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the actual universe while force-carrying particles are indeed bosons, fundamental matter particles (like electrons) have half-integral spin, that is, they are fermions. So a theory that describes a world consisting entirely of bosons does not describe the real universe. Nonetheless, we start here because it is an easier way to approach string theory and we can learn the nuts and bolts in a slightly simpler context. We are going to approach bosonic strings in three steps. In this chapter, we will develop the theory of classical, relativistic strings starting with the action principle and deriving the equations of motion. In Chap. 3, we will learn about the stress-energy tensor and conserved currents, speci cally conserved worldsheet currents. Finally, in the last chapter of this part of the book, we will quantize the strings using a procedure of rst quantization (i.e., rst quantization of point particles gives single-particle states). In the end you have a quantized relativistic theory. To this end, we begin our journey into the world of classical relativistic point particle moving in space-time to illustrate the techniques used.

public void connectionErrorOccurred(javax.sql.ConnectionEvent event) { System.out.println("We are executing UCConnectionEventListener.connectorErrorOccurred"); } }

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The task at hand is to describe the motion of a free (relativistic) point particle in space-time. One way to approach the problem is by using an action principle. Before we do that, let s set up the arena in which the particle moves. Let its motion be de ned with respect to space-time coordinates X where X 0 is the timelike coordinate (i.e., X 0 = ct) and X i where i 0 are the spacelike coordinates (say x, y, and z). While you are probably used to lowercase letters like x to represent coordinates, in string theory uppercase letters are used, so we will stick to that convention. Anticipating the fact that string theory takes place in a higher-dimensional arena, rather than the usual one time dimension and three spatial dimensions we are used to, we consider motion in a D-dimensional space-time. There is one time dimension but now we allow for the possibility of d = D 1 spatial dimensions. We reserve 0 to index the time dimension hence our coordinates range over = 0, . . . , d . Now, the motion or trajectory of a particle is described such that the coordinates are parameterized by , which parameterizes the world-line of the particle. That is, this is the time given by a clock that is moving or carried along with the particle itself. We can emphasize this parameterization by writing the coordinates as functions of the proper time: X = X ( ) (2.1)

14. Locate your helloworld.png image on your desktop and drag it into the Resources folder. I d like you to get into the habit of saving your images here. It s a good habit that will help you to stay organized. Later on, if you begin working with huge, image-driven files, you may want to create your own Images folder. For now, drop your images into the Resources folder. 15. Check the box that states: Copy items into your destination group s folder. Doing so ensures that even if you change the location of your folder or delete the image, this image will still appear in your application file because Xcode has made a copy of it in your Resources folder. For example, right now you have the image stored on your desktop. If you delete it from there, or send this folder to the Internet or an iPhone, without checking this box, then it will not be a part of your program. Checking this box guarantees that the helloworld.png you re putting into the Resources folder will be wherever the program is. To complete this step, click the Add button or hit your Return key. 16. Once you have opened the Resources folder, double-click on the nib file, as shown in Figure 4 9. As you know already, this is the file that ends with .xib specifically the helloWorld_004ViewController.xib file and opening a nib file automatically opens up Interface Builder, which is how and where we visually control our app. We want to do this because it s time to connect pictures, buttons, and labels to the code you ve been writing.

The UCConnectionMetaData class provides meta-information for example, the maximum number of connections allowed, and so on regarding the managed connection and the underlying physical connection class:

To describe distance measurements, we are going to need a metric, that is, a function which allows us to de ne the distance between two points. Here we will stick with special relativity and use the at space Minkowski metric which is usually denoted by . You may recall that the time and spatial components of the metric have different sign; the choice used is referred to as the signature of the metric. In string theory, it is convenient to place the negative sign with the time component, so in the case of d = 3 spatial dimensions we can write the Minkowski metric as a matrix 1 0 = 0 0 0 1 0 0 0 0 1 0 0 0 0 1

package ucnyjca; import javax.resource.ResourceException; import javax.resource.spi.*;

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