共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
Andrei A. Zagorodni German Salazar-Alvarez Mamoun Muhammed 《Journal of nanoparticle research》2008,10(2):377-381
Formation of elongated nanoparticles was observed when was precipitated from solutions containing excess of Fe2+. The average diameter of the particles was 23 nm; the length to diameter ratio was up to 14. This shape was an unexpected
phenomenon because bar- or needle-like nanoparticles have been earlier reported only for Fe(III)-based materials. Chemical
analysis revealed Fe(OH)2 nature of the obtained particles. In addition, this conclusion was verified with a new simple method for quantitative evaluation
of the particle morphology. Application of this method to the mixed samples allowed to distinguish between the two different compounds and to attribute different morphologies to Fe(OH)2 or Results indicate that bars are frequent shapes of nano-sized iron oxides/hydroxides. 相似文献
3.
4.
Clifford H. Taubes 《Communications in Mathematical Physics》2006,267(1):25-64
I describe a functional integral for maps from
to a Lie group or its quotient which has a simple renormalization that leads to a quantum field theory for maps from
into the Lie group or its quotient whose Hamiltonian is the time translation generator for a unitary action of the n+1 dimensional Poincaré group on the quantum Hilbert space. I also explain how the renormalization provides a functional integral for maps from a Riemann surface to a compact Lie group or its quotient that exhibits many conformal field theoretic properties.Support in part by a grant from the National Science Foundation 相似文献
5.
6.
Rod-like ZnO nanoparticles were prepared by the hydrolysis of zinc acetate under heating in diethylene glycol (DEG). Structural
characterization of the synthesized powders was investigated by XRD, FT-IR, electron paramagnetic resonance (EPR) and transmission
electron microscopy (TEM). The size of the particles increased as the amount of H2O added increased in the nano size range. The average crystallite size calculated from the XRD patterns varied from 6 to 64 nm
corresponding to the amount of H2O added. The ZnO nanopartilces possess the wurtzite type crystallographic structure. It was found that these ZnO nanoparticles
had singly ionized oxygen vacancy defect () and superoxide ions from the EPR investigations. A strong near UV emission of the ZnO nanoparticles at about 380 nm was observed
and its intensity decreased as the amount of H2O increased. This emission of ZnO nanoparticles is found to be particles size dependent due to the confinement effect. A green
emission at about 540 nm due to the recombination of electrons trapped at singly ionized oxygen vacancies defect () appeared when the amount of H2O increased. The intensity of the green emission increases as the concentration of increases. 相似文献
7.
Jürg Fröhlich B. Lars G. Jonsson Enno Lenzmann 《Communications in Mathematical Physics》2007,274(1):1-30
We study the nonlinear equation
which is known to describe the dynamics of pseudo-relativistic boson stars in the mean-field limit. For positive mass parameters,
m > 0, we prove existence of travelling solitary waves, , for some and with speed |v| < 1, where c = 1 corresponds to the speed of light in our units. Due to the lack of Lorentz covariance, such travelling solitary waves
cannot be obtained by applying a Lorentz boost to a solitary wave at rest (with v = 0). To overcome this difficulty, we introduce and study an appropriate variational problem that yields the functions as minimizers, which we call boosted ground states. Our existence proof makes extensive use of concentration-compactness-type
arguments.
In addition to their existence, we prove orbital stability of travelling solitary waves and pointwise exponential decay of in x. 相似文献
8.
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
9.
Jonathan Weitsman 《Communications in Mathematical Physics》2008,277(1):101-125
We show how to construct measures on Banach manifolds associated to supersymmetric quantum field theories. These measures
are mathematically well-defined objects inspired by the formal path integrals appearing in the physics literature on quantum
field theory. We give three concrete examples of our construction. The first example is a family of measures on a space of functions on the two-torus, parametrized by a polynomial P (the Wess-Zumino-Landau-Ginzburg model). The second is a family of measures on a space of maps from to a Lie group (the Wess-Zumino-Novikov-Witten model). Finally we study a family of measures on the product of a space of connections on the trivial principal bundle with structure group G on a three-dimensional manifold M with a space of -valued three-forms on M.
We show that these measures are positive, and that the measures are Borel probability measures. As an application we show that formulas arising from expectations in the measures reproduce formulas discovered by Frenkel and Zhu in the theory of vertex operator algebras. We conjecture that a similar
computation for the measures , where M is a homology three-sphere, will yield the Casson invariant of M.
Dedicated to the memory of Raoul Bott
Supported in part by NSF grant DMS 04/05670. 相似文献
10.
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
11.
We show here what kind of modification of the interphase morphology of SnO2 nanoparticles in silica (average nanocrystal radius, in undoped material; in erbium doped material) brings to the passivation of interfacial defects. Surface states, which may preclude the exploitation
of UV excitonic emission, are reduced after doping by rare earth ions. We demonstrate, by means of transmission-electron-microscopy
and small-angle-neutron-scattering data, that a smooth interphase with a non negligible thickness takes the place of the fractal
and discontinuous boundary observed in undoped material. 相似文献
12.
