spinor coordinate. In the case we are studying here, for a point particle, these are functions of , that is, Aa = Aa ( ). The index A ranges over the number of supersymmetries in the theory. If there are N of them, then A = 1, ..., N Hence, if we have an N = 2 supersymmetry, then we have the two fermionic coordinates 1a and 2 a. You may be a little confused by the notation. We actually have a second index here. The second index is the spinor index. Consider a general Dirac spinor. In D dimensions it has 2 D/ 2 components. So, a = 1, ..., 2 D / 2 For Majorana spinors, this number is cut in half. Now, we are actually going to proceed in a manner which is not too different from what you learned for worldsheet supersymmetry. Once again, we consider a constant Majorana spinor that we denote by A (suppressing the spinor index) to emphasize that it is in nitesimal. Now we introduce the following SUSY transformations:

Create Code 128 Code Set C In JavaUsing Barcode generation for Java Control to generate, create ANSI/AIM Code 128 image in Java applications.

Making GTIN - 13 In JavaUsing Barcode drawer for Java Control to generate, create GTIN - 13 image in Java applications.

x = i A A A = A A = A

Draw Identcode In JavaUsing Barcode maker for Java Control to generate, create Identcode image in Java applications.

Code 39 Extended Generation In JavaUsing Barcode encoder for BIRT Control to generate, create Code-39 image in BIRT applications.

In addition, we have to worry about the auxiliary eld. We suppose that the SUSY transformation in this case is (9.7)

Painting Data Matrix 2d Barcode In JavaUsing Barcode creation for Android Control to generate, create Data Matrix 2d barcode image in Android applications.

Paint Code 128A In VS .NETUsing Barcode generation for Visual Studio .NET Control to generate, create USS Code 128 image in VS .NET applications.

e = 0

Bar Code Printer In NoneUsing Barcode creator for Office Word Control to generate, create barcode image in Office Word applications.

Scanning UCC.EAN - 128 In Visual C#Using Barcode decoder for VS .NET Control to read, scan read, scan image in .NET framework applications.

(9.8)

DataMatrix Drawer In NoneUsing Barcode creator for Microsoft Word Control to generate, create ECC200 image in Word applications.

UCC-128 Creation In NoneUsing Barcode creator for Font Control to generate, create GS1 128 image in Font applications.

The simplest supersymmetric action that can be conceived of is an extension of the action in Eq. (9.5) written as follows: S= 1 1 A A 2 d e ( x i ) 2 (9.9)

Now, since A is a constant, it does not depend on and hence A = 0 . Given that plus Eq. (9.7), it s very easy to see that Eq. (9.9) is invariant under a SUSY transformation. First note that d A d d ( A ) = A = A = =0 d d d

String Theory Demysti ed

Now of course we can ignore the 1 e term when varying the action since the SUSY transformation is Eq. (9.8). Proceeding

S =

1 1 A A 2 d e ( x i ) 2 1 1 = d ( x i A A )2 2 e 1 = d ( x i A A ) ( x i A A ) e 1 = d ( x i A A ) x i ( A A ) e

Ok, now we have

( A A ) = ( A ) A + A ( A )

= ( A ) A = A A Using Eq. (9.7) then, we have

x i ( A A ) = i A A i A A = 0

Therefore, S = 0 and the action is invariant under a SUSY transformation. Since we are dealing with an enlargement of space-time coordinates, take a step back and recall that the actions described in Chap. 2 Are invariant under space-time translations a . Are invariant under Lorentz transformations x . We combine these two results in the Poincar group and note that the action in Eq. (9.4) is invariant under