Seminarium KMMF "Teoria Dwoistości"

In classical electrodynamics on simply connected space, equation dF=0 is equivalent to existence of electrodynamic potential (standard Poincare lemma). From a mathematical point of view, de Rham complex (algebra of total antisymmetric tensor fields with operator d fulfilling d^2=0) is the foundation of classical electrodynamics. In other tensor field theories we work with field T of more complicated symmetry and one of the field equations is DT=0, where "D" is some first order differential operator. In this talk I will define N-complex (algebra of tensor fields of given Young symmetry with operator D fulfilling D^N=0) and generalized Poincare lemma, which is the reason for existence of field potential in every integer-spin field theory.