Fock representation of the renormalized higher powers of white noise and the Virasoro--Zamolodchikov--w∞∗w_{\infty} *--Lie algebra

The identification of the $*$--Lie algebra of the renormalized higher powers of white noise (RHPWN) and the analytic continuation of the second quantized Virasoro--Zamolodchikov--$w_{\infty} *$--Lie algebra of conformal field theory and high-energy physics, was recently established in \cite{id} based on results obtained in [1] and [2]. In the present paper we show how the RHPWN Fock kernels must be truncated in order to be positive definite and we obtain a Fock representation of the two algebras. We show that the truncated renormalized higher powers of white noise (TRHPWN) Fock spaces of order $\geq 2$ host the continuous binomial and beta processes

Quantum stochastic equation for test particle interacting with dilute Bose gas

We use the stochastic limit method to study long time quantum dynamics of a test particle interacting with a dilute Bose gas. The case of arbitrary form-factors and an arbitrary, not necessarily equilibrium, quasifree low density state of the Bose gas is considered. Starting from microscopic dynamics we derive in the low density limit a quantum white noise equation for the evolution operator. This equation is equivalent to a quantum stochastic equation driven by a quantum Poisson process with intensity $S-1$, where $S$ is the one-particle $S$ matrix. The novelty of our approach is that the equations are derived directly in terms of correlators, without use of a Fock-antiFock (or Gel'fand-Naimark-Segal) representation. Advantages of our approach are the simplicity of derivation of the limiting equation and that the algebra of the master fields and the Ito table do not depend on the initial state of the Bose gas. The notion of a causal state is introduced. We construct master fields (white noise and number operators) describing the dynamics in the low density limit and prove the convergence of chronological (causal) correlators of the field operators to correlators of the master fields in the causal state.Comment: 21 pages, LaTeX, published version (few improvements

A stochastic golden rule and quantum Langevin equation for the low density limit

A rigorous derivation of quantum Langevin equation from microscopic dynamics in the low density limit is given. We consider a quantum model of a microscopic system (test particle) coupled with a reservoir (gas of light Bose particles) via interaction of scattering type. We formulate a mathematical procedure (the so-called stochastic golden rule) which allows us to determine the quantum Langevin equation in the limit of large time and small density of particles of the reservoir. The quantum Langevin equation describes not only dynamics of the system but also the reservoir. We show that the generator of the corresponding master equation has the Lindblad form of most general generators of completely positive semigroups

Nuclear physics with a medium-energy Electron-Ion Collider

A polarized ep/eA collider (Electron-Ion Collider, or EIC) with variable center-of-mass energy sqrt(s) ~ 20-70 GeV and a luminosity ~ 10^{34} cm^{-2} s^{-1} would be uniquely suited to address several outstanding questions of Quantum Chromodynamics (QCD) and the microscopic structure of hadrons and nuclei: (i) the three-dimensional structure of the nucleon in QCD (sea quark and gluon spatial distributions, orbital motion, polarization, correlations); (ii) the fundamental color fields in nuclei (nuclear parton densities, shadowing, coherence effects, color transparency); (iii) the conversion of color charge to hadrons (fragmentation, parton propagation through matter, in-medium jets). We briefly review the conceptual aspects of these questions and the measurements that would address them, emphasizing the qualitatively new information that could be obtained with the collider. Such a medium-energy EIC could be realized at Jefferson Lab after the 12 GeV Upgrade (MEIC), or at Brookhaven National Lab as the low-energy stage of eRHIC.Comment: 9 pages, 5 figures. Mini-review compiled in preparation for the MEIC Conceptual Design Report, Jefferson Lab (2011

Hadron mass corrections in semi-inclusive deep inelastic scattering

We derive mass corrections for semi-inclusive deep inelastic scattering of leptons from nucleons using a collinear factorization framework which incorporates the initial state mass of the target nucleon and the final state mass of the produced hadron. The formalism is constructed specifically to ensure that physical kinematic thresholds for the semi-inclusive process are explicitly respected. A systematic study of the kinematic dependencies of the mass corrections to semi-inclusive cross sections reveals that these are even larger than for inclusive structure functions, especially at very small and very large hadron momentum fractions. The hadron mass corrections compete with the experimental uncertainties at kinematics typical of current facilities, and will be important to efforts at extracting parton distributions or fragmentation functions from semi-inclusive processes at intermediate energies.Comment: 22 pages, 6 figures; expanded discussion of kinematics and new scaling variable; appendix comparing collinear frames included; version to appear in JHE