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1.
In this paper we investigate the Schwinger parametric representation for the Feynman amplitudes of the recently discovered
renormalizable quantum field theory on the Moyal non commutative space. This representation involves new hyperbolic polynomials which are the non-commutative analogs of the usual “Kirchoff” or “Symanzik” polynomials of commutative field
theory, but contain richer topological information.
Work supported by ANR grant NT05-3-43374 “GenoPhy”. 相似文献
2.
Dongho Chae 《Communications in Mathematical Physics》2007,273(1):203-215
We prove that there exists no self-similar finite time blowing up solution to the 3D incompressible Euler equations if the
vorticity decays sufficiently fast near infinity in . By a similar method we also show nonexistence of self-similar blowing up solutions to the divergence-free transport equation
in . This result has direct applications to the density dependent Euler equations, the Boussinesq system, and the quasi-geostrophic
equations, for which we also show nonexistence of self-similar blowing up solutions.
The work was supported partially by the KOSEF Grant no. R01-2005-000-10077-0, and KRF Grant (MOEHRD, Basic Research Promotion
Fund). 相似文献
3.
Quantum Conjugacy Classes of Simple Matrix Groups 总被引:1,自引:0,他引:1
A. Mudrov 《Communications in Mathematical Physics》2007,272(3):635-660
Let G be a simple complex classical group and its Lie algebra. Let be the Drinfeld-Jimbo quantization of the universal enveloping algebra . We construct an explicit -equivariant quantization of conjugacy classes of G with Levi subgroups as the stabilizers.
Dedicated to the memory of Joseph Donin
This research is partially supported by the Emmy Noether Research Institute for Mathematics, the Minerva Foundation of Germany,
the Excellency Center “Group Theoretic Methods in the study of Algebraic Varieties” of the Israel Science foundation, by the
EPSRC grant C511166, and by the RFBR grant no. 06-01-00451. 相似文献
4.
5.
Let
be a finite dimensional complex Lie algebra and
a Lie subalgebra equipped with the structure of a factorizable quasitriangular Lie bialgebra. Consider the Lie group Exp
with the Semenov-Tjan-Shansky Poisson bracket as a Poisson Lie manifold for the double Lie bialgebra
. Let
be an open domain parameterizing a neighborhood of the identity in Exp
by the exponential map. We present dynamical r-matrices with values in
over the Poisson Lie base manifold
.*This research is partially supported by the Emmy Noether Research Institute for Mathematics, the Minerva Foundation of Germany, the Excellency Center Group Theoretic Methods in the study of Algebraic Varieties of the Israel Science foundation, and by the RFBR grant no. 03-01-00593. 相似文献
6.
Kenneth S. Alexander 《Communications in Mathematical Physics》2008,279(1):117-146
We consider a polymer, with monomer locations modeled by the trajectory of a Markov chain, in the presence of a potential
that interacts with the polymer when it visits a particular site 0. We assume that probability of an excursion of length n is given by for some 1 < c < 2 and slowly varying . Disorder is introduced by having the interaction vary from one monomer to another, as a constant u plus i.i.d. mean-0 randomness. There is a critical value of u above which the polymer is pinned, placing a positive fraction (called the contact fraction) of its monomers at 0 with high
probability. To see the effect of disorder on the depinning transition, we compare the contact fraction and free energy (as
functions of u) to the corresponding annealed system. We show that for c > 3/2, at high temperature, the quenched and annealed curves differ significantly only in a very small neighborhood of the
critical point—the size of this neighborhood scales as , where β is the inverse temperature. For c < 3/2, given , for sufficiently high temperature the quenched and annealed curves are within a factor of for all u near the critical point; in particular the quenched and annealed critical points are equal. For c = 3/2 the regime depends on the slowly varying function .
Research supported by NSF grant DMS-0405915. 相似文献
7.
An Algebra of Deformation Quantization for Star-Exponentials on Complex Symplectic Manifolds 总被引:1,自引:0,他引:1
The cotangent bundle T
*
X to a complex manifold X is classically endowed with the sheaf of k-algebras of deformation quantization, where k := is a subfield of . Here, we construct a new sheaf of k-algebras which contains as a subalgebra and an extra central parameter t. We give the symbol calculus for this algebra and prove that quantized symplectic transformations operate on it. If P is any section of order zero of , we show that is well defined in . 相似文献
8.
