A chaotic lattice field theory in one dimension*

Abstract Motivated by Gutzwiller’s semiclassical quantization, in which unstable periodic orbits of low-dimensional deterministic dynamics serve as a WKB ‘skeleton’ for chaotic quantum mechanics, we construct the corresponding skeleton infinite-dimensional lattice-discretized scalar field theories. In field-theoretical formulation, there is no evolution time, and ‘Lyapunov horizon’; only an enumeration lattice states that contribute to theory’s partition sum, each global spatiotemporal solution system’s Euler–Lagrange equations. The reformulation aligns ‘chaos theory’ with standard solid state, theory, statistical mechanics. spatiotemporal, crystallographer time-periodic dynamical systems theory are replaced d -dimensional Bravais cell tilings spacetime, weighted inverse its instability, Hill determinant. Hyperbolic shadowing large cells smaller ones ensures predictions dominated smallest cells. form function given determined group symmetries, is, space discretization, best studied on reciprocal lattice. Already one-dimensional discretization sufficient interest be focus this paper. particular, from perspective, ‘time’-reversal purely crystallographic notion, reflection point group, leading novel, symmetry quotienting perspective time-reversible theories associated topological zeta functions.