240 research outputs found
Life Time Analysis of MCrAlY Coatings for Industrial Gas Turbine Blades (Calculational and Experimental Approach)
Feigin-Frenkel center in types B, C and D
For each simple Lie algebra g consider the corresponding affine vertex
algebra V_{crit}(g) at the critical level. The center of this vertex algebra is
a commutative associative algebra whose structure was described by a remarkable
theorem of Feigin and Frenkel about two decades ago. However, only recently
simple formulas for the generators of the center were found for the Lie
algebras of type A following Talalaev's discovery of explicit higher Gaudin
Hamiltonians. We give explicit formulas for generators of the centers of the
affine vertex algebras V_{crit}(g) associated with the simple Lie algebras g of
types B, C and D. The construction relies on the Schur-Weyl duality involving
the Brauer algebra, and the generators are expressed as weighted traces over
tensor spaces and, equivalently, as traces over the spaces of singular vectors
for the action of the Lie algebra sl_2 in the context of Howe duality. This
leads to explicit constructions of commutative subalgebras of the universal
enveloping algebras U(g[t]) and U(g), and to higher order Hamiltonians in the
Gaudin model associated with each Lie algebra g. We also introduce analogues of
the Bethe subalgebras of the Yangians Y(g) and show that their graded images
coincide with the respective commutative subalgebras of U(g[t]).Comment: 29 pages, constructions of Pfaffian-type Sugawara operators and
commutative subalgebras in universal enveloping algebras are adde
Manin matrices and Talalaev's formula
We study special class of matrices with noncommutative entries and
demonstrate their various applications in integrable systems theory. They
appeared in Yu. Manin's works in 87-92 as linear homomorphisms between
polynomial rings; more explicitly they read: 1) elements in the same column
commute; 2) commutators of the cross terms are equal: (e.g. ). We claim
that such matrices behave almost as well as matrices with commutative elements.
Namely theorems of linear algebra (e.g., a natural definition of the
determinant, the Cayley-Hamilton theorem, the Newton identities and so on and
so forth) holds true for them.
On the other hand, we remark that such matrices are somewhat ubiquitous in
the theory of quantum integrability. For instance, Manin matrices (and their
q-analogs) include matrices satisfying the Yang-Baxter relation "RTT=TTR" and
the so--called Cartier-Foata matrices. Also, they enter Talalaev's
hep-th/0404153 remarkable formulas: ,
det(1-e^{-\p}T_{Yangian}(z)) for the "quantum spectral curve", etc. We show
that theorems of linear algebra, after being established for such matrices,
have various applications to quantum integrable systems and Lie algebras, e.g
in the construction of new generators in (and, in general,
in the construction of quantum conservation laws), in the
Knizhnik-Zamolodchikov equation, and in the problem of Wick ordering. We also
discuss applications to the separation of variables problem, new Capelli
identities and the Langlands correspondence.Comment: 40 pages, V2: exposition reorganized, some proofs added, misprints
e.g. in Newton id-s fixed, normal ordering convention turned to standard one,
refs. adde
A quantum isomonodromy equation and its application to N=2 SU(N) gauge theories
We give an explicit differential equation which is expected to determine the
instanton partition function in the presence of the full surface operator in
N=2 SU(N) gauge theory. The differential equation arises as a quantization of a
certain Hamiltonian system of isomonodromy type discovered by Fuji, Suzuki and
Tsuda.Comment: 15 pages, v2: typos corrected and references added, v3: discussion,
appendix and references adde
Integrable Models From Twisted Half Loop Algebras
This paper is devoted to the construction of new integrable quantum
mechanical models based on certain subalgebras of the half loop algebra of
gl(N). Various results about these subalgebras are proven by presenting them in
the notation of the St Petersburg school. These results are then used to
demonstrate the integrability, and find the symmetries, of two types of
physical system: twisted Gaudin magnets, and Calogero-type models of particles
on several half-lines meeting at a point.Comment: 22 pages, 1 figure, Introduction improved, References adde
Limits of Gaudin algebras, quantization of bending flows, Jucys--Murphy elements and Gelfand--Tsetlin bases
Gaudin algebras form a family of maximal commutative subalgebras in the
tensor product of copies of the universal enveloping algebra U(\g) of a
semisimple Lie algebra \g. This family is parameterized by collections of
pairwise distinct complex numbers . We obtain some new commutative
subalgebras in U(\g)^{\otimes n} as limit cases of Gaudin subalgebras. These
commutative subalgebras turn to be related to the hamiltonians of bending flows
and to the Gelfand--Tsetlin bases. We use this to prove the simplicity of
spectrum in the Gaudin model for some new cases.Comment: 11 pages, references adde
Measurement of the J/Psi Production Cross Section in 920 GeV/c Fixed-Target Proton-Nucleus Interactions
The mid-rapidity (dsigma_(pN)/dy at y=0) and total sigma_(pN) production
cross sections of J/Psi mesons are measured in proton-nucleus interactions.
Data collected by the HERA-B experiment in interactions of 920 GeV/c protons
with carbon, titanium and tungsten targets are used for this analysis. The
J/Psi mesons are reconstructed by their decay into lepton pairs. The total
production cross section obtained is sigma_(pN)(J/Psi) = 663 +- 74 +- 46
nb/nucleon. In addition, our result is compared with previous measurements
Open and Hidden Charm Production in 920 GeV Proton-Nucleus Collisions
The HERA-B collaboration has studied the production of charmonium and open
charm states in collisions of 920 GeV protons with wire targets of different
materials. The acceptance of the HERA-B spectrometer covers negative values of
xF up to xF=-0.3 and a broad range in transverse momentum from 0.0 to 4.8
GeV/c. The studies presented in this paper include J/psi differential
distributions and the suppression of J/psi production in nuclear media.
Furthermore, production cross sections and cross section ratios for open charm
mesons are discussed.Comment: 5 pages, 9 figures, to be published in the proceedings of the 6th
International Conference on Hyperons, Charm & Beauty Hadrons (BEACH04),
Chicago, IL, June 27 - July 3, 200
Transverse-momentum-dependent Multiplicities of Charged Hadrons in Muon-Deuteron Deep Inelastic Scattering
A semi-inclusive measurement of charged hadron multiplicities in deep
inelastic muon scattering off an isoscalar target was performed using data
collected by the COMPASS Collaboration at CERN. The following kinematic domain
is covered by the data: photon virtuality (GeV/), invariant
mass of the hadronic system GeV/, Bjorken scaling variable in the
range , fraction of the virtual photon energy carried by the
hadron in the range , square of the hadron transverse momentum
with respect to the virtual photon direction in the range 0.02 (GeV/ (GeV/). The multiplicities are presented as a
function of in three-dimensional bins of , , and
compared to previous semi-inclusive measurements. We explore the
small- region, i.e. (GeV/), where
hadron transverse momenta are expected to arise from non-perturbative effects,
and also the domain of larger , where contributions from
higher-order perturbative QCD are expected to dominate. The multiplicities are
fitted using a single-exponential function at small to study
the dependence of the average transverse momentum on , and . The power-law behaviour of the
multiplicities at large is investigated using various
functional forms. The fits describe the data reasonably well over the full
measured range.Comment: 28 pages, 20 figure
Search for the Flavor-Changing Neutral Current Decay with the HERA-B Detector
We report on a search for the flavor-changing neutral current decay using events recorded with a dimuon trigger in
interactions of 920 GeV protons with nuclei by the HERA-B experiment. We find
no evidence for such decays and set a 90% confidence level upper limit on the
branching fraction .Comment: 17 pages, 4 figures (of which 1 double), paper to be submitted to
Physics Letters
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