167,018 research outputs found
On Goldstone bosons decoupling from high-lying hadrons
In this paper, we discuss a decoupling of the Goldstone bosons from highly
excited hadrons in relation to the restoration of chiral symmetry in such
hadrons. We use a generalised Nambu-Jona-Lasinio model with the interaction
between quarks in the form of an instantaneous Lorentz-vector confining
potential. This model is known to provide spontaneous breaking of chiral
symmetry in the vacuum via the standard selfenergy loops for valence quarks.
For highly excited hadrons, where the typical momentum of valence quarks is
large, the loop contributions represent only a small correction to the
chiral-invariant classical contributions and asymptotically vanish.
Consequently the chiral symmetry violating Lorentz-scalar dynamical mass of
quarks vanishes. Then the conservation of the axial vector current in the
chiral limit requires, via the Goldberger-Treiman relation, that the valence
quarks decouple from the Goldstone boson. As a consequence, the whole hadron
decouples from the Goldstone boson as well, which implies that its axial
constant also vanishes.Comment: RevTeX4, 21 pages, 5 Postscript figures, uses epsfig.sty, new chapter
with numerical estimates added, to appear in Phys.Rev.
Massless fields over space-time and coherent states for the Lorentz group
The solutions of the arbitrary-spin massless wave equations over space are obtained using the generalized coherent states for the
Lorentz group. The use of these solutions for the construction of invariant
propagators of quantized massless fields with an arbitrary spin over the space is considered. The expression for the scalar propagator
is obtained in the explicit form.Comment: 6 pages, LATEX, no figures. To appear in Modern Phys. Lett.
On bosonic limits of two recent supersymmetric extensions of the Harry Dym hierarchy
Two generalized Harry Dym equations, recently found by Brunelli, Das and
Popowicz in the bosonic limit of new supersymmetric extensions of the Harry Dym
hierarchy [J. Math. Phys. 44:4756--4767 (2003)], are transformed into
previously known integrable systems: one--into a pair of decoupled KdV
equations, the other one--into a pair of coupled mKdV equations from a
bi-Hamiltonian hierarchy of Kupershmidt.Comment: 7 page
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