A trajectory attractor is constructed for the 2D Euler system containing an additional dissipation term −ru, r > 0, with periodic boundary conditions. The corresponding dissipative 2D Navier-Stokes system with the same term −ru and with viscosity v > 0 also has a trajectory attractor, . Such systems model large-scale geophysical processes in atmosphere and ocean (see [1]). We prove that → as v → 0+ in the corresponding metric space. Moreover, we establish the existence of the minimal limit of the trajectory attractors as v → 0+. We prove that is a connected invariant subset of . The connectedness problem for the trajectory attractor by itself remains open.
Dedicated to the memory of Leonid Volevich
Partially supported by the Russian Foundation for Basic Research (projects no 08-01-00784 and 07-01-00500). The first author
has been partially supported by a research grant from the Caprio Foundation, Landau Network-Cento Volta. 相似文献
9.
We consider finite-range asymmetric exclusion processes on with non-zero drift. The diffusivity D(t) is expected to be of . We prove that D(t) ≥ Ct
1/3 in the weak (Tauberian) sense that as . The proof employs the resolvent method to make a direct comparison with the totally asymmetric simple exclusion process,
for which the result is a consequence of the scaling limit for the two-point function recently obtained by Ferrari and Spohn.
In the nearest neighbor case, we show further that tD(t) is monotone, and hence we can conclude that D(t) ≥ Ct
1/3(log
t)−7/3 in the usual sense.
Supported by the Natural Sciences and Engineering Research Council of Canada.
Partially supported by the Hungarian Scientific Research Fund grants T37685 and K60708. 相似文献
10.
In this letter, first we give a decomposition for any Lie–Poisson structure associated to the modular vector. In particular, splits into two compatible Lie–Poisson structures if . As an application, we classified quadratic deformations of Lie– Poisson structures on up to linear diffeomorphisms.
Research partially supported by NSF of China and the Research Project of “Nonlinear Science”. 相似文献
11.
We give holomorphic Chern-Simons-like action functionals on supertwistor space for self-dual supergravity theories in four
dimensions, dealing with supersymmetries, the cases where different parts of the R-symmetry are gauged, and with or without a cosmological constant. The gauge group is formally the group of holomorphic Poisson
transformations of supertwistor space where the form of the Poisson structure determines the amount of R-symmetry gauged and the value of the cosmological constant. We give a formulation in terms of a finite deformation of an
integrable -operator on a supertwistor space, i.e., on regions in . For , we also give a formulation that does not require the choice of a background. 相似文献
12.
We show that there is a natural gauge invariant presymplectic structure on the spaceA of all vector potentials. The covariant axial anomaly
is found to be the essentially unique infinitestimally equivariant momentum mapping for the action of the group of gauge transformations on (A,). The infinitesimal equivariance of
is shown to be equivalent to the Wess-Zumino consistency condition for the consistent axial anomalyG. We also show that theX operator of Bardeen and Zumino, which relatesG and
, corresponds to the one-form (onA) of the presymplectic structure.Research supported in part by NSF grant MCS 81-08814(A03)Research supported by the U.S. Department of Energy under contract number DE AC02 76 ER 02220 相似文献
13.
14.
Tadayoshi Adachi 《Letters in Mathematical Physics》2007,82(1):1-8
For an N-body Stark Hamiltonian , the resolvent estimate holds uniformly in with Re and Im , where , and is a compact interval. This estimate is well known as the limiting absorption principle. In this paper, we report that by
introducing the localization in the configuration space, a refined resolvent estimate holds uniformly in with Re and Im .
Dedicated to Professor Hideo Tamura on the occasion of his 60th birthday 相似文献
15.
Asao Arai 《Letters in Mathematical Physics》2007,80(3):211-221
Let H be a self-adjoint operator on a complex Hilbert space . A symmetric operator T on is called a time operator of H if, for all , (D(T) denotes the domain of T) and . In this paper, spectral properties of T are investigated. The following results are obtained: (i) If H is bounded below, then σ(T), the spectrum of T, is either (the set of complex numbers) or . (ii) If H is bounded above, then is either or . (iii) If H is bounded, then . The spectrum of time operators of free Hamiltonians for both nonrelativistic and relativistic particles is exactly identified.
Moreover spectral analysis is made on a generalized time operator.
This work is supported by the Grant-in-Aid No.17340032 for Scientific Research from the JSPS. 相似文献
16.
