static void TestPotential(Func <LorentzVectorVariableU, LorentzVectorU> createPotential, EuclideanVector3 v)
{
LorentzVectorVariableU coordinates = new LorentzVectorVariableU("t", "x", "y", "z");
LorentzVectorU potential = createPotential(coordinates);
LorentzVectorOperatorL del = coordinates.Del;
ElectromagneticField field0 = new ElectromagneticField(potential, del);
TestField(field0);
ElectromagneticField field1 = field0.Transform(v);
TestField(field1);
TestFieldTransforms(field0.ElectricField, field0.MagneticField, field1.ElectricField, field1.MagneticField, v);
CompareInvariantScalars(field0, field1);
ElectromagneticField field2 = field1.Transform(-v);
TestField(field2);
TestFieldTransforms(field1.ElectricField, field1.MagneticField, field2.ElectricField, field2.MagneticField, -v);
CompareInvariantScalars(field1, field2);
Assert.AreEqual(field0.Potential, field2.Potential, "A dual transform");
Assert.AreEqual(field0.Del.ToString(), field2.Del.ToString(), "Del dual transform");
Assert.AreEqual(field0.ElectricField, field2.ElectricField, "E dual transform");
Assert.AreEqual(field0.MagneticField, field2.MagneticField, "B dual transform");
Assert.AreEqual(field0.CurrentDensity, field2.CurrentDensity, "J dual transform");
}
public ElectromagneticField(LorentzVectorU potential, LorentzVectorOperatorL del)
{
this.Potential = potential;
this.Del = del;
this.ElectricField = -this.Del.Vector * potential.Scalar - this.Del.Scalar * potential.Vector;
this.MagneticField = this.Del.Vector.Cross(potential.Vector);
this.FieldStrengthTensor = potential.Curl(this.Del.Invert());
this.CurrentDensity = this.Del * this.FieldStrengthTensor;
this.DualFieldStrengthTensor = new LorentzMatrixLL((i, j) =>
{
Symbol symbol = Symbol.Zero;
for (int k = 0; k < 4; k++)
{
for (int l = 0; l < 4; l++)
{
symbol = symbol - LeviCivita.Four[i, j, k, l] * this.FieldStrengthTensor[k, l] / 2;
}
}
return(symbol);
});
}
static void TestCurrentDensity(LorentzVectorU J, LorentzVectorOperatorL del)
{
Assert.AreEqual(del.Dot(J), Symbol.Zero, "Divergence of current density");
}
