5 research outputs found
Accurate calculation of resonances in multiple-well oscillators
Quantum--mechanical multiple--well oscillators exhibit curious complex
eigenvalues that resemble resonances in models with continuum spectra. We
discuss a method for the accurate calculation of their real and imaginary
parts
Variational Quark Mass Expansion and the Order Parameters of Chiral Symmetry Breaking
We investigate in some detail a "variational mass" expansion approach,
generalized from a similar construction developed in the Gross-Neveu model, to
evaluate the basic order parameters of the dynamical breaking of the and chiral symmetries in QCD. The
method starts with a reorganization of the ordinary perturbation theory with
the addition of an arbitrary quark mass . The new perturbative series can be
summed to all orders thanks to renormalization group properties, with specific
boundary conditions, and advocated analytic continuation in properties. In
the approximation where the explicit breakdown of the chiral symmetries due to
small current quark masses is neglected, we derive ansatzes for the dynamical
contribution to the "constituent" masses of the quarks; the pion
decay constant ; and the quark condensate in terms of
the basic QCD scale . Those ansatzes are then optimized,
in a sense to be specified, and also explicit symmetry breaking mass terms can
be consistently introduced in the framework. The obtained values of and
are roughly in agreement with what is expected from other
non-perturbative methods. In contrast we obtain quite a small value of within our approach. The possible interpretation of the latter results
is briefly discussed.Comment: 40 pages, LaTex, 2 PS figures. Additions in section 2.2 to better
explain the relation between the current mass and the dynamical mass ansatz.
Minor misprints corrected. Version to appear in Phys. Rev.
(Borel) convergence of the variationally improved mass expansion and the O(N) Gross-Neveu model mass gap
We reconsider in some detail a construction allowing (Borel) convergence of
an alternative perturbative expansion, for specific physical quantities of
asymptotically free models. The usual perturbative expansions (with an explicit
mass dependence) are transmuted into expansions in 1/F, where
for while for m \lsim \Lambda,
being the basic scale and given by renormalization group
coefficients. (Borel) convergence holds in a range of which corresponds to
reach unambiguously the strong coupling infrared regime near , which
can define certain "non-perturbative" quantities, such as the mass gap, from a
resummation of this alternative expansion. Convergence properties can be
further improved, when combined with expansion (variationally improved
perturbation) methods. We illustrate these results by re-evaluating, from
purely perturbative informations, the O(N) Gross-Neveu model mass gap, known
for arbitrary from exact S matrix results. Comparing different levels of
approximations that can be defined within our framework, we find reasonable
agreement with the exact result.Comment: 33 pp., RevTeX4, 6 eps figures. Minor typos, notation and wording
corrections, 2 references added. To appear in Phys. Rev.