A zero modes’ Fock space is constructed for the extended chiral WZNW model. It gives room to a realization of the fusion ring of representations of the restricted quantum universal enveloping
algebra at an even root of unity, and of its infinite dimensional extension by the Lusztig operators We provide a streamlined derivation of the characteristic equation for the Casimir invariant from the defining relations
of A central result is the characterization of the Grothendieck ring of both and in Theorem 3.1. The properties of the fusion ring in are related to the braiding properties of correlation functions of primary fields of the conformal current algebra model.
相似文献
17.
Manjunath Krishnapur 《Journal of statistical physics》2006,124(6):1399-1423
We consider the point process of zeroes of certain Gaussian analytic functions and find the asymptotics for the probability that there are more than m points of the process in a fixed disk of radius r, as . For the planar Gaussian analytic function, , we show that this probability is asymptotic to . For the hyperbolic Gaussian analytic functions, , we show that this probability decays like .In the planar case, we also consider the problem posed by Mikhail Sodin2 on moderate and very large deviations in a disk of radius r, as . We partially solve the problem by showing that there is a qualitative change in the asymptotics of the probability as we move from the large deviation regime to the moderate.Research supported by NSF grant #DMS-0104073 and NSF-FRG grant #DMS-0244479. 相似文献
18.
Asao Arai 《Letters in Mathematical Physics》2008,85(1):15-25
Let (T, H) be a weak Weyl representation of the canonical commutation relation (CCR) with one degree of freedom. Namely T is a symmetric operator and H is a self-adjoint operator on a complex Hilbert space satisfying the weak Weyl relation: for all (the set of real numbers), e−itH
D(T) ⊂ D(T) (i is the imaginary unit and D(T) denotes the domain of T) and . In the context of quantum theory where H is a Hamiltonian, T is called a strong time operator of H. In this paper we prove the following theorem on uniqueness of weak Weyl representations: Let be separable. Assume that H is bounded below with and , where is the set of complex numbers and, for a linear operator A on a Hilbert space, σ(A) denotes the spectrum of A. Then ( is the closure of T) is unitarily equivalent to a direct sum of the weak Weyl representation on the Hilbert space , where is the multiplication operator by the variable and with . Using this theorem, we construct a Weyl representation of the CCR from the weak Weyl representation .
This work is supported by the Grant-in-Aid No.17340032 for Scientific Research from Japan Society for the Promotion of Science
(JSPS). 相似文献
19.
S. Lievens N. I. Stoilov J. Van der Jeugt 《Communications in Mathematical Physics》2008,281(3):805-826
It is known that the defining relations of the orthosymplectic Lie superalgebra are equivalent to the defining (triple) relations of n pairs of paraboson operators . In particular, with the usual star conditions, this implies that the “parabosons of order p” correspond to a unitary irreducible (infinite-dimensional) lowest weight representation V(p) of . Apart from the simple cases p = 1 or n = 1, these representations had never been constructed due to computational difficulties, despite their importance. In the
present paper we give an explicit and elegant construction of these representations V(p), and we present explicit actions or matrix elements of the generators. The orthogonal basis vectors of V(p) are written in terms of Gelfand-Zetlin patterns, where the subalgebra of plays a crucial role. Our results also lead to character formulas for these infinite-dimensional representations. Furthermore, by considering the branching , we find explicit infinite-dimensional unitary irreducible lowest weight representations of and their characters.
NIS was supported by a project from the Fund for Scientific Research – Flanders (Belgium) and by project P6/02 of the Interuniversity
Attraction Poles Programme (Belgian State – Belgian Science Policy).
An erratum to this article can be found at 相似文献
20.
Ya-Jun Gao 《General Relativity and Gravitation》2005,37(1):1-17
A so-called extended elliptical-complex (EEC) function method is proposed and used to further study the Einstein–Maxwell-dilaton-axion theory with p vector fields (EMDA-p theory, for brevity) for
. An Ernst-like
matrix EEC potential is introduced and the motion equations of the stationary axisymmetric EMDA-p theory are written as a so-called Hauser–Ernst-like self-dual relation for the EEC matrix potential. In particular, for the EMDA-2 theory, two Hauser–Ernst-type EEC linear systems are established and based on their solutions some new parametrized symmetry transformations are explicitly constructed. These hidden symmetries are verified to constitute an infinite-dimensional Lie algebra, which is the semidirect product of the Kac–Moody algebra
and Virasoro algebra (without centre charges). These results show that the studied EMDA-p theories possess very rich symmetry structures and the EEC function method is necessary and effective. 相似文献