Reality of Complex Affine Toda Solitons

There are infinitely many topological solitons in any given complex affine Toda theories and most of them have complex energy density. When we require the energy density of the solitons to be real, we find that the reality condition is related to a simple ``pairing condition.'' Unfortunately, rather few soliton solutions in these theories survive the reality constraint, especially if one also demands positivity. The resulting implications for the physical applicability of these theories are briefly discussed.Comment: LaTeX, 15 pages, UBTH-049

Low-lying even parity meson resonances and spin-flavor symmetry

A study is presented of the $s-$wave meson-meson interactions involving members of the $\rho-$nonet and of the $\pi-$octet. The starting point is an SU(6) spin-flavor extension of the SU(3) flavor Weinberg-Tomozawa Lagrangian. SU(6) symmetry breaking terms are then included to account for the physical meson masses and decay constants, while preserving partial conservation of the axial current in the light pseudoscalar sector. Next, the $T-$matrix amplitudes are obtained by solving the Bethe Salpeter equation in coupled-channel with the kernel built from the above interactions. The poles found on the first and second Riemann sheets of the amplitudes are identified with their possible Particle Data Group (PDG) counterparts. It is shown that most of the low-lying even parity PDG meson resonances, specially in the $J^P=0^+$ and $1^+$ sectors, can be classified according to multiplets of the spin-flavor symmetry group SU(6). The $f_0(1500)$, $f_1(1420)$ and some $0^+(2^{++})$ resonances cannot be accommodated within this SU(6) scheme and thus they would be clear candidates to be glueballs or hybrids. Finally, we predict the existence of five exotic resonances ($I \ge 3/2$ and/or $|Y|=2$) with masses in the range 1.4--1.6 GeV, which would complete the $27_1$, $10_3$, and $10_3^*$ multiplets of SU(3)$\otimes$SU(2).Comment: 43 pages, 2 figures, 61 tables. Improved discussion of Section II. To appear in Physical Review

Ward-Takahashi Identity with External Field in Ladder QED

We derive the Ward-Takahashi identity obeyed by the fermion-antifermion-gauge boson vertex in ladder QED in the presence of a constant magnetic field. The general structure in momentum space of the fermion mass operator with external electromagnetic field is discussed. Using it we find the solutions of the ladder WT identity with magnetic field. The consistency of our results with the solutions of the corresponding Schwinger-Dyson equation ensures the gauge invariance of the magnetic field induced chiral symmetry breaking recently found in ladder QED.Comment: new references(refs.10,11) added, 18 pages, Late

Flux-tubes in three-dimensional lattice gauge theories

Flux-tubes in different representations of SU(2) and U(1) lattice gauge theories in three dimensions are measured. Wilson loops generate heavy ``quark-antiquark'' pairs in fundamental ($j=1/2$), adjoint ($j=1$), and quartet ($j=3/2$) representations of SU(2). The first direct lattice measurements of the flux-tube cross-section ${\cal A}_j$ as a function of representation are made. It is found that ${\cal A}_j \approx {\rm constant}$, to about 10\%. Results are consistent with a connection between the string tension $\sigma_j$ and ${\cal A}_j$ suggested by a simplified flux-tube model, $\sigma_j = g^2 j(j+1) / (2 {\cal A}_j)$ [$g$ is the gauge coupling], given that $\sigma_j$ scales like the Casimir $j(j+1)$, as observed in previous lattice studies in both three and four dimensions. The results can discriminate among phenomenological models of the physics underlying confinement. Flux-tubes for singly- and doubly-charged Wilson loops in compact QED$_3$ are also measured. It is found that the string tension scales as the squared-charge and the flux-tube cross-section is independent of charge to good approximation. These SU(2) and U(1) simulations lend some support, albeit indirectly, to a conjecture that the dual superconductor mechanism underlies confinement in compact gauge theories in both three and four dimensions.Comment: 15 pages (REVTEX 2.1). Figures: 11, not included (available by request from [email protected] by regular mail, postscript files, or one self-unpacking uuencoded file

