Ground State Energy for Massive Fields and Renormalisation

We discuss the renormalisation of the ground state energy of massive fields obeying boundary conditions, i.e., of the Casimir effect, and emphasise the role of the mass for its understanding. This is an extended abstract of a talk given at the topical group meeting on Casimir Forces at the Harvard-Smithsonian Center for Astrophysics on March 15-29, 1998. Renormalisation is a key to the understanding of the structure of quantum field theory. The kind of ultraviolet divergencies occurring divide the perturbative field theoretical models into renormalizable and non or super renormalizable ones. The ultraviolet divergencies occurring during the calculation of ground state energy in different backgrounds (including boundary conditions, i.e., the Casimir effect) carry information on the classical system which one is forced to associate in order to remove resp. interprete the divergencies. In the present note which is an extended abstract of a talk we discuss the renormalisation using different examples. These are the Casimir effect for massive scalar [1] and spinor [2] fields and the radiative corrections [3] to the electromagnetic Casimir effect with boundary conditions on a sphere. In addition we consider the ground state energy of a scalar field in a spherically symmetric smooth background field [4]. For all questions and references not given in this note we refer to the cited papers. The necessity to associate some classical system with any ground state energy arises from its very nature. The ground state energy is the amount of energy left in a quantised system when all excitations are gone. To any excitated level it given at the topical group meeting on Casimir Forces at the Harvard-Smithsonian Center for Astrophysics on March 15-29, 1998.