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The phase structure of the scalar field theory with arbitrary powers of the gradient operator and a local non-analytic potential is investigated by the help of the RG in Euclidean space. The RG equation for the generating function of the derivative part of the action is derived. Infinitely many non-trivial fixed points of the RG transformations are found. The corresponding effective actions are unbounded from below and do probably not exhibit any particle content. Therefore they do not provide physically sensible theories.
If the local color symmetry in a quark-gluon matter is broken, the expectation value of the gluon field 〈Aμa(x)〉 may be different from zero. Such a gluon-condensed phase has been found in mean field approximation. The gluon-condensed phase is characterized by a static, periodic chromomagnetic field, which is coupled to a periodic spin-color density distribution of quarks and antiquarks. Transitions of first and second order type have been found between the gluon-condensed and normal phases, the latter characterized by the vanishing value of the mean gluon field.
The properties of nuclear matter are studied in the framework of quantum hadrodynamics. Assuming an ω-meson field, periodic in space, a self-consistent set of equations is derived in the mean-field approximation for the description of nucleons interacting via σ-meson and ω-meson fields. Solutions of these self-consistent equations have been found: The baryon density is constant in space, however, the baryon current density is periodic. This high density phase of nuclear matter can be produced by anisotropic external pressure, occurring, e.g., in relativistic heavy ion reactions. The self-consistent fields developing beyond the instability limit have a special screw symmetry. In the presence of such an ω field, the energy spectrum of the relativistic nucleons exhibits allowed and forbidden bands, similar to the energy spectrum of the electrons in solids.