Paolo Aschieri Leonardo Castellani Marija Dimitrijević 《Letters in Mathematical Physics》2008,85(1):39-53
A -product is defined via a set of commuting vector fields , and used in a theory coupled to the fields. The -product is dynamical, and the vacuum solution , reproduces the usual Moyal product. The action is invariant under rigid translations and Lorentz rotations, and the conserved
energy–momentum and angular momentum tensors are explicitly derived.
相似文献
13.
We compute the first cohomology spaces
of the Lie superalgebra with coefficients in the superspace of linear differential operators acting on weighted densities on the supercircle S
1|1. The structure of these spaces was conjectured in (Gargoubi et al. in Lett Math Phys 79:5165, 2007). In fact, we prove here
that the situation is a little bit more complicated.
相似文献
14.
We consider a class of singular Riemannian manifolds, the deformed spheres , defined as the classical spheres with a one parameter family g[k] of singular Riemannian structures, that reduces for k = 1 to the classical metric. After giving explicit formulas for the eigenvalues and eigenfunctions of the metric Laplacian
, we study the associated zeta functions . We introduce a general method to deal with some classes of simple and double abstract zeta functions, generalizing the
ones appearing in . An application of this method allows to obtain the main zeta invariants for these zeta functions in all dimensions, and
in particular and . We give explicit formulas for the zeta regularized determinant in the low dimensional cases, N = 2,3, thus generalizing a result of Dowker [25], and we compute the first coefficients in the expansion of these determinants
in powers of the deformation parameter k.
Partially supported by FAPESP: 2005/04363-4 相似文献
15.
We study a large class of Poisson manifolds, derived from Manin triples, for which we construct explicit partitions into regular
Poisson submanifolds by intersecting certain group orbits. Examples include all varieties of Lagrangian subalgebras of reductive quadratic Lie algebras with Poisson structures defined by Lagrangian splittings of . In the special case of , where is a complex semi-simple Lie algebra, we explicitly compute the ranks of the Poisson structures on defined by arbitrary Lagrangian splittings of . Such Lagrangian splittings have been classified by P. Delorme, and they contain the Belavin–Drinfeld splittings as special
cases. 相似文献
16.
Dyson’s Constants in the Asymptotics of the Determinants of Wiener-Hopf-Hankel Operators with the Sine Kernel 总被引:1,自引:1,他引:0
Torsten Ehrhardt 《Communications in Mathematical Physics》2007,272(3):683-698
Let stand for the integral operators with the sine kernels acting on L
2[0,α]. Dyson conjectured that the asymptotics of the Fredholm determinants of are given by
as α→∞. In this paper we are going to give a proof of these two asymptotic formulas. 相似文献
17.
We exhibit a finitely generated group whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping
class group associated to a surface of infinite genus, and contains all the pure mapping class groups of compact surfaces of genus g with n boundary components, for any g ≥ 0 and n > 0. We construct a representation of into the restricted symplectic group of the real Hilbert space generated by the homology classes of non-separating circles on , which generalizes the classical symplectic representation of the mapping class groups. Moreover, we show that the first
universal Chern class in is the pull-back of the Pressley-Segal class on the restricted linear group via the inclusion .
L. F. was partially supported by the ANR Repsurf:ANR-06-BLAN-0311. 相似文献
18.
Consider in the operator family . P
0 is the quantum harmonic oscillator with diophantine frequency vector ω, F
0 a bounded pseudodifferential operator with symbol decreasing to zero at infinity in phase space, and . Then there exist independent of and an open set such that if and , the quantum normal form near P
0 converges uniformly with respect to . This yields an exact quantization formula for the eigenvalues, and for the classical Cherry theorem on convergence of Birkhoff’s normal form for complex frequencies is recovered.
Partially supported by PAPIIT-UNAM IN106106-2. 相似文献
19.
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
20.
We continue our study of the collision of two solitons for the subcritical generalized KdV equations
Solitons are solutions of the type where c
0 > 0. In [21], mainly devoted to the case f (u) = u
4, we have introduced a new framework to understand the collision of two solitons , for (0.1) in the case (or equivalently, ). In this paper, we consider the case of a general nonlinearity f (u) for which , are nonlinearly stable. In particular, since f is general and c
1 can be large, the results are not perturbations of the ones for the power case in [21].
First, we prove that the two solitons survive the collision up to a shift in their trajectory and up to a small perturbation
term whose size is explicitly controlled from above: after the collision, , where is close to c
j
(j = 1, 2). Then, we exhibit new exceptional solutions similar to multi-soliton solutions: for all , there exists a solution such that
where (j = 1, 2) and converges to 0 in a neighborhood of the solitons as .
The analysis is split in two distinct parts. For the interaction region, we extend the algebraic tools developed in [21] for
the power case, by expanding f (u) as a sum of powers plus a perturbation term. To study the solutions in large time, we rely on previous tools on asymptotic
stability in [17,22] and [18], refined in [19,20].
This research was supported in part by the Agence Nationale de la Recherche (ANR ONDENONLIN). 相似文献