Perfect Actions for Scalar Theories

We construct an optimally local perfect lattice action for free scalars of arbitrary mass, and truncate its couplings to a unit hypercube. Spectral and thermodynamic properties of this ``hypercube scalar'' are drastically improved compared to the standard action. We also discuss new variants of perfect actions, using anisotropic or triangular lattices, or applying new types of RGTs. Finally we add a \lambda \phi^4 term and address perfect lattice perturbation theory. We report on a lattice action for the anharmonic oscillator, which is perfect to O(\lambda).Comment: 3 pages, LaTex, 4 figures, talk presented at LATTICE'97, Ref. [1] correcte

Tensor-multi-scalar theories from multidimensional cosmology

Inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold M=M_0 x M_1 x ... M_n are investigated under dimensional reduction to tensor-multi-scalar theories. In the Einstein conformal frame, these theories take the shape of a flat sigma-model. For the singular case where M_0 is 2-dimensional, the dimensional reduction to dilaton gravity is preformed with different distinguished representations of the action.Comment: 14 pages, latex, to appear in Phys. Rev.

Reflection positivity in higher derivative scalar theories

Reflection positivity constitutes an integral prerequisite in the Osterwalder-Schrader reconstruction theorem which relates quantum field theories defined on Euclidean space to their Lorentzian signature counterparts. In this work we rigorously prove the violation of reflection positivity in a large class of free scalar fields with a rational propagator. This covers in particular higher-derivative theories where the propagator admits a partial fraction decomposition as well as degenerate cases including e.g. p^4 -type propagators.Comment: 9 pages, 1 figur

Isotropic stars in higher-order torsion scalar theories

Two tetrad spaces reproducing spherically symmetric spacetime are applied to the equations of motion of higher-order torsion theories. Assuming the existence of conformal Killing vector, two isotropic solutions are derived. We show that the first solution is not stable while the second one confirms a stable behavior. We also discuss the construction of the stellar model and show that one of our solution capable of such construction while the other cannot. Finally, we discuss the generalized Tolman-Oppenheimer-Volkoff and show that one of our models has a tendency to equilibrium.Comment: 16 pages Latex, 5 figures, will appear in Adv. High Energy Phys. (2016