The transfer matrix in four-dimensional CDT

The Causal Dynamical Triangulation model of quantum gravity (CDT) has a transfer matrix, relating spatial geometries at adjacent (discrete lattice) times. The transfer matrix uniquely determines the theory. We show that the measurements of the scale factor of the (CDT) universe are well described by an effective transfer matrix where the matrix elements are labeled only by the scale factor. Using computer simulations we determine the effective transfer matrix elements and show how they relate to an effective minisuperspace action at all scales.Comment: 32 pages, 19 figure

Quantum gravity, from the entropy of geometries

This article describes an attempt to reconcile the theory of general relativitywith quantum theory fromfirst principles.The universe is assembled frombuilding blocks, and computer simulations reveal their collective behaviour. For small universes quantumfluctuations are large and dominant, but still some semiclassical concepts of geometry surviv

Measurement of pion, kaon and proton production in proton–proton collisions at √s = 7 TeV

The measurement of primary $$\pi ^{\pm }$$π±, $$K^{\pm }$$K±, $$p$$p and $${\overline{{p}}}$$p¯ production at mid-rapidity (|y| <|y|< 0.5) in proton–proton collisions at $$\sqrt{s}$$s$$=$$= 7 TeV performed with a large ion collider experiment at the large hadron collider (LHC) is reported. Particle identification is performed using the specific ionisation energy-loss and time-of-flight information, the ring-imaging Cherenkov technique and the kink-topology identification of weak decays of charged kaons. Transverse momentum spectra are measured from 0.1 up to 3 GeV/$$c$$c for pions, from 0.2 up to 6 GeV/$$c$$c for kaons and from 0.3 up to 6 GeV/$$c$$c for protons. The measured spectra and particle ratios are compared with quantum chromodynamics-inspired models, tuned to reproduce also the earlier measurements performed at the LHC. Furthermore, the integrated particle yields and ratios as well as the average transverse momenta are compared with results at lower collision energies. © 2015, CERN for the benefit of the ALICE collaboration