New and more powerful methods for eliminating background intensity are needed in order to make possible the development of neutrino astronomy into a new, far-reaching branch of science.

The energy spectra of the two GOLDSTONE models are investigated using the RITz variational method. More quantum mechanical ground states ate obtained, but they do not belong to the same Hilbert space. One can solve the eigenvalue problem using only one Hilbert space but in this case the ground state does not show aH the symmetries possessed by the Hamiltonian. w 1. For the understanding of spontaneous symmetry breakdown the GOLDSTONE model seems to be the most simple example [1]. Here the ground state possesses a broken symmetry already in the classical theory. It was this model in which GOLDSTON]g recognised the so-called GOLDSTONV theorem, according to whieh spontaneous breaking of a continuous symmetry is neeessarily connected with the appearance of zero mass bosons. For the understanding of the physical consequences of the GOLDSTONE model the ScrnFF representation seems to be the most convenient one i.e. working in a representation in which not the particle number but the field potential is diagonal [2]. In the following approximate solutions of the two GOLDSTO~E models will be given and the physical causes and consequences of the symmetry breaking will be discussed. w 2. Let us consider the first GOLDSTO/~E modeh a self-coupled real scalar field described by the field equation~=o. 2 The Hamiltonian of the field has the following form: J[ 2 ~ (V_ ~)2 _ _4_/~~ q2 + -4-o ~4 d 3 r. (I) The field equation and the Hamiltonian are invariant with respeat to the substitution r ~(x)--+--zt(x).(2) 5* Acta Phys. Hung. Toro. XIX., 1965.

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By considering a theory based on a simple model the mathematical possibilities are analysed when the same energy operator may have in quantum theory two (approximatively) orthogonal ground states and eigenfunction systems. The consequences for the elementary particle physies are discussed.1. In theories of solid state physics based on certain models one can show that while the ground state of the unperturbed eaergy H 0 is of a "normal" type, the grouad state of the total energy H has a "superconducting" character. This latter caImot be considered as the perturbation of the normal ground state, since it is non-regular in the coupling constant. Since the two types of states are connected by a HAAG transformation [1], they ate approximatively or (when the degrees of freedom of the system grow to infinity) exactly orthogonal. The field theoretical role of sucll superconducting solutions was emphasized first by ~ 9[2]. Recently MXRSnAK and OKVBO [3] considered the possibility that the same Hamiltonian may have two types of solutions, a normal solution which may be obtained by the perturbation theory starting from the mathematical vacnum state, and a superconducting solution depending singularly on the coupling constant, the two solutions being orthogonal to each other. Thus one field operator, one Hamihonian may describe two types of particles, e. g. leptons and baryons.In the following a simple one-dimensional model having two types of solutions will be discussed and some remarks about the existence of such a twofold system of solutions in quantum field theory will be added.2. Let us considera one-dimensional anharmonic oseillator as ottr first model, having the Hamiltonian