Geant4 is a toolkit for simulating the passage of particles through matter. It includes a complete range of functionality including tracking, geometry, physics models and hits. The physics processes offered cover a comprehensive range, including electromagnetic, hadronic and optical processes, a large set of long-lived particles, materials and elements, over a wide energy range starting, in some cases, from View the MathML source and extending in others to the TeV energy range. It has been designed and constructed to expose the physics models utilised, to handle complex geometries, and to enable its easy adaptation for optimal use in different sets of applications. The toolkit is the result of a worldwide collaboration of physicists and software engineers. It has been created exploiting software engineering and object-oriented technology and implemented in the C++ programming language. It has been used in applications in particle physics, nuclear physics, accelerator design, space engineering and medical physics

No abstract

An extension of the ideal hadron resonance gas (HRG) model is constructed which includes the attractive and repulsive van der Waals (VDW) interactions between baryons. This VDW-HRG model yields the nuclear liquid-gas transition at low temperatures and high baryon densities. The VDW parameters a and b are fixed by the ground state properties of nuclear matter, and the temperature dependence of various thermodynamic observables at zero chemical potential are calculated within the VDW-HRG model. Compared to the ideal HRG model, the inclusion of VDW interactions between baryons leads to a qualitatively different behavior of second and higher moments of fluctuations of conserved charges, in particular in the so-called crossover region T∼140-190  MeV. For many observables this behavior resembles closely the results obtained from lattice QCD simulations. This hadronic model also predicts nontrivial behavior of net-baryon fluctuations in the region of phase diagram probed by heavy-ion collision experiments. These results imply that VDW interactions play a crucial role in the thermodynamics of hadron gas. Thus, the commonly performed comparisons of the ideal HRG model with the lattice and heavy-ion data may lead to misconceptions and misleading conclusions.

No abstract

The first principle lattice QCD methods allow to calculate the thermodynamic observables at finite temperature and imaginary chemical potential. These can be compared to the predictions of various phenomenological models. We argue that Fourier coefficients with respect to imaginary baryochemical potential are sensitive to modeling of baryonic interactions. As a first application of this sensitivity, we consider the hadron resonance gas (HRG) model with repulsive baryonic interactions, which are modeled by means of the excluded volume correction. The Fourier coefficients of the imaginary part of the net-baryon density at imaginary baryochemical potentialcorresponding to the fugacity or virial expansion at real chemical potential -are calculated within this model, and compared with the Nt = 12 lattice data. The lattice QCD behavior of the first four Fourier coefficients up to T 185 MeV is described fairly well by an interacting HRG with a single baryon-baryon eigenvolume interaction parameter b 1 fm 3 , while the available lattice data on the difference χ B 2 − χ B 4 of baryon number susceptibilities is reproduced up to T 175 MeV.

A generalization of the quantum van der Waals equation of state for a multi-component system in the grand canonical ensemble is proposed. The model includes quantum statistical effects and allows to specify the parameters characterizing repulsive and attractive forces for each pair of particle species.The model can be straightforwardly applied to the description of asymmetric nuclear matter and also for mixtures of interacting nucleons and nuclei. Applications of the model to the equation of state of an interacting hadron resonance gas are discussed.

In this paper, the generic part of the gauge theory of gravity is derived, based merely on the action principle and on the general principle of relativity. We apply the canonical transformation framework to formulate geometrodynamics as a gauge theory. The starting point of our paper is constituted by the general De Donder-Weyl Hamiltonian of a system of scalar and vector fields, which is supposed to be form-invariant under (global) Lorentz transformations. Following the reasoning of gauge theories, the corresponding locally form-invariant system is worked out by means of canonical transformations. The canonical transformation approach ensures by construction that the form of the action functional is maintained. We thus encounter amended Hamiltonian systems which are form-invariant under arbitrary spacetime transformations. This amended system complies with the general principle of relativity and describes both, the dynamics of the given physical system's fields and their coupling to those quantities which describe the dynamics of the spacetime geometry. In this way, it is unambiguously determined how spin-0 and spin-1 fields couple to the dynamics of spacetime.A term that describes the dynamics of the "free" gauge fields must finally be added to the amended Hamiltonian, as common to all gauge theories, to allow for a dynamic spacetime geometry. The choice of this "dynamics" Hamiltonian is outside of the scope of gauge theory as presented in this paper. It accounts for the remaining indefiniteness of any gauge theory of gravity and must be chosen "by hand" on the basis of physical reasoning. The final Hamiltonian of the gauge theory of gravity is shown to be at least quadratic in the conjugate momenta of the gauge fields-this is beyond the Einstein-Hilbert theory of general relativity.

The deconfinement transition region between hadronic matter and quarkgluon plasma is studied for finite volumes. Assuming simple model equations of state and a first order phase transition, we find that fluctuations in finite volumes hinder a sharp separation between the two phases around the critical temperature, leading to a rounding of the phase transition. For reaction volumes expected in heavy ion experiments, the softening of the equation of state is reduced considerably. This is especially true when the requirement of exact color-singletness is included in the QGP equation of state. * Supported by GSI, BMBF, DFG 1 I. MOTIVATIONA primary goal of relativistic nuclear collisions is the observation of a phase transition of confined, hadronic matter to a deconfined quark-gluon plasma. One of the proposed signatures, namely hydrodynamic flow, is based on the presumed softening of the eqution of state due to the rapid increase of the entropy density. It has been investigated in the framework of relativistic hydrodynamic models [1,2]. The expansion of once compressed matter is predicted to be delayed in the case of a QGP, which in turn leads to a reduction of the transverse (directed) flow [3,4] 1 . This is mainly due to the fact that the sound velocity vanishes for energy densities in the mixed phase. A smooth crossover transition within an assumed interval of ∆T = 0.1T C , on the other hand, results in drastically reduced time delays as compared to a sharp transition [6].As is well known, a rounding of sharp first order phase transitions is expected due to explicit finite size effects [7]. The importance of fluctuations of the coexisting phases in small volumes of strongly interacting matter has already been pointed out in [8] for the case of a liquid-gas phase transition, and in [9] for the deconfinement phase transition. As a consequence, it was claimed that the observation of two separate phases in heavy ion collisions might be hindered. In this work we explore this behaviour in more detail, starting from rather simple model equations of state. We put special emphasis on the question, how the requirement of color singletness of the QGP phase affects the phase transition on top of the fluctuation effect.The limited reaction size of a heavy ion collision is a generally ignored problem of the experimental search for a quark-gluon plasma. According to one-fluid dynamical model 1 However, in a three-fluid hydrodynamical model [5] the directed nucleon flow is already lowered as compared to the usual one-fluid models (which assume instantaneous local thermalization between projectile and target). It will be exciting to learn whether the softening of the EOS is also signaled in this model. However, the longitudinal flow velocities exceed the thermal motion by far. Thus, only subsystems of smaller volume can be regarded as being in approximate "global" thermal equilibrium. Only the latter are suitable for the study of finite size effects. Therefore, if we require the local thermal motion to be of the same ord...