11,984 research outputs found
A Physical Realization of the Generalized PT-, C-, and CPT-Symmetries and the Position Operator for Klein-Gordon Fields
Generalized parity (P), time-reversal (T), and charge-conjugation
(C)operators were initially definedin the study of the pseudo-Hermitian
Hamiltonians. We construct a concrete realization of these operators for
Klein-Gordon fields and show that in this realization PT and C operators
respectively correspond to the ordinary time-reversal and charge-grading
operations. Furthermore, we present a complete description of the quantum
mechanics of Klein-Gordon fields that is based on the construction of a Hilbert
space with a relativistically invariant, positive-definite, and conserved inner
product. In particular we offer a natural construction of a position operator
and the corresponding localized and coherent states. The restriction of this
position operator to the positive-frequency fields coincides with the
Newton-Wigner operator. Our approach does not rely on the conventional
restriction to positive-frequency fields. Yet it provides a consistent quantum
mechanical description of Klein-Gordon fields with a genuine probabilistic
interpretation.Comment: 20 pages, published versio
Dissipative effects from transport and viscous hydrodynamics
We compare 2->2 covariant transport theory and causal Israel-Stewart
hydrodynamics in 2+1D longitudinally boost invariant geometry with RHIC-like
initial conditions and a conformal e = 3p equation of state. The pressure
evolution in the center of the collision zone and the final differential
elliptic flow v2(pT) from the two theories agree remarkably well for a small
shear viscosity to entropy density ratio eta/s ~ 1/(4 pi), and also for a large
cross section sigma ~ 50 mb. A key to this agreement is keeping ALL terms in
the Israel-Stewart equations of motion. Our results indicate promising
prospects for the applicability of Israel-Stewart dissipative hydrodynamics at
RHIC, provided the shear viscosity of hot and dense quark-gluon matter is
indeed very small for the relevant temperatures T ~ 200-500 MeV.Comment: Presentation at Quark Matter 2008. 4 pages, 3 figure
Momentum of an electromagnetic wave in dielectric media
Almost a hundred years ago, two different expressions were proposed for the
energy--momentum tensor of an electromagnetic wave in a dielectric. Minkowski's
tensor predicted an increase in the linear momentum of the wave on entering a
dielectric medium, whereas Abraham's tensor predicted its decrease. Theoretical
arguments were advanced in favour of both sides, and experiments proved
incapable of distinguishing between the two. Yet more forms were proposed, each
with their advocates who considered the form that they were proposing to be the
one true tensor. This paper reviews the debate and its eventual conclusion:
that no electromagnetic wave energy--momentum tensor is complete on its own.
When the appropriate accompanying energy--momentum tensor for the material
medium is also considered, experimental predictions of all the various proposed
tensors will always be the same, and the preferred form is therefore
effectively a matter of personal choice.Comment: 23 pages, 3 figures, RevTeX 4. Removed erroneous factor of mu/mu_0
from Eq.(44
Energy conservation for dynamical black holes
An energy conservation law is described, expressing the increase in
mass-energy of a general black hole in terms of the energy densities of the
infalling matter and gravitational radiation. For a growing black hole, this
first law of black-hole dynamics is equivalent to an equation of Ashtekar &
Krishnan, but the new integral and differential forms are regular in the limit
where the black hole ceases to grow. An effective gravitational-radiation
energy tensor is obtained, providing measures of both ingoing and outgoing,
transverse and longitudinal gravitational radiation on and near a black hole.
Corresponding energy-tensor forms of the first law involve a preferred time
vector which plays the role for dynamical black holes which the stationary
Killing vector plays for stationary black holes. Identifying an energy flux,
vanishing if and only if the horizon is null, allows a division into
energy-supply and work terms, as in the first law of thermodynamics. The energy
supply can be expressed in terms of area increase and a newly defined surface
gravity, yielding a Gibbs-like equation, with a similar form to the so-called
first law for stationary black holes.Comment: 4 revtex4 pages. Many (mostly presentational) changes; emphasizes the
definition of gravitational radiation in the strong-field regim
Thermalization of gluons in ultrarelativistic heavy ion collisions by including three-body interactions in a parton cascade
We develop a new 3+1 dimensional Monte Carlo cascade solving the kinetic
on-shell Boltzmann equations for partons including the inelastic gg ggg
pQCD processes. The back reaction channel is treated -- for the first time --
fully consistently within this scheme. An extended stochastic method is used to
solve the collision integral. The frame dependence and convergency are studied
for a fixed tube with thermal initial conditions. The detailed numerical
analysis shows that the stochastic method is fully covariant and that
convergency is achieved more efficiently than within a standard geometrical
formulation of the collision term, especially for high gluon interaction rates.
The cascade is then applied to simulate parton evolution and to investigate
thermalization of gluons for a central Au+Au collision at RHIC energy. For this
study the initial conditions are assumed to be generated by independent
minijets with p_T > p_0=2 GeV. With that choice it is demonstrated that overall
kinetic equilibration is driven mainly by the inelastic processes and is
achieved on a scale of 1 fm/c. The further evolution of the expanding gluonic
matter in the central region then shows almost an ideal hydrodynamical
behavior. In addition, full chemical equilibration of the gluons follows on a
longer timescale of about 3 fm/c.Comment: 121 pages with 55 figures, revised version. Two eps-figures and
comments are added. Formula (54) which has typo in journal version is given
correctl
The applicability of causal dissipative hydrodynamics to relativistic heavy ion collisions
We utilize nonequilibrium covariant transport theory to determine the region
of validity of causal Israel-Stewart dissipative hydrodynamics (IS) and
Navier-Stokes theory (NS) for relativistic heavy ion physics applications. A
massless ideal gas with 2->2 interactions is considered in a 0+1D Bjorken
scenario, appropriate for the early longitudinal expansion stage of the
collision. In the scale invariant case of a constant shear viscosity to entropy
density ratio eta/s ~ const, we find that Israel-Stewart theory is 10% accurate
in calculating dissipative effects if initially the expansion timescale exceeds
half the transport mean free path tau0/lambda0 > ~2. The same accuracy with
Navier-Stokes requires three times larger tau0/lambda0 > ~6. For dynamics
driven by a constant cross section, on the other hand, about 50% larger
tau0/lambda0 > ~3 (IS) and ~9 (NS) are needed. For typical applications at RHIC
energies s_{NN}**(1/2) ~ 100-200 GeV, these limits imply that even the
Israel-Stewart approach becomes marginal when eta/s > ~0.15. In addition, we
find that the 'naive' approximation to Israel-Stewart theory, which neglects
products of gradients and dissipative quantities, has an even smaller range of
applicability than Navier-Stokes. We also obtain analytic Israel-Stewart and
Navier-Stokes solutions in 0+1D, and present further tests for numerical
dissipative hydrodynamics codes in 1+1, 2+1, and 3+1D based on generalized
conservation laws.Comment: 30 pages, 26 EPS figures, revtex stylefil
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