JSci.physics.quantum
Class GammaMatrix

java.lang.Object
  JSci.maths.matrices.Matrix
      JSci.maths.matrices.AbstractComplexMatrix
          JSci.maths.matrices.AbstractComplexSquareMatrix
              JSci.maths.matrices.ComplexSquareMatrix
                  JSci.physics.quantum.GammaMatrix

All Implemented Interfaces:

java.io.Serializable, Algebra.Member, BanachSpace.Member, CStarAlgebra.Member, Module.Member, VectorSpace.Member, Ring.Member, AbelianGroup.Member, SquareMatrix, Member

public final class GammaMatrix
extends ComplexSquareMatrix

The GammaMatrix class provides an object for encapsulating the gamma matrices.

See Also:

Serialized Form

Field Summary

static GammaMatrix	Y0_D Gamma 0 matrix (Dirac representation).
static GammaMatrix	Y0_M Gamma 0 matrix (Majorana representation).
static GammaMatrix	Y0_W Gamma 0 matrix (Weyl representation).
static GammaMatrix	Y1_D Gamma 1 matrix (Dirac representation).
static GammaMatrix	Y1_M Gamma 1 matrix (Majorana representation).
static GammaMatrix	Y1_W Gamma 1 matrix (Weyl representation).
static GammaMatrix	Y2_D Gamma 2 matrix (Dirac representation).
static GammaMatrix	Y2_M Gamma 2 matrix (Majorana representation).
static GammaMatrix	Y2_W Gamma 2 matrix (Weyl representation).
static GammaMatrix	Y3_D Gamma 3 matrix (Dirac representation).
static GammaMatrix	Y3_M Gamma 3 matrix (Majorana representation).
static GammaMatrix	Y3_W Gamma 3 matrix (Weyl representation).
static GammaMatrix	Y5_D Gamma 5 matrix (Dirac representation).
static GammaMatrix	Y5_M Gamma 5 matrix (Majorana representation).
static GammaMatrix	Y5_W Gamma 5 matrix (Weyl representation).

Fields inherited from class JSci.maths.matrices.ComplexSquareMatrix

matrixIm, matrixRe

Fields inherited from class JSci.maths.matrices.AbstractComplexSquareMatrix

luCache

Fields inherited from class JSci.maths.matrices.Matrix

numCols, numRows

Method Summary

Complex	det() Returns the determinant.
boolean	isUnitary() Returns true if this matrix is unitary.
Complex	trace() Returns the trace.

Methods inherited from class JSci.maths.matrices.ComplexSquareMatrix

add, add, conjugate, directSum, equals, frobeniusNorm, getElement, getImagElement, getRealElement, hermitianAdjoint, imag, infNorm, inverse, luDecompose, luDecompose, mapElements, multiply, multiply, multiply, negate, polarDecompose, real, scalarMultiply, scalarMultiply, setElement, setElement, subtract, subtract, tensor, toString, transpose

Methods inherited from class JSci.maths.matrices.AbstractComplexSquareMatrix

add, involution, isHermitian, luDecompose_cache, norm, operatorNorm, scalarDivide, scalarDivide, scalarProduct, scalarProduct, subtract

Methods inherited from class JSci.maths.matrices.AbstractComplexMatrix

add, directSum, equals, equals, getSet, hashCode, multiply, multiply, scalarDivide, scalarMultiply, subtract, tensor

Methods inherited from class JSci.maths.matrices.Matrix

columns, getInvalidElementMsg, rows

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface JSci.maths.fields.Ring.Member

multiply

Methods inherited from interface JSci.maths.algebras.VectorSpace.Member

scalarDivide

Methods inherited from interface JSci.maths.algebras.Module.Member

scalarMultiply

Field Detail

Y0_D

public static final GammaMatrix Y0_D

Gamma 0 matrix (Dirac representation).

Y1_D

public static final GammaMatrix Y1_D

Gamma 1 matrix (Dirac representation).

Y2_D

public static final GammaMatrix Y2_D

Gamma 2 matrix (Dirac representation).

Y3_D

public static final GammaMatrix Y3_D

Gamma 3 matrix (Dirac representation).

Y5_D

public static final GammaMatrix Y5_D

Gamma 5 matrix (Dirac representation).

Y0_W

public static final GammaMatrix Y0_W

Gamma 0 matrix (Weyl representation).

Y1_W

public static final GammaMatrix Y1_W

Gamma 1 matrix (Weyl representation).

Y2_W

public static final GammaMatrix Y2_W

Gamma 2 matrix (Weyl representation).

Y3_W

public static final GammaMatrix Y3_W

Gamma 3 matrix (Weyl representation).

Y5_W

public static final GammaMatrix Y5_W

Gamma 5 matrix (Weyl representation).

Y0_M

public static final GammaMatrix Y0_M

Gamma 0 matrix (Majorana representation).

Y1_M

public static final GammaMatrix Y1_M

Gamma 1 matrix (Majorana representation).

Y2_M

public static final GammaMatrix Y2_M

Gamma 2 matrix (Majorana representation).

Y3_M

public static final GammaMatrix Y3_M

Gamma 3 matrix (Majorana representation).

Y5_M

public static final GammaMatrix Y5_M

Gamma 5 matrix (Majorana representation).

Method Detail

isUnitary

public boolean isUnitary()

Returns true if this matrix is unitary.

Overrides:

isUnitary in class AbstractComplexSquareMatrix

det

public Complex det()

Returns the determinant.

Overrides:

det in class ComplexSquareMatrix

trace

public Complex trace()

Returns the trace.

Overrides:

trace in class ComplexSquareMatrix