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

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

Unitary Quantum Physics with Time-Space Noncommutativity

In this work quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. The Moyal plane is treated in detail. In the context of noncommutative quantum mechanics, some important points are explored, such as the formal construction of the theory, symmetries, causality, simultaneity and observables. The dynamics generated by a noncommutative Schrodinger equation is studied. We prove in particular the following: suppose the Hamiltonian of a quantum mechanical particle on spacetime has no explicit time dependence, and the spatial coordinates commute in its noncommutative form (the only noncommutativity being between time and a space coordinate). Then the commutative and noncommutative versions of the Hamiltonian have identical spectra.Comment: 18 pages, published versio

Local equilibrium of the quark-gluon plasma

Within kinetic theory, we look for local equilibrium configurations of the quark-gluon plasma by maximizing the local entropy. We use the well-established transport equations in the Vlasov limit, supplemented with the Waldmann-Snider collision terms. Two different classes of local equilibrium solutions are found. The first one corresponds to the configurations that comply with the so-called collisional invariants. The second one is given by the distribution functions that cancel the collision terms, representing the most probable binary interactions with soft gluon exchange in the t-channel. The two sets of solutions agree with each other if we go beyond these dominant processes and take into account subleading quark-antiquark annihilation/creation and gluon number non-conserving processes. The local equilibrium state appears to be colorful, as the color charges are not locally neutralized. Properties of such an equilibrium state are analyzed. In particular, the related hydrodynamic equations of a colorful fluid are derived. Possible neutralization processes are also briefly discussed.Comment: 20 pages; minor changes, to be published in Phys. Rev.

Non-Abelian Fluid Dynamics in Lagrangian Formulation

Non-Abelian extensions of fluid dynamics, which can have applications to the quark-gluon plasma, are given. These theories are presented in a symplectic/Lagrangian formulation and involve a fluid generalization of the Kirillov-Kostant form well known in Lie group theory. In our simplest model the fluid flows with velocity v and in presence of non-Abelian chromoelectric/magnetic E^a / B^a fields, the fluid feels a Lorentz force of the form Q_a E^a + (v / c) \times Q_a B^a, where Q_a is a space-time local non-Abelian charge satisfying a fluid Wong equation [ (D_t + v \cdot D) Q ]_a = 0 with gauge covariant derivatives.Comment: 14 pp., REVTeX 4; a reference added; email correspondence to [email protected]

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

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

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