Physical Degrees of Freedom of Non-local Theories

TL;DR

This paper investigates the physical phase space of non-local theories, including p-adic string theory and string field theory, revealing fixed points with trivial, finite, or infinite dimensional phase spaces, and analyzing their constraints and symplectic structure.

Contribution

It provides a detailed analysis of the physical phase space structure of non-local theories around fixed points, highlighting differences between various models and configurations.

Findings

Phase space around q=0 is trivial in p-adic string theory.

Phase space around q=1/g is infinite dimensional in p-adic string theory.

In string field theory, phase space is two-dimensional near q=0 and infinite dimensional near q=M^2/g.

Abstract

We analyze the physical (reduced) space of non-local theories, around the fixed points of these systems, by analyzing: i) the Hamiltonian constraints appearing in the 1+1 formulation of those theories, ii) the symplectic two form in the surface on constraints. P-adic string theory for spatially homogeneous configurations has two fixed points. The physical phase space around $q=0$ is trivial, instead around $q=\frac 1g$ is infinite dimensional. For the special case of the rolling tachyon solutions it is an infinite dimensional lagrangian submanifold. In the case of string field theory, at lowest truncation level, the physical phase space of spatially homogeneous configurations is two dimensional around $q=0$, which is the relevant case for the rolling tachyon solutions, and infinite dimensional around $q=\frac {M^2}g$.