Identities among relations for higher-dimensional rewriting systems

We generalize the notion of identities among relations, well known for presentations of groups, to presentations of n-categories by polygraphs. To each polygraph, we associate a track n-category, generalizing the notion of crossed module for groups, in order to define the natural system of identities among relations. We relate the facts that this natural system is finitely generated and that the polygraph has finite derivation type.Comment: 16 pages, corrected version after review, to appear in S\'eminaires et Congr\`e

Application of the non-extensive statistical approach to high energy particle collisions

In high-energy collisions the number of the created particles is far less than the thermodynamic limit, especially in small colliding systems (e.g. proton-proton). Therefore final-state effects and fluctuations in the one-particle energy distribution are appreciable. As a consequence the characterization of identified hadron spectra with the Boltzmann\,--\,Gibbs thermodynamical approach is insufficient. Instead particle spectra measured in high-energy collisions can be described very well with Tsallis\,--\,Pareto distributions, derived from non-extensive thermodynamics. Using the Tsallis q-entropy formula, a generalization of the Boltzmann\,--\,Gibbs entropy, we interpret the microscopical physics by analysing the Tsallis $q$ and $T$ parameters. In this paper we give a quick overview on these parameters, analyzing identified hadron spectra from recent years in a wide center of mass energy range. We demonstrate that the fitted Tsallis-parameters show dependency on this energy and on the particle species. Our findings are described well by a QCD inspired evolution ansatz

Systematic analysis of the non-extensive statistical approach in high energy particle collisions-experiment vs. theory

The analysis of high-energy particle collisions is an excellent testbed for the non-extensive statistical approach. In these reactions we are far from the thermodynamical limit. In small colliding systems, such as electron-positron or nuclear collisions, the number of particles is several orders of magnitude smaller than the Avogadro number; therefore, finite-size and fluctuation effects strongly influence the final-state one-particle energy distributions. Due to the simple characterization, the description of the identified hadron spectra with the Boltzmann-Gibbs thermodynamical approach is insufficient. These spectra can be described very well with Tsallis-Pareto distributions instead, derived from non-extensive thermodynamics. Using the $q$-entropy formula, we interpret the microscopic physics in terms of the Tsallis $q$ and $T$ parameters. In this paper we give a view on these parameters, analyzing identified hadron spectra from recent years in a wide center-of-mass energy range. We demonstrate that the fitted Tsallis-parameters show dependency on the center-of-mass energy and particle species (mass). Our findings are described well by a QCD (Quantum Chromodynamics) inspired parton evolution ansatz. Based on this comprehensive study, apart from the evolution, both mesonic and baryonic components found to be non-extensive ($q>1$), besides the mass ordered hierarchy observed in the parameter $T$. We also study and compare in details the theory-obtained parameters for the case of PYTHIA8 Monte Carlo Generator, perturbative QCD and quark coalescence models.Comment: 21 pages, 12 figures. This is an extended version of our paper at the 36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2016), 10-15 July 2016, Ghent, Belgiu

The non-Abelian gauge theory of matrix big bangs

We study at the classical and quantum mechanical level the time-dependent Yang-Mills theory that one obtains via the generalisation of discrete light-cone quantisation to singular homogeneous plane waves. The non-Abelian nature of this theory is known to be important for physics near the singularity, at least as far as the number of degrees of freedom is concerned. We will show that the quartic interaction is always subleading as one approaches the singularity and that close enough to t=0 the evolution is driven by the diverging tachyonic mass term. The evolution towards asymptotically flat space-time also reveals some surprising features.Comment: 29 pages, 8 eps figures, v2: minor changes, references added: v3 small typographical changes

Sommerfeld effect in heavy quark chemical equilibration

Bödeker D, Laine M. Sommerfeld effect in heavy quark chemical equilibration. Journal of High Energy Physics. 2013;2013(1): 37.The chemical equilibration of heavy quarks in a quark-gluon plasma proceeds via annihilation or pair creation. For temperatures T much below the heavy quark mass M, when kinetically equilibrated heavy quarks move very slowly, the annihilation in the colour singlet channel is enhanced because the quark and antiquark attract each other which increases their probability to meet, whereas the octet contribution is suppressed. This is the so-called Sommerfeld effect. It has not been taken into account in previous calculations of the chemical equilibration rate, which are therefore incomplete for T < alphas^2 M. We compute the leading-order equilibration rate in this regime/ there is a large enhancement in the singlet channel, but the rate is dominated by the octet channel, and therefore the total effect is small. In the course of the computation we demonstrate how operators that represent the annihilation of heavy quarks in non-relativistic QCD can be incorporated into the imaginary-time formalism