Giuseppe Nardelli

Localization of nonlocal theories

We show that a certain class of nonlocal scalar models, with a kinetic operator inspired by string field theory, is equivalent to a system which is local in the coordinates but nonlocal in an auxiliary evolution variable. This system admits both Lagrangian and Hamiltonian formulations, and its Cauchy problem and quantization are well-defined. We classify exact nonperturbative solutions of the localized model which can be found via the diffusion equation governing the fields.

Route to nonlocal cosmology

An analytic approach to phenomenological models inspired by cubic string field theory is introduced and applied to some examples. We study a class of actions for a minimally coupled, homogeneous scalar field whose energy density contains infinitely many time derivatives. These nonlocal systems are systematically localized and an algorithm to find cosmological solutions of the dynamical equations is provided. Our formalism is able to define the nonlocal field in regions of the parameter space which are inaccessible by standard methods. Also, problems related to nonlocality are reinterpreted under a novel perspective and naturally overcome. We consider phenomenological models living on a Friedmann-Robertson-Walker background with power-law scale factor, both in four dimensions and on a high-energy braneworld. The quest for solutions unravels general features of nonlocal dynamics indicating several future directions of investigation.

Gauge invariance and anomalous dimensions of a light-cone Wilson loop in light-like axial gauge

Complete two-loop calculation of a dimensionally regularized Wilson loop with light-like segments is performed in the light-like axial gauge with the Mandelstam-Leibbrandt prescription for the gluon propagator. We find an expression which {\it exactly} coincides with the one previously obtained for the same Wilson loop in covariant Feynman gauge. The renormalization of Wilson loop is performed in the

Nonlocal gravity and the diffusion equation

\MS-

A new rolling tachyon solution of cubic string field theory

scheme using a general procedure tailored to the light-like axial gauge. We find that the renormalized Wilson loop obeys a renormalization group equation with the same anomalous dimensions as in covariant gauges. Physical implications of our result for investigation of infrared asymptotics of perturbative QCD are pointed out.Complete two-loop calculation of a dimensionally regularized Wilson loop with light-like segments is performed in the light-like axial gauge with the Mandelstam-Leibbrandt prescription for the gluon propagator. We find an expression which exactly coincides with the one previously obtained for the same Wilson loop in covariant Feynman gauge. The renormalization of the Wilson loop is performed in the MS-scheme using a general procedure tailored to the light-like axial gauge. We find that the renormalized Wilson loop obeys a renormalization group equation with the same anomalous dimensions as in covariant gauges. Physical implications of our result for the investigation of infrared asymptotics of perturbative QCD are pointed out.

COSMOLOGICAL ROLLING SOLUTIONS OF NONLOCAL THEORIES

We propose a nonlocal scalar-tensor model of gravity with pseudodifferential operators inspired by the effective action of p-adic string and string field theory on flat spacetime. An infinite number of derivatives act both on the metric and scalar field sector. The system is localized via the diffusion equation approach and its cosmology is studied. We find several exact dynamical solutions, also in the presence of a barotropic fluid, which are stationary in the diffusion flow. In particular, and contrary to standard general relativity, there exist solutions with exponential and power-law scale factor also in an open universe, as well as solutions with sudden future singularities or a bounce. Also, from the point of view of quantum field theory, spontaneous symmetry breaking can be naturally realized in the class of actions we consider.

Momentum transforms and Laplacians in fractional spaces

We present a new analytic time dependent solution of cubic string field theory at the lowest order in the level truncation scheme. The tachyon profile we have found is a bounce in time, a C ∞ function which represents an almost exact solution, with an extremely good degree of accuracy, of the classical equations of motion of the truncated string field theory. Such a finite energy solution describes a tachyon which at x 0 = -∞ is at the maximum of the potential, at later times rolls toward the stable minimum and then up to the other side of the potential toward the inversion point and then back to the unstable maximum for x 0 → +∞. The energy-momentum tensor associated with this rolling tachyon solution can be explicitly computed. The energy density is constant, the pressure is an even function of time which can change sign while the tachyon rolls toward the minimum of its potential. A new form of tachyon matter is realized which might be relevant for cosmological applications.

Quantum mechanics in fractional and other anomalous spacetimes

We find nonperturbative solutions of a nonlocal scalar field equation, with cubic or exponential potential on a cosmological background. The former case corresponds to the lowest level effective tachyon action of cubic string field theory. While the well known Minkowski solution is wildly oscillating, due to Hubble friction its cosmological counterpart describes smooth rolling toward the local minimum of the potential.

Kinks of open superstring field theory

We define an infinite class of unitary transformations between position and momentum fractional spaces, thus generalizing the Fourier transform to a special class of fractal geometries. Each transform diagonalizes a unique Laplacian operator. We also introduce a new version of fractional spaces, where coordinates and momenta span the whole real line. In one topological dimension, these results are extended to more general measures.

Perturbative Wilson loop in two-dimensional non-commutative Yang–Mills theory

We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenbergs principle is proven and the wave-functions minimizing the uncertainty are found. In spite of the fact that ordinary time and spatial translations are broken and the dynamics is not unitary, the theory is in one-to-one correspondence with a unitary one, thus allowing us to employ standard tools of analysis. These features are illustrated in the examples of the free particle and the harmonic oscillator. While fractional (and the more general anomalous-spacetime) free models are formally indistinguishable from ordinary ones at the classical level, at the quantum level they differ both in the Hilbert space and for a topological term fixing the classical action in the path integral formulation. Thus, all non-unitarity in fractional quantum dynamics is encoded in a contribution depending only on the initial and...