14 research outputs found
Quaternionic Madelung Transformation and Non-Abelian Fluid Dynamics
In the 1920's, Madelung noticed that if the complex Schroedinger wavefunction
is expressed in polar form, then its modulus squared and the gradient of its
phase may be interpreted as the hydrodynamic density and velocity,
respectively, of a compressible fluid. In this paper, we generalize Madelung's
transformation to the quaternionic Schroedinger equation. The non-abelian
nature of the full SU(2) gauge group of this equation leads to a richer, more
intricate set of fluid equations than those arising from complex quantum
mechanics. We begin by describing the quaternionic version of Madelung's
transformation, and identifying its ``hydrodynamic'' variables. In order to
find Hamiltonian equations of motion for these, we first develop the canonical
Poisson bracket and Hamiltonian for the quaternionic Schroedinger equation, and
then apply Madelung's transformation to derive non-canonical Poisson brackets
yielding the desired equations of motion. These are a particularly natural set
of equations for a non-abelian fluid, and differ from those obtained by
Bistrovic et al. only by a global gauge transformation. Because we have
obtained these equations by a transformation of the quaternionic Schroedinger
equation, and because many techniques for simulating complex quantum mechanics
generalize straightforwardly to the quaternionic case, our observation leads to
simple algorithms for the computer simulation of non-abelian fluids.Comment: 15 page
U(1) Gauge Theory as Quantum Hydrodynamics
It is shown that gauge theories are most naturally studied via a polar
decomposition of the field variable. Gauge transformations may be viewed as
those that leave the density invariant but change the phase variable by
additive amounts. The path integral approach is used to compute the partition
function. When gauge fields are included, the constraint brought about by gauge
invariance simply means an appropriate linear combination of the gradients of
the phase variable and the gauge field is invariant. No gauge fixing is needed
in this approach that is closest to the spirit of the gauge principle.
We derive an exact formula for the condensate fraction and in case it is
zero, an exact formula for the anomalous exponent. We also derive a formula for
the vortex strength which involves computing radiation corrections.Comment: 15 pages, Plain LaTeX, final published versio
Generalizations of Yang-Mills Theory with Nonlinear Constitutive Equations
We generalize classical Yang-Mills theory by extending nonlinear constitutive
equations for Maxwell fields to non-Abelian gauge groups. Such theories may or
may not be Lagrangian. We obtain conditions on the constitutive equations
specifying the Lagrangian case, of which recently-discussed non-Abelian
Born-Infeld theories are particular examples. Some models in our class possess
nontrivial Galilean (c goes to infinity) limits; we determine when such limits
exist, and obtain them explicitly.Comment: Submitted to the Proceedings of the 3rd Symposium on Quantum Theory
and Symmetries (QTS3) 10-14 September 2003. Preprint 9 pages including
reference
Metafluid dynamics and Hamilton-Jacobi formalism
Metafluid dynamics was investigated within Hamilton-Jacobi formalism and the
existence of the hidden gauge symmetry was analyzed. The obtained results are
in agreement with those of Faddeev-Jackiw approach.Comment: 7 page
K -> pi pi and a light scalar meson
We explore the Delta-I= 1/2 rule and epsilon'/epsilon in K -> pi pi
transitions using a Dyson-Schwinger equation model. Exploiting the feature that
QCD penguin operators direct K^0_S transitions through 0^{++} intermediate
states, we find an explanation of the enhancement of I=0 K -> pi pi transitions
in the contribution of a light sigma-meson. This mechanism also affects
epsilon'/epsilon.Comment: 7 pages, REVTE
Valence-quark distributions in the pion
We calculate the pion's valence-quark momentum-fraction probability
distribution using a Dyson-Schwinger equation model. Valence-quarks with an
active mass of 0.30 GeV carry 71% of the pion's momentum at a resolving scale
q_0=0.54 GeV = 1/(0.37 fm). The shape of the calculated distribution is
characteristic of a strongly bound system and, evolved from q_0 to q=2 GeV, it
yields first, second and third moments in agreement with lattice and
phenomenological estimates, and valence-quarks carrying 49% of the pion's
momentum. However, pointwise there is a discrepancy between our calculated
distribution and that hitherto inferred from parametrisations of extant
pion-nucleon Drell-Yan data.Comment: 8 pages, 3 figures, REVTEX, aps.sty, epsfig.sty, minor corrections,
version to appear in PR
Ladder Dyson-Schwinger calculation of the anomalous gamma-3pi form factor
The anomalous processes, \gamma \to 3 \pi and \gamma \pi \to \pi\pi, are
investigated within the Dyson-Schwinger framework using the rainbow-ladder
approximation. Calculations reveal that a complete set of ladder diagrams
beyond the impulse approximation are necessary to reproduce the fundamental
low-energy theorem for the anomalous form factor. Higher momentum calculations
also agree with the limited form factor data and exhibit the same resonance
behavior as the phenomenological vector meson dominance model.Comment: 9 pages, 8 .eps figures, Revte
Perfect Fluid Theory and its Extensions
We review the canonical theory for perfect fluids, in Eulerian and Lagrangian
formulations. The theory is related to a description of extended structures in
higher dimensions. Internal symmetry and supersymmetry degrees of freedom are
incorporated. Additional miscellaneous subjects that are covered include
physical topics concerning quantization, as well as mathematical issues of
volume preserving diffeomorphisms and representations of Chern-Simons terms (=
vortex or magnetic helicity).Comment: 3 figure