191 research outputs found
Spin and Resonant States in QCD
I make the case that the nucleon excitations do not exist as isolated higher
spin states but are fully absorbed by (K/2,K/2)*[(1/2,0)+ (0,1/2)] multiplets
taking their origin from the rotational and vibrational excitations of an
underlying quark--diquark string. The \Delta (1232) spectrum presents itself as
the exact replica (up to \Delta (1600)) of the nucleon spectrum with the K-
clusters being shifted upward by about 200 MeV. QCD inspired arguments support
legitimacy of the quark-diquark string. The above K multiplets can be mapped
(up to form-factors) onto Lorentz group representation spaces of the type
\psi_\mu_1...\mu_K, thus guaranteeing covariant description of resonant states.
The quantum \psi_\mu_1...\mu_K states are of multiple spins at rest, and of
undetermined spins elsewhere.Comment: Added Ref. M. Kirchbach, D.V. Ahluwlalia, Phys. Lett. B529, 131
(2002) as the source of Figure 1. No further change
Quantum states of indefinite spins: From baryons to massive gravitino
I review theory and phenomenology of
(K/2,K/2)*[(1/2,0)+(0,1/2)] states.
First I make the case that the observed nucleon and Delta (1232) excitations
(up to Delta(1600)) are exhausted by unconstrained (K/2,K/2)*[(1/2,0)+(0,1/2)]
states with K=1,3, and 5, which originate from rotational and vibrational
excitations of an underlying quark--diquark configuration.
Second, I consider the simplest case of K=1 and show that the
\gamma^\mu\psi_\mu =0 constraint of the Rarita-Schwinger framework is a
short-hand of:
- 1/3 (1/m^2 W^2 +3/4)\psi_\mu = \psi_\mu, the covariant definition of the
unique invariant subspace of the squared Pauli-Lubanski vector, W^2, that is a
parity singlet and of highest spin-3/2 at rest.
I suggest to work in the 16 dimensional vector spinor space
\Psi= A *\psi rather than keeping Lorentz and spinor indices separated and
show that the above second order equation guarantees the covariant description
of a has-been spin-3/2 states at rest without invoking further supplementary
conditions.
In gauging the latter equation minimally and, in calculating the determinant,
one obtains a pathology-free energy-momentum dispersion relation, thus avoiding
the classical Velo-Zwanziger problem of imaginary energies in the presence of
an external electromagnetic field.Comment: Review talk at "Zacatecas Forum in Physics 2002" on theory and
phenomenology of (K/2,K/2)*[(1/2,0)+(0,1/2)] state
Lagrangians for invariant sub-spaces of the squared Pauli-Lubanski vector
We present an alternative formalism to the Rarita-Schwinger framework for the
description of "has-been" higher spins at rest that avoids the Velo-Zwanziger
problem.Comment: 3 pages, Contribution to the X Mexican School on Particles and
Fields, 2002; The calculations by the symbolic program Mathematica have been
performed by us during the time period Sept. 10, 2002-Febr. 05, 2003 at the
computer heritage.reduaz,mx, courtesy D.V.Ahluwali
Linear Wave Equations and Effective Lagrangians for Wigner Supermultiplets
The relevance of the contracted SU(4) group as a symmetry group of the pion
nucleon scattering amplitudes in the large limit of QCD raises the
problem on the construction of effective Lagrangians for SU(4) supermultiplets.
In the present study we suggest effective Lagrangians for selfconjugate
representations of SU(4) in exploiting isomorphism between so(6) and ist
universal covering su(4). The model can be viewed as an extension of the linear
model with SO(6) symmetry in place of SO(4) and generalizes the
concept of the linear wave equations for particles with arbitrary spin. We show
that the vector representation of SU(4) reduces on the SO(4) level to a
complexified quaternion. Its real part gives rise to the standard linear
model with a hedgehog configuration for the pion field, whereas the
imaginary part describes vector meson degrees of freedom via purely transversal
mesons for which a helical field configuration is predicted. As a
minimal model, baryonic states are suggested to appear as solitons of that
quaternion.Comment: 16 pages, LaTe
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