Lagrangian-Hamiltonian unified formalism for field theory

The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description comprises the main features of the Lagrangian and Hamiltonian formalisms, both for the regular and singular cases. This formulation is a first step toward further applications in optimal control theory for PDE's.Comment: LaTeX file, 23 pages. Minor changes have been made. References are update

Searching for a Connection Between Matroid Theory and String Theory

We make a number of observations about matter-ghost string phase, which may eventually lead to a formal connection between matroid theory and string theory. In particular, in order to take advantage of the already established connection between matroid theory and Chern-Simons theory, we propose a generalization of string theory in terms of some kind of Kahler metric. We show that this generalization is closely related to the Kahler-Chern-Simons action due to Nair and Schiff. In addition, we discuss matroid/string connection via matroid bundles and a Schild type action, and we add new information about the relationship between matroid theory, D=11 supergravity and Chern-Simons formalism.Comment: 28 pages, LaTex, section 6 and references adde

Σ(1385)± resonance production in Pb–Pb collisions at √sNN = 5.02 TeV

Hadronic resonances are used to probe the hadron gas produced in the late stage of heavy-ion collisions since they decay on the same timescale, of the order of 1 to 10 fm/c, as the decoupling time of the system. In the hadron gas, (pseudo)elastic scatterings among the products of resonances that decayed before the kinetic freeze-out and regeneration processes counteract each other, the net effect depending on the resonance lifetime, the duration of the hadronic phase, and the hadronic cross sections at play. In this context, the Σ(1385)± particle is of particular interest as models predict that regeneration dominates over rescattering despite its relatively short lifetime of about 5.5 fm/c. The first measurement of the Σ(1385)± resonance production at midrapidity in Pb-Pb collisions at sNN−−−√=5.02 TeV with the ALICE detector is presented in this Letter. The resonances are reconstructed via their hadronic decay channel, Λπ, as a function of the transverse momentum (pT) and the collision centrality. The results are discussed in comparison with the measured yield of pions and with expectations from the statistical hadronization model as well as commonly employed event generators, including PYTHIA8/Angantyr and EPOS3 coupled to the UrQMD hadronic cascade afterburner. None of the models can describe the data. For Σ(1385)±, a similar behaviour as K∗(892)0 is observed in data unlike the predictions of EPOS3 with afterburner