61,990 research outputs found
Theories, models, simulations: a computational challenge
In this talk I would like to illustrate with examples taken from Quantum
Field Theory and Biophysics how an intelligent exploitation of the
unprecedented power of today's computers could led not only to the solution of
pivotal problems in the theory of Strong Interactions, but also to the
emergence of new lines of interdisciplinary research, while at the same time
pushing the limits of modeling to the realm of living systems.Comment: 19 pages, 1 figure, conference pape
Isospin Mixing of Narrow Pentaquark States
Interpreting the recently discovered narrow exotic baryons as pentaquark
states, we discuss, along an old argument of ours, the isospin mixing occurring
within the two doublets of and Q=0 states lying inside the
(-cascade) sector. We argue that, at least within the Jaffe-Wilczek
assignment, presently available data already indicate that mixing should occur
at an observable level in both charge sectors, with mixing angles that can be
predicted in terms of ratios of observable mass splittings.Comment: 11 pages, 2 figures, to be submitted to PL
Note on lattice regularization and equal-time correlators for parton distribution functions
We show that a recent interesting idea to circumvent the difficulties with
the continuation of parton distribution functions to the Euclidean region, that
consists in looking at equal time correlators between proton states of infinite
momentum, encounters some problems related to the power divergent mixing
pattern of DIS operators, when implemented within the lattice regularization.Comment: 15 pages, no figures, Physical Review D (2017
Hilbert Functions of Filtered Modules
In this presentation we shall deal with some aspects of the theory of Hilbert
functions of modules over local rings, and we intend to guide the reader along
one of the possible routes through the last three decades of progress in this
area of dynamic mathematical activity. Motivated by the ever increasing
interest in this field, our goal is to gather together many new developments of
this theory into one place, and to present them using a unifying approach which
gives self-contained and easier proofs. In this text we shall discuss many
results by different authors, following essentially the direction typified by
the pioneering work of J. Sally. Our personal view of the subject is most
visibly expressed by the presentation of Chapters 1 and 2 in which we discuss
the use of the superficial elements and related devices. Basic techniques will
be stressed with the aim of reproving recent results by using a more elementary
approach. Over the past few years several papers have appeared which extend
classical results on the theory of Hilbert functions to the case of filtered
modules. The extension of the theory to the case of general filtrations on a
module has one more important motivation. Namely, we have interesting
applications to the study of graded algebras which are not associated to a
filtration, in particular the Fiber cone and the Sally-module. We show here
that each of these algebras fits into certain short exact sequences, together
with algebras associated to filtrations. Hence one can study the Hilbert
function and the depth of these algebras with the aid of the know-how we got in
the case of a filtration.Comment: 127 pages, revised version. Comments and remarks are welcom
A non-perturbative mechanism for elementary particle mass generation
Taking inspiration from lattice QCD data, we argue that a finite
non-perturbative contribution to the quark mass is generated as a consequence
of the dynamical phenomenon of spontaneous chiral symmetry breaking, in turn
triggered by the explicitly breaking of chiral symmetry induced by the critical
Wilson term in the action. In pure lattice QCD this mass term cannot be
separated from the unavoidably associated linearly divergent contribution.
However, if QCD is enlarged to a theory where also a scalar field is present,
coupled to an SU(2) doublet of fermions via a Yukawa and a Wilson-like term,
then in the phase where the scalar field takes a non-vanishing expectation
value, a dynamically generated and "naturally" light fermion mass (numerically
unrelated to the expectation value of the scalar field) is conjectured to
emerge at a critical value of the Yukawa coupling where the symmetry of the
model is maximally enhanced. Masses dynamically generated in this way display a
natural hierarchy according to which the stronger is the strongest of the
interactions the fermion is subjected to the larger is its mass.Comment: Added more information in Fig 1. Added Fig. 10. Added an extra
Appendix. Restructured a few sentences according to referee suggestions.
Corrected a few misprints. All results unchanged. Now 50 pages and 10 Figure
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