Partial and Complete Observables for Hamiltonian Constrained Systems

We will pick up the concepts of partial and complete observables introduced by Rovelli in order to construct Dirac observables in gauge systems. We will generalize these ideas to an arbitrary number of gauge degrees of freedom. Different methods to calculate such Dirac observables are developed. For background independent field theories we will show that partial and complete observables can be related to Kucha\v{r}'s Bubble Time Formalism. Moreover one can define a non-trivial gauge action on the space of complete observables and also state the Poisson brackets of these functions. Additionally we will investigate, whether it is possible to calculate Dirac observables starting with partially invariant partial observables, for instance functions, which are invariant under the spatial diffeomorphism group.Comment: 38 page

Exact flow equation for composite operators

We propose an exact flow equation for composite operators and their correlation functions. This can be used for a scale-dependent partial bosonization or "flowing bosonization" of fermionic interactions, or for an effective change of degrees of freedom in dependence on the momentum scale. The flow keeps track of the scale dependent relation between effective composite fields and corresponding composite operators in terms of the fundamental fields.Comment: 7 pages, 1 figure, minor changes, published versio

Entanglement entropy between real and virtual particles in ϕ4\phi ^{4} quantum field theory

The aim of this work is to compute the entanglement entropy of real and virtual particles by rewriting the generating functional of $\phi ^{4}$ theory as a mean value between states and observables defined through the correlation functions. Then the von Neumann definition of entropy can be applied to these quantum states and in particular, for the partial traces taken over the internal or external degrees of freedom. This procedure can be done for each order in the perturbation expansion showing that the entanglement entropy for real and virtual particles behaves as $\ln (m_{0})$. In particular, entanglement entropy is computed at first order for the correlation function of two external points showing that mutual information is identical to the external entropy and that conditional entropies are negative for all the domain of $m_{0}$. In turn, from the definition of the quantum states, it is possible to obtain general relations between total traces between different quantum states of a r theory. Finally, discussion about the possibility of taking partial traces over external degrees of freedom is considered, which implies the introduction of some observables that measure space-time points where interaction occurs.Comment: 4 figure

3N Scattering in a Three-Dimensional Operator Formulation

A recently developed formulation for a direct treatment of the equations for two- and three-nucleon bound states as set of coupled equations of scalar functions depending only on vector momenta is extended to three-nucleon scattering. Starting from the spin-momentum dependence occurring as scalar products in two- and three-nucleon forces together with other scalar functions, we present the Faddeev multiple scattering series in which order by order the spin-degrees can be treated analytically leading to 3D integrations over scalar functions depending on momentum vectors only. Such formulation is especially important in view of awaiting extension of 3N Faddeev calculations to projectile energies above the pion production threshold and applications of chiral perturbation theory 3N forces, which are to be most efficiently treated directly in such three-dimensional formulation without having to expand these forces into a partial wave basis.Comment: 25 pages, 0 figure

Highly-Smooth Zero-th Order Online Optimization Vianney Perchet

The minimization of convex functions which are only available through partial and noisy information is a key methodological problem in many disciplines. In this paper we consider convex optimization with noisy zero-th order information, that is noisy function evaluations at any desired point. We focus on problems with high degrees of smoothness, such as logistic regression. We show that as opposed to gradient-based algorithms, high-order smoothness may be used to improve estimation rates, with a precise dependence of our upper-bounds on the degree of smoothness. In particular, we show that for infinitely differentiable functions, we recover the same dependence on sample size as gradient-based algorithms, with an extra dimension-dependent factor. This is done for both convex and strongly-convex functions, with finite horizon and anytime algorithms. Finally, we also recover similar results in the online optimization setting.Comment: Conference on Learning Theory (COLT), Jun 2016, New York, United States. 201