Motivated by recent work on integrable flows of curves and 1+1 dimensional sigma models, several O(N)-invariant classes of hyperbolic equations Utx = f(U,Ut, Ux) for an N -component vector U(t, x) are considered. In each class we find all scalinghomogeneous equations admitting a higher symmetry of least possible scaling weight. Sigma model interpretations of these equations are presented.

1. THE PROBLEM On a square lattice (we consider here a D=2+1 lattice for simplicity) the exact rotational symmetry is confined to rotations that are integer multiples of π/2. If we attempt to build operators of spin J from basic components that are identical – that is, related by a lattice symmetry – then there is an ambiguity: exp(iJθ) ≡ exp(iJ ′ θ) ∀θ = nπ 2 (1) if J ′ = J + 4N ∀N (2) Thus, f...

We examine a particular kind of six-dimensional Cremonian universe featuring one dimension of space, three dimensions of time and other two dimensions that cannot be ranked as either time or space. One of these two, generated by a one-parametric aggregate of (straight-)lines lying on a quadratic cone, is more similar to the spatial dimension. The other, represented by a singly-parametrical set ...

Conventional lattice gauge theory assigns the lowest spin compatible with the symmetry channel of a given operator to the state coupling to that operator. Operators on a cubic lattice, however, are only defined on angles of π/2, hence states with spin equal modulo 4 may overlap significantly. This paper explores a new technique for generating lattice operators that may be placed onto the lattic...

Motivated by recent work on integrable flows of curves and 1+1 dimensional sigma models, several O(N)-invariant classes of hyperbolic equations Utx = f(U,Ut, Ux) for an N -component vector U(t, x) are considered. In each class we find all scalinghomogeneous equations admitting a higher symmetry of least possible scaling weight. Sigma model interpretations of these equations are presented.