1,175 research outputs found
S-matrix bootstrap for resonances
We study the -matrix element of a generic, gapped and
Lorentz invariant QFT in space time dimensions. We derive an analytical
bound on the coupling of the asymptotic states to unstable particles (a.k.a.
resonances) and its physical implications. This is achieved by exploiting the
connection between the S-matrix phase-shift and the roots of the S-matrix in
the physical sheet. We also develop a numerical framework to recover the
analytical bound as a solution to a numerical optimization problem. This later
approach can be generalized to spacetime dimensions.Comment: Minor typos corrected, matches published versio
Ideals of general forms and the ubiquity of the Weak Lefschetz property
Let be positive integers and let be an
ideal generated by general forms of degrees , respectively, in a
polynomial ring with variables. When all the degrees are the same we
give a result that says, roughly, that they have as few first syzygies as
possible. In the general case, the Hilbert function of has been
conjectured by Fr\"oberg. In a previous work the authors showed that in many
situations the minimal free resolution of must have redundant terms which
are not forced by Koszul (first or higher) syzygies among the (and hence
could not be predicted from the Hilbert function), but the only examples came
when . Our second main set of results in this paper show that further
examples can be obtained when . We also show that if
Fr\"oberg's conjecture on the Hilbert function is true then any such redundant
terms in the minimal free resolution must occur in the top two possible degrees
of the free module. Related to the Fr\"oberg conjecture is the notion of Weak
Lefschetz property. We continue the description of the ubiquity of this
property. We show that any ideal of general forms in has
it. Then we show that for certain choices of degrees, any complete intersection
has it and any almost complete intersection has it. Finally, we show that most
of the time Artinian ``hypersurface sections'' of zeroschemes have it.Comment: 24 page
Un objecte singular en os a la Timba del Barenys (Riudoms, Baix Camp): botó, penjoll o Ãdol cruciforme?
S-matrix bootstrap for resonances
We study the -matrix element of a generic, gapped and
Lorentz invariant QFT in space time dimensions. We derive an analytical
bound on the coupling of the asymptotic states to unstable particles (a.k.a.
resonances) and its physical implications. This is achieved by exploiting the
connection between the S-matrix phase-shift and the roots of the S-matrix in
the physical sheet. We also develop a numerical framework to recover the
analytical bound as a solution to a numerical optimization problem. This later
approach can be generalized to spacetime dimensions.Comment: Minor typos corrected, matches published versio
THE MITE ORNITHONYSSUS SYLVARIUM (C. AND F.) (ARACHNIDA: ACARINA-MACRONYSSIDAE) ATTACKING FOWL IN PUERTO RICO
THE MITE ORNITHONYSSUS SYLVARIUM (C. AND F.) (ARACHNIDA: ACARINA-MACRONYSSIDAE) ATTACKING FOWL IN PUERTO RIC
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