added another relativistic electrodynamics check (energy density and Poynting

[ginac.git] / check / exam_indexed.cpp

diff --git a/check/exam_indexed.cpp b/check/exam_indexed.cpp
index 8e80e4ecc4becdd3dd6f896e3fa2da96eea1db28..e5a3772f5fc02a25dbccb21b99486209fffbdb3b 100644 (file)
--- a/check/exam_indexed.cpp
+++ b/check/exam_indexed.cpp
@@ -143,8 +143,10 @@ static unsigned symmetry_check(void)
 
 static unsigned edyn_check(void)
 {
-       // relativistic electrodynamics: check transformation laws of electric
-       // and magnetic fields by applying a Lorentz boost to the field tensor
+       // Relativistic electrodynamics
+
+       // Test 1: check transformation laws of electric and magnetic fields by
+       // applying a Lorentz boost to the field tensor
 
        unsigned result = 0;
 
@@ -202,6 +204,39 @@ static unsigned edyn_check(void)
        result += check_equal(By_p, gamma * (By + beta * Ez));
        result += check_equal(Bz_p, gamma * (Bz - beta * Ey));
 
+       // Test 2: check energy density and Poynting vector of electromagnetic field
+
+       // Minkowski metric
+       matrix eta(4, 4);
+       eta.set(0, 0, 1);
+       eta.set(1, 1, -1);
+       eta.set(2, 2, -1);
+       eta.set(3, 3, -1);
+
+       // Covariant field tensor
+       ex F_mu_nu = (indexed(eta, mu.toggle_variance(), rho.toggle_variance())
+                   * indexed(eta, nu.toggle_variance(), sigma.toggle_variance())
+                   * indexed(F, rho, sigma)).simplify_indexed();
+
+       // Energy-momentum tensor
+       ex T = (-indexed(eta, rho, sigma) * F_mu_nu.subs(s_nu == s_rho) 
+               * F_mu_nu.subs(lst(s_mu == s_nu, s_nu == s_sigma))
+             + indexed(eta, mu.toggle_variance(), nu.toggle_variance())
+               * F_mu_nu.subs(lst(s_mu == s_rho, s_nu == s_sigma))
+               * indexed(F, rho, sigma) / 4).simplify_indexed() / (4 * Pi);
+
+       // Extract energy density and Poynting vector
+       ex E = T.subs(lst(s_mu == 0, s_nu == 0)).normal();
+       ex Px = T.subs(lst(s_mu == 0, s_nu == 1));
+       ex Py = T.subs(lst(s_mu == 0, s_nu == 2)); 
+       ex Pz = T.subs(lst(s_mu == 0, s_nu == 3));
+
+       // Check results
+       result += check_equal(E, (Ex*Ex+Ey*Ey+Ez*Ez+Bx*Bx+By*By+Bz*Bz) / (8 * Pi));
+       result += check_equal(Px, (Ez*By-Ey*Bz) / (4 * Pi));
+       result += check_equal(Py, (Ex*Bz-Ez*Bx) / (4 * Pi));
+       result += check_equal(Pz, (Ey*Bx-Ex*By) / (4 * Pi));
+
        return result;
 }