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Java > Open Source Codes > JSci > maths > algebras > su2Dim3


1 package JSci.maths.algebras;
2
3 import JSci.maths.*;
4 import JSci.maths.matrices.AbstractComplexMatrix;
5 import JSci.maths.matrices.AbstractComplexSquareMatrix;
6 import JSci.maths.matrices.ComplexSquareMatrix;
7 import JSci.maths.matrices.AbstractDoubleSquareMatrix;
8 import JSci.maths.matrices.DoubleSquareMatrix;
9 import JSci.maths.vectors.AbstractDoubleVector;
10 import JSci.maths.vectors.Double3Vector;
11 import JSci.maths.vectors.VectorDimensionException;
12 import JSci.maths.fields.ComplexField;
13
14 /**
15 * The su2Dim3 class encapsulates su(2) algebras using
16 * the 3 dimensional (adjoint) representation.
17 * Elements are represented by 3-vectors with a matrix basis.
18 * @version 1.2
19 * @author Mark Hale
20 */
21 public final class su2Dim3 extends LieAlgebra {
22         /**
23         * Basis array.
24         */
25         private final static Complex t1[][]={
26                 {Complex.ZERO,ComplexField.SQRT_HALF,Complex.ZERO},
27                 {ComplexField.SQRT_HALF,Complex.ZERO,ComplexField.SQRT_HALF},
28                 {Complex.ZERO,ComplexField.SQRT_HALF,Complex.ZERO}
29         };
30         private final static Complex t2[][]={
31                 {Complex.ZERO,ComplexField.MINUS_SQRT_HALF_I,Complex.ZERO},
32                 {ComplexField.SQRT_HALF_I,Complex.ZERO,ComplexField.MINUS_SQRT_HALF_I},
33                 {Complex.ZERO,ComplexField.SQRT_HALF_I,Complex.ZERO}
34         };
35         private final static Complex t3[][]={
36                 {Complex.ONE,Complex.ZERO,Complex.ZERO},
37                 {Complex.ZERO,Complex.ZERO,Complex.ZERO},
38                 {Complex.ZERO,Complex.ZERO,ComplexField.MINUS_ONE}
39         };
40         /**
41         * Basis.
42         */
43         private final static AbstractComplexSquareMatrix basisMatrices[]={
44                 new ComplexSquareMatrix(t1),
45                 new ComplexSquareMatrix(t2),
46                 new ComplexSquareMatrix(t3)
47         };
48         /**
49         * Metric array.
50         */
51         private final static double g[][]={
52                 {-2.0,0.0,0.0},
53                 {0.0,-2.0,0.0},
54                 {0.0,0.0,-2.0}
55         };
56         /**
57         * Cartan metric.
58         */
59         private final static AbstractDoubleSquareMatrix metricMatrix=new DoubleSquareMatrix(g);
60
61         private final static su2Dim3 _instance = new su2Dim3();
62         /**
63         * Constructs an su(2) algebra.
64         */
65         private su2Dim3() {
66                 super("su(2) [3]");
67         }
68         /**
69         * Singleton.
70         */
71         public static final su2Dim3 getInstance() {
72                 return _instance;
73         }
74         /**
75         * Returns an element as a matrix (vector*basis).
76         */
77         public AbstractComplexSquareMatrix getElement(final AbstractDoubleVector v) {
78                 AbstractComplexMatrix m=basisMatrices[0].scalarMultiply(v.getComponent(0));
79                 m=m.add(basisMatrices[1].scalarMultiply(v.getComponent(1)));
80                 m=m.add(basisMatrices[2].scalarMultiply(v.getComponent(2)));
81                 return (AbstractComplexSquareMatrix)m.scalarMultiply(Complex.I);
82         }
83         /**
84         * Returns the Lie bracket (commutator) of two elements.
85         * Same as the vector cross product.
86         */
87         public AbstractDoubleVector multiply(final AbstractDoubleVector a, final AbstractDoubleVector b) {
88                 if(!(a instanceof Double3Vector) || !(b instanceof Double3Vector))
89                         throw new VectorDimensionException("Vectors must be 3-vectors.");
90                 return ((Double3Vector)b).multiply((Double3Vector)a);
91         }
92         /**
93         * Returns the Killing Form of two elements (scalar product).
94         */
95         public double killingForm(final AbstractDoubleVector a, final AbstractDoubleVector b) {
96                 return a.scalarProduct(metricMatrix.multiply(b));
97         }
98         /**
99         * Returns the basis used to represent the Lie algebra.
100         */
101         public AbstractComplexSquareMatrix[] basis() {
102                 return basisMatrices;
103         }
104         /**
105         * Returns the Cartan metric.
106         */
107         public AbstractDoubleSquareMatrix cartanMetric() {
108                 return metricMatrix;
109         }
110 }
111
112
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