GammaMatrix


1   package JSci.physics.quantum;
2   
3   import JSci.maths.Complex;
4   import JSci.maths.matrices.ComplexSquareMatrix;
5   import JSci.maths.fields.ComplexField;
6   
7   /**
8   * The GammaMatrix class provides an object for encapsulating the gamma matrices.
9   * @version 1.2
10  * @author Mark Hale
11  */
12  public final class GammaMatrix extends ComplexSquareMatrix {
13          private static final Complex y0_D[][]={
14                  {ComplexField.ONE,ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO},
15                  {ComplexField.ZERO,ComplexField.ONE,ComplexField.ZERO,ComplexField.ZERO},
16                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.MINUS_ONE,ComplexField.ZERO},
17                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO,ComplexField.MINUS_ONE}
18          };
19          private static final Complex y1_D[][]={
20                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO,ComplexField.ONE},
21                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.ONE,ComplexField.ZERO},
22                  {ComplexField.ZERO,ComplexField.MINUS_ONE,ComplexField.ZERO,ComplexField.ZERO},
23                  {ComplexField.MINUS_ONE,ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO}
24          };
25          private static final Complex y2_D[][]={
26                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO,ComplexField.I},
27                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.MINUS_I,ComplexField.ZERO},
28                  {ComplexField.ZERO,ComplexField.MINUS_I,ComplexField.ZERO,ComplexField.ZERO},
29                  {ComplexField.I,ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO}
30          };
31          private static final Complex y3_D[][]={
32                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.ONE,ComplexField.ZERO},
33                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO,ComplexField.MINUS_ONE},
34                  {ComplexField.MINUS_ONE,ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO},
35                  {ComplexField.ZERO,ComplexField.ONE,ComplexField.ZERO,ComplexField.ZERO}
36          };
37          private static final Complex y5_D[][]={
38                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.ONE,ComplexField.ZERO},
39                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO,ComplexField.ONE},
40                  {ComplexField.ONE,ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO},
41                  {ComplexField.ZERO,ComplexField.ONE,ComplexField.ZERO,ComplexField.ZERO}
42          };
43          private static final Complex y0_M[][]={
44                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO,ComplexField.I},
45                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.MINUS_I,ComplexField.ZERO},
46                  {ComplexField.ZERO,ComplexField.I,ComplexField.ZERO,ComplexField.ZERO},
47                  {ComplexField.MINUS_I,ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO}
48          };
49          private static final Complex y1_M[][]={
50                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.I,ComplexField.ZERO},
51                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO,ComplexField.MINUS_I},
52                  {ComplexField.I,ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO},
53                  {ComplexField.ZERO,ComplexField.MINUS_I,ComplexField.ZERO,ComplexField.ZERO}
54          };
55          private static final Complex y2_M[][]={
56                  {ComplexField.I,ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO},
57                  {ComplexField.ZERO,ComplexField.I,ComplexField.ZERO,ComplexField.ZERO},
58                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.MINUS_I,ComplexField.ZERO},
59                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO,ComplexField.MINUS_I}
60          };
61          private static final Complex y3_M[][]={
62                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO,ComplexField.MINUS_I},
63                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.MINUS_I,ComplexField.ZERO},
64                  {ComplexField.ZERO,ComplexField.MINUS_I,ComplexField.ZERO,ComplexField.ZERO},
65                  {ComplexField.MINUS_I,ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO}
66          };
67          private static final Complex y5_M[][]={
68                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.I,ComplexField.ZERO},
69                  {ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO,ComplexField.I},
70                  {ComplexField.MINUS_I,ComplexField.ZERO,ComplexField.ZERO,ComplexField.ZERO},
71                  {ComplexField.ZERO,ComplexField.MINUS_I,ComplexField.ZERO,ComplexField.ZERO}
72          };
73          /**
74          * Gamma 0 matrix (Dirac representation).
75          */
76          public static final GammaMatrix Y0_D=new GammaMatrix(y0_D);
77          /**
78          * Gamma 1 matrix (Dirac representation).
79          */
80          public static final GammaMatrix Y1_D=new GammaMatrix(y1_D);
81          /**
82          * Gamma 2 matrix (Dirac representation).
83          */
84          public static final GammaMatrix Y2_D=new GammaMatrix(y2_D);
85          /**
86          * Gamma 3 matrix (Dirac representation).
87          */
88          public static final GammaMatrix Y3_D=new GammaMatrix(y3_D);
89          /**
90          * Gamma 5 matrix (Dirac representation).
91          */
92          public static final GammaMatrix Y5_D=new GammaMatrix(y5_D);
93          /**
94          * Gamma 0 matrix (Weyl representation).
95          */
96          public static final GammaMatrix Y0_W=Y5_D;
97          /**
98          * Gamma 1 matrix (Weyl representation).
99          */
100         public static final GammaMatrix Y1_W=Y1_D;
101         /**
102         * Gamma 2 matrix (Weyl representation).
103         */
104         public static final GammaMatrix Y2_W=Y2_D;
105         /**
106         * Gamma 3 matrix (Weyl representation).
107         */
108         public static final GammaMatrix Y3_W=Y3_D;
109         /**
110         * Gamma 5 matrix (Weyl representation).
111         */
112         public static final GammaMatrix Y5_W=Y0_D;
113         /**
114         * Gamma 0 matrix (Majorana representation).
115         */
116         public static final GammaMatrix Y0_M=new GammaMatrix(y0_M);
117         /**
118         * Gamma 1 matrix (Majorana representation).
119         */
120         public static final GammaMatrix Y1_M=new GammaMatrix(y1_M);
121         /**
122         * Gamma 2 matrix (Majorana representation).
123         */
124         public static final GammaMatrix Y2_M=new GammaMatrix(y2_M);
125         /**
126         * Gamma 3 matrix (Majorana representation).
127         */
128         public static final GammaMatrix Y3_M=new GammaMatrix(y3_M);
129         /**
130         * Gamma 5 matrix (Majorana representation).
131         */
132         public static final GammaMatrix Y5_M=new GammaMatrix(y5_M);
133         /**
134         * Constructs a gamma matrix.
135         */
136         private GammaMatrix(Complex gammaArray[][]) {
137                 super(gammaArray);
138         }
139         /**
140         * Returns true if this matrix is unitary.
141         */
142         public boolean isUnitary() {
143                 return true;
144         }
145         /**
146         * Returns the determinant.
147         */
148         public Complex det() {
149                 return ComplexField.MINUS_ONE;
150         }
151         /**
152         * Returns the trace.
153         */
154         public Complex trace() {
155                 return ComplexField.ZERO;
156         }
157 }
158 
159
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