On the spectral density from instantons in quenched QCD

We investigate the contribution of instantons to the eigenvalue spectrum of the Dirac operator in quenched QCD. The instanton configurations that we use have been derived, elsewhere, from cooled SU(3) lattice gauge fields and, for comparison, we also analyse a random `gas' of instantons. Using a set of simplifying approximations, we find a non-zero chiral condensate. However we also find that the spectral density diverges for small eigenvalues, so that the chiral condensate, at zero quark mass, diverges in quenched QCD. The degree of divergence decreases with the instanton density, so that it is negligible for the smallest number of cooling sweeps but becomes substantial for larger number of cools. We show that the spectral density scales, that finite volume corrections are small and we see evidence for the screening of topological charges. However we also find that the spectral density and chiral condensate vary rapidly with the number of cooling sweeps -- unlike, for example, the topological susceptibility. Whether the problem lies with the cooling or with the identification of the topological charges is an open question. This problem needs to be resolved before one can determine how important is the divergence we have found for quenched QCD.Comment: 33 pages, 16 figures (RevTex), substantial revisions; to appear in Phys.Rev.

Direct Instantons in QCD Nucleon Sum Rules

We study the role of direct (i.e. small-scale) instantons in QCD correlation functions for the nucleon. They generate sizeable, nonperturbative corrections to the conventional operator product expansion, which improve the quality of both QCD nucleon sum rules and cure the long-standing stability problem, in particular, of the chirally odd sum-rule.Comment: 10 pages, UMD PP#93-17

On Clifford representation of Hopf algebras and Fierz identities

We present a short review of the action and coaction of Hopf algebras on Clifford algebras as an introduction to physically meaningful examples. Some q-deformed Clifford algebras are studied from this context and conclusions are derived.Comment: 27 pages, Latex2e, to appear in Found. of Phy

Electromagnetic Moments of the Baryon Decuplet

We compute the leading contributions to the magnetic dipole and electric quadrupole moments of the baryon decuplet in chiral perturbation theory. The measured value for the magnetic moment of the $\Omega^-$ is used to determine the local counterterm for the magnetic moments. We compare the chiral perturbation theory predictions for the magnetic moments of the decuplet with those of the baryon octet and find reasonable agreement with the predictions of the large--$N_c$ limit of QCD. The leading contribution to the quadrupole moment of the $\Delta$ and other members of the decuplet comes from one--loop graphs. The pionic contribution is shown to be proportional to $I_z$ (and so will not contribute to the quadrupole moment of $I=0$ nuclei), while the contribution from kaons has both isovector and isoscalar components. The chiral logarithmic enhancement of both pion and kaon loops has a coefficient that vanishes in the $SU(6)$ limit. The third allowed moment, the magnetic octupole, is shown to be dominated by a local counterterm with corrections arising at two loops. We briefly mention the strange counterparts of these moments.Comment: Uses harvmac.tex, 15 pages with 3 PostScript figures packed using uufiles. UCSD/PTH 93-22, QUSTH-93-05, Duke-TH-93-5

Lagrangian and Hamiltonian Formalism on a Quantum Plane

We examine the problem of defining Lagrangian and Hamiltonian mechanics for a particle moving on a quantum plane $Q_{q,p}$. For Lagrangian mechanics, we first define a tangent quantum plane $TQ_{q,p}$ spanned by noncommuting particle coordinates and velocities. Using techniques similar to those of Wess and Zumino, we construct two different differential calculi on $TQ_{q,p}$. These two differential calculi can in principle give rise to two different particle dynamics, starting from a single Lagrangian. For Hamiltonian mechanics, we define a phase space $T^*Q_{q,p}$ spanned by noncommuting particle coordinates and momenta. The commutation relations for the momenta can be determined only after knowing their functional dependence on coordinates and velocities. Thus these commutation relations, as well as the differential calculus on $T^*Q_{q,p}$, depend on the initial choice of Lagrangian. We obtain the deformed Hamilton's equations of motion and the deformed Poisson brackets, and their definitions also depend on our initial choice of Lagrangian. We illustrate these ideas for two sample Lagrangians. The first system we examine corresponds to that of a nonrelativistic particle in a scalar potential. The other Lagrangian we consider is first order in time derivative