7,021 research outputs found
Timeless path integral for relativistic quantum mechanics
Starting from the canonical formalism of relativistic (timeless) quantum
mechanics, the formulation of timeless path integral is rigorously derived. The
transition amplitude is reformulated as the sum, or functional integral, over
all possible paths in the constraint surface specified by the (relativistic)
Hamiltonian constraint, and each path contributes with a phase identical to the
classical action divided by . The timeless path integral manifests the
timeless feature as it is completely independent of the parametrization for
paths. For the special case that the Hamiltonian constraint is a quadratic
polynomial in momenta, the transition amplitude admits the timeless Feynman's
path integral over the (relativistic) configuration space. Meanwhile, the
difference between relativistic quantum mechanics and conventional
nonrelativistic (with time) quantum mechanics is elaborated on in light of
timeless path integral.Comment: 41 pages; more references and comments added; version to appear in
CQ
High Spin Glueballs from the Lattice
We discuss the principles underlying higher spin glueball calculations on the
lattice. For that purpose, we develop numerical techniques to rotate Wilson
loops by arbitrary angles in lattice gauge theories close to the continuum. As
a first application, we compute the glueball spectrum of the SU(2) gauge theory
in 2+1 dimensions for both parities and for spins ranging from 0 up to 4
inclusive. We measure glueball angular wave functions directly, decomposing
them in Fourier modes and extrapolating the Fourier coefficients to the
continuum. This allows a reliable labelling of the continuum states and gives
insight into the way rotation symmetry is recovered. As one of our results, we
demonstrate that the D=2+1 SU(2) glueball conventionally labelled as J^P = 0^-
is in fact 4^- and that the lightest ``J=1'' state has, in fact, spin 3.Comment: Minor changes in the text; the spin 4 glueball mass is taken further
out in Euclidean time at higher beta values. 41 pages, 20 figure
Effective Field Theory of Nuclear Forces
The application of the effective field theory (EFT) method to nuclear systems
is reviewed. The roles of degrees of freedom, QCD symmetries, power counting,
renormalization, and potentials are discussed. EFTs are constructed for various
energy regimes of relevance in nuclear physics, and are used in systematic
expansions to derive nuclear forces in terms of a number of parameters that
embody information about QCD dynamics. Two-, three-, and many-nucleon systems,
including external probes, are considered.Comment: 83 pages, 20 figures, commissioned for Prog. Part. Nucl. Phy
Reconstruction subgrid models for nonpremixed combustion
Large-eddy simulation of combustion problems involves highly nonlinear terms that, when filtered, result in a contribution from subgrid fluctuations of scalars, Z, to the dynamics of the filtered value. This subgrid contribution requires modeling. Reconstruction models try to recover as much information as possible from the resolved field Z, based on a deconvolution procedure to obtain an intermediate field ZM. The approximate reconstruction using moments (ARM) method combines approximate reconstruction, a purely mathematical procedure, with additional physics-based information required to match specific scalar moments, in the simplest case, the Reynolds-averaged value of the subgrid variance. Here, results from the analysis of the ARM model in the case of a spatially evolving turbulent plane jet are presented. A priori and a posteriori evaluations using data from direct numerical simulation are carried out. The nonlinearities considered are representative of reacting flows: power functions, the dependence of the density on the mixture fraction (relevant for conserved scalar approaches) and the Arrhenius nonlinearity (very localized in Z space). Comparisons are made against the more popular beta probability density function (PDF) approach in the a priori analysis, trying to define ranges of validity for each approach. The results show that the ARM model is able to capture the subgrid part of the variance accurately over a wide range of filter sizes and performs well for the different nonlinearities, giving uniformly better predictions than the beta PDF for the polynomial case. In the case of the density and Arrhenius nonlinearities, the relative performance of the ARM and traditional PDF approaches depends on the size of the subgrid variance with respect to a characteristic scale of each function. Furthermore, the sources of error associated with the ARM method are considered and analytical bounds on that error are obtained
- …