We investigate the field theory of strings having as a target space an arbitrary discrete onedimensional manifold. The existence of the continuum limit is guaranteed if the target space is a Dynkin diagram of a simply laced Lie algebra or its affine extension. In this case the theory can be mapped onto the theory of strings embedded in the infinite discrete line ZZ which is the target space of ...

We investigate the field theory of strings having as a target space an arbitrary discrete one-dimensional manifold. The existence of the continuum limit is guaranteed if the target space is a Dynkin diagram of a simply laced Lie algebra or its affine extension. In this case the theory can be mapped onto the theory of strings embedded in the infinite discrete line ZZ which is the target space of...

We study two limit cases λ→∞ and λ→ 0 in Born-Infeld equations. Here the parameter λ > 0 is interpreted as the maximal electric field in the electromagnetic theory and the case λ = 0 corresponds to the string theory. Formal limits are governed by the classical Maxwell equations and pressureless magnetohydrodynamics system, respectively. For studying the limit λ → ∞, a new scaling is introduced....

We consider the empirical process Gt of a one-dimensional diffusion with finite speed measure, indexed by a collection of functions F . By the central limit theorem for diffusions, the finite-dimensional distributions of Gt converge weakly to those of a zero-mean Gaussian random process G. We prove that the weak convergence Gt ⇒ G takes place in l(F) if and only if the limit G exists as a tight...

We solve a long-standing problem in particle physics: that of deriving the Deep Inelastic structure functions of the proton from the fundamental theory of strong interactions, Quantum ChromoDynamics (QCD). In the Bjorken limit, the momenta of the constituents of the proton (the partons) can be assumed to be in a two-dimensional plane in Minkowski space: a dimensional reduction of QCD to two spa...

We analyze the self-averaging properties of time-reversed solutions of the paraxial wave equation with random coefficients, which we take to be Markovian in the direction of propagation. This allows us to construct an approximate martingale for the phase space Wigner transform of two wave fields. Using a priori L-bounds available in the time-reversal setting, we prove that the Wigner transform ...