We present a variational approach for relativistic ideal hydrodynamics interacting with electromagnetic fields. The momentum of fluid is introduced as the canonical conjugate variable of the position of a fluid element, which coincides with the conse
rved quantity derived from the Noether theorem. We further show that our formulation can reproduce the usual electromagnetic hydrodynamics which is obtained so as to satisfy the conservation of the inertia of fluid motion.
Quantization of electromagnetic fields is investigated in the framework of stochastic variational method (SVM). Differently from the canonical quantization, this method does not require canonical form and quantization can be performed directly from t
he gauge invariant Lagrangian. The gauge condition is used to choose dynamically independent variables. We verify that, in the Coulomb gauge condition, SVM result is completely equivalent to the traditional result. On the other hand, in the Lorentz gauge condition, SVM quantization can be performed without introducing the indefinite metric. The temporal and longitudinal components of the gauge filed, then, behave as c-number functionals affected by quantum fluctuation through the interaction with charged matter fields. To see further the relation between SVM and the canonical quantization, we quantize the usual gauge Lagrangian with the Fermi term and argue a stochastic process with a negative second order correlation is introduced to reproduce the indefinite metric.
We propose analytical forms, in both momentum transfer and impact parameter spaces, for the amplitudes of elastic pp scattering, giving coherent and accurate description of the observables at all energies $sqrt{s}geq 20$ GeV. The real and imaginary p
arts are separately identified through their roles at small and large t values. The study of the differential cross sections in b-space leads to the understanding of the effective interaction ranges contributing to elastic and inelastic processes.
Stochastic Variational Method (SVM) is the generalization of the variation method to the case with stochastic variables. In the series of papers, we investigate the applicability of SVM as an alternative field quantization scheme. Here, we discuss th
e complex Klein-Gordon equation. In this scheme, the Euler-Lagrangian equation for the stochastic fields leads to the functional Schroedinger equation, which in turn can be interpreted as the ideal fluid equation in the functional space. We show that the Fock state vector is given by the stationary solution of these differential equations and various results in the usual canonical quantization can be reproduced, including the effect of anti-particles. The present formulation is a quantization scheme based on commutable variables, so that there appears no ambiguity associated with the ordering of operators, for example, in the definition of Noether charges.
The data on p$mathrm{bar p}$ elastic scattering at 1.8 and 1.96 TeV are analysed in terms of real and imaginary amplitudes, in a treatment with high accuracy, covering the whole t-range and satisfying the expectation of dispersion relation for amplit
udes and for slopes. A method is introduced for determination of the total cross section and the other forward scattering parameters and to check compatibility of E-710, CDF and the recent D0 data. Slopes $B_R$ and $ B_I$ of the real and imaginary amplitudes, treated as independent quantities, influence the amplitudes in the whole t-range and are important for the determination of the total cross section. The amplitudes are fully constructed, and a prediction is made of a marked dip in $ dsigma/dt$ in the $|t|$ range 3 - 5 GeV$^2$ due to the universal contribution of the process of three gluon exchange.
We report on the spectroscopic confirmation of a huge cosmic structure around the CL0016 cluster at z=0.55. We made wide-field imaging observations of the surrounding regions of the cluster and identified more than 30 concentrations of red galaxies n
ear the cluster redshift. The follow-up spectroscopic observations of the most prominent part of the structure confirmed 14 systems close to the cluster redshift, roughly half of which have a positive probability of being bound to the cluster dynamically. We also made an X-ray follow-up, which detected extended X-ray emissions from 70% of the systems in the X-ray surveyed region. The observed structure is among the richest ever observed in the distant Universe. It will be an ideal site for quantifying environmental variations in the galaxy properties and effects of large-scale structure on galaxy evolution.
We extended our formulation of causal dissipative hydrodynamics [T. Koide textit{et al.}, Phys. Rev. textbf{C75}, 034909 (2007)] to be applicable to the ultra-relativistic regime by considering the extensiveness of irreversible currents. The new equa
tion has a non-linear term which suppresses the effect of viscosity. We found that such a term is necessary to guarantee the positive definiteness of the inertia term and stabilize numerical calculations in ultra-relativistic initial conditions. Because of the suppression of the viscosity, the behavior of the fluid is more close to that of the ideal fluid. Our result is essentially same as that from the extended irreversible thermodynamics, but is different from the Israel-Stewart theory. A possible origin of the difference is discussed.
A new formula to calculate the transport coefficients of the causal dissipative hydrodynamics is derived by using the projection operator method (Mori-Zwanzig formalism) in [T. Koide, Phys. Rev. E75, 060103(R) (2007)]. This is an extension of the Gre
en-Kubo-Nakano (GKN) formula to the case of non-Newtonian fluids, which is the essential factor to preserve the relativistic causality in relativistic dissipative hydrodynamics. This formula is the generalization of the GKN formula in the sense that it can reproduce the GKN formula in a certain limit. In this work, we extend the previous work so as to apply to more general situations.
(Abridged) We report on the environmental dependence of properties of galaxies around the RDCSJ0910+54 cluster at z=1.1. We have obtained multi-band wide-field images of the cluster with Suprime-Cam and MOIRCS on Subaru and WFCAM on UKIRT. Also, an i
ntensive spectroscopic campaign has been carried out using LRIS on Keck and FOCAS on Subaru. We discover a possible large-scale structure around the cluster in the form of three clumps of galaxies. This is potentially one of the largest structures found so far in the z>1 Universe. We then examine stellar populations of galaxies in the structure. Red galaxies have already become the dominant population in the cores of rich clusters at z~1, and the fraction of red galaxies has not strongly changed since then. The red fraction depends on richness of clusters in the sense that it is higher in rich clusters than in poor groups. The luminosity function of red galaxies in rich clusters is consistent with that in local clusters. On the other hand, luminosity function of red galaxies in poor groups shows a deficit of faint red galaxies. This confirms our earlier findings that galaxies follow an environment-dependent down-sizing evolution. There seems to be a large variation in the evolutionary phases of galaxies in groups with similar masses. Further studies of high-z clusters will be a promising way of addressing the role of nature and nurture effects on galaxy evolution.
The stability and causality of the Landau-Lifshitz theory and the Israel-Stewart type causal dissipative hydrodynamics are discussed. We show that the problem of acausality and instability are correlated in relativistic dissipative hydrodynamics and
instability is induced by acausality. We further discuss the stability of the scaling solution. The scaling solution of the causal dissipative hydrodynamics can be unstable against inhomogeneous perturbations.
