Journal of Mathematical Physics · 1963 · 658 citations · 9 references
Natural SciencesMathematicsPhysicsDifferential EquationsMathematical PhysicsRepresentation TheoryEigenvalue ProblemsLie AlgebrasLie GroupsOperator TheorySystems Of Differential EquationsTime IntegrationEigenfunction ExpansionsEigenvectorsFinite-dimensional Lie AlgebrasGeneralized EigenvectorsLie Algebra TheoryLie Group RepresentationsOperatorsRepresentation Theory Of Lie Algebras
The solution U(t) to the linear differential equation dU/dt = h(t)U can be represented by a finite product of exponential operators; In many interesting cases the representation is global. U(t) = exp[g1(t)H1] exp [g2(t)H2] … exp[gn(t)Hn] where gi(t) are scalar functions and Hi are constant operators. The number, n, of terms in this expansion is equal to the dimension of the Lie algebra generated by H(t). Each term in this product has time-independent eigenvectors. Some applications of this solution to physical problems are given.
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