共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
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
3.
Przemysław Górka 《Letters in Mathematical Physics》2007,79(2):193-201
In this paper we deal with the following equation: on a three-dimensional Riemannian manifold . We assume that the volume of Σ, the norm , and are small enough. Using a rather simple argument we show the existence of solution to the problem.
Dedicated to Gosia and Basia. 相似文献
4.
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
5.
The space of linear polyvector fields on is a Lie subalgebra of the (graded) Lie algebra , equipped with the Schouten bracket. In this paper, we compute the cohomology of this subalgebra for the adjoint representation
in , restricting ourselves to the case of cochains defined with purely aerial Kontsevich’s graphs, as in Pac. J. Math. 218(2):201–239,
2005. We find a result which is very similar to the cohomology for the vector case Pac. J. Math. 229(2):257–292, 2007.
This work was supported by the CMCU contract 06 S 1502. W. Aloulou and R. Chatbouri thank the Université de Bourgogne and
D. Arnal the Faculté des Sciences de Monastir for their kind hospitalities during their stay. 相似文献
6.
7.
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
8.
Let
be the Haag--Kastler net generated by the
(2) chiral current algebra at level 1. We classify the SL(2,
)-covariant subsystems
by showing that they are all fixed points nets
H
for some subgroup H of the gauge automorphisms group SO(3) of
. Then, using the fact that the net
1 generated by the
(1) chiral current can be regarded as a subsystem of
, we classify the subsystems of
1. In this case, there are two distinct proper subsystems: the one generated by the energy-momentum tensor and the gauge invariant subsystem
. 相似文献
9.
Jean-Pierre Magnot 《Letters in Mathematical Physics》2006,75(2):111-127
Using renormalized (or weighted) traces of classical pseudo-differential operators and calculus on formal symbols. We exhibit three cocycles on the Lie algebra of classical pseudo-differential operators $Cl(S^1,\mathbb{C}^n)Using renormalized (or weighted) traces of classical pseudo-differential operators and calculus on formal symbols. We exhibit
three cocycles on the Lie algebra of classical pseudo-differential operators
acting on
. We first show that the Schwinger functional
associated to the Dirac operator is a cocycle on
, and not only on a restricted algebra
Then, we investigate two bilinear functionals
and
, which satisfies
We show that
and
are two cocycles in
, and
and
have the same nonvanishing cohomology class. We finaly calculate
on classical pseudo-differential operators of order 1 and on differential operators of order 1, in terms of partial symbols.
By this last computation, we recover the Virasoro cocyle and the K?hler form of the loop group.
Mathematics Subject Classification (1991). 47G30, 47N50 相似文献
10.
Asao Arai 《Letters in Mathematical Physics》2006,77(3):283-290
A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and the total Hamiltonian is unitarily equivalent to the direct integral
of a family of self-adjoint operators
acting in the Hilbert space
, where
is the Hilbert space of the quantum radiation field. The fiber operator
is called the Hamiltonian of the Dirac polaron with total momentum
. The main result of this paper is concerned with the non-relativistic (scaling) limit of
. It is proven that the non-relativistic limit of
yields a self-adjoint extension of a Hamiltonian of a polaron with spin 1/2 in non-relativistic quantum electrodynamics. 相似文献
11.
Orlin Stoytchev 《Letters in Mathematical Physics》2007,79(3):235-249
Any -graded C
*-dynamical system with a self-adjoint graded-Kubo-Martin-Schwinger (KMS) functional on it can be represented (canonically)
as a -graded algebra of bounded operators on a -graded Hilbert space, so that the grading of the latter is compatible with the functional. The modular conjugation operator
plays a crucial role in this reconstruction. The results are generalized to the case of an unbounded graded-KMS functional
having as dense domain the union of a net of C
*-subalgebras. It is shown that the modulus of such an unbounded graded-KMS functional is KMS.
相似文献
12.
Atsushi Nakayashiki 《Letters in Mathematical Physics》2009,89(1):85-100
The space of functions A over the phase space of KdV-hierarchy is studied as a module over the ring generated by commuting derivations. A -free resolution of A is constructed by Babelon, Bernard and Smirnov by taking the classical limit of the construction in quantum integrable models
assuming a