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Hence, any amplitude taken between a physical state and a null state vanishes. This implies a result, which is somewhat akin to the idea of a phase factor in ordinary quantum mechanics. Two states a , b = ei a represent the same physical state in quantum mechanics since the resulting amplitudes are the same. Likewise, since any inner product between a physical state and a null state vanishes, adding a null state = Q to a physical state generates a new state which is physically equivalent to :

/* - (void)viewDidLoad { [super viewDidLoad]; // Uncomment the following line to display an Edit button in the navigation bar for this view controller. // self.navigationItem.rightBarButtonItem = self.editButtonItem; } */

n The classes to instantiate are specified at runtime. n You need to avoid building a class hierarchy of factories that parallels the

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because the second term on the right does not contribute to any inner product and hence does not change the physical predictions of the theory, which are the amplitudes. Since Q raises the ghost number of a state by 1, if the ghost number of is m, then the ghost number of is m 1. Important special cases are states with ghost number 0. If the ghost number is 0, then U =0 Looking at the form of U, namely, Eq. (6.7), we see that this implies that bk = 0. Furthermore, a state annihilated by the ghost elds bk cannot be annihilated by the ghost elds c k. Since u = ci bi = ii bi ci = n bi ci we see that

The Java SE API associated with the Prototype pat-

U = n bi ci = n bi ci i i Hence if bk = 0, the c k cannot annihilate the state since this would result in a contradiction. When bk = 0, it immediately follows that U = 0, but the above result shows that if c k = 0 also, we would have U = n 0 , a contradiction. The key result for states with zero ghost number is the following. Looking at Q in Eq. (6.5), it is clear that if bk = 0 then Q = ci K i

Example Code The following is example Java code for demonstrating the Prototype pattern. There are two viewpoints on the Prototype pattern. The first is that it is there to simplify creating new instances of objects without knowing their concrete class. The second is it is there to simplify creating exact copies (or clones) of an original object. The following example does not contain any state information in the objects prior to the call to getClone(). It demonstrates the first form of Prototype.

You need to delete the two comment markers: /* and */, and then delete the line comments starting with the // so the section now appears like this:

package javaee.architect.Prototype; public class PrototypePattern { public static void main(String[] args) { System.out.println("Prototype Pattern Demonstration."); System.out.println("--------------------------------"); // Create prototypes System.out.println("Constructing prototypes."); PrototypeIF prototype1 = new ConcretePrototype1(); PrototypeIF prototype2 = new ConcretePrototype2(); // Get clones from prototypes System.out.println("Constructing clones from prototypes."); PrototypeIF clone1 = prototype1.getClone(); PrototypeIF clone2 = prototype2.getClone(); // Call actions on the clones System.out.println("Calling actions on the clones."); clone1.action();

This implies that for a state with zero ghost number Ki = 0 (6.9)

clone2.action(); System.out.println(); } } package javaee.architect.Prototype; public class ConcretePrototype1 implements PrototypeIF { public ConcretePrototype1() { System.out.println("ConcretePrototype1 constructed."); } public PrototypeIF getClone() { // if required, put deep copy code here return new ConcretePrototype1(); } public void action() { System.out.println("ConcretePrototype1.action() called"); } } package javaee.architect.Prototype; public class ConcretePrototype2 implements PrototypeIF { public ConcretePrototype2() { System.out.println("ConcretePrototype2 constructed."); } public PrototypeIF getClone() { // if required, put deep copy code here return new ConcretePrototype1(); } public void action() { System.out.println("ConcretePrototype2.action() called."); } } package javaee.architect.Prototype; public interface PrototypeIF { public PrototypeIF getClone(); // as opposed to Object.clone() public void action(); }

So, we can say that a state which is BRST invariant with zero ghost number is also invariant under the symmetry described by the generators K i. Furthermore, if a state has ghost number zero, this tells us that the state is not a ghost state, hence we avoid negative probabilities.

- (void)viewDidLoad { [super viewDidLoad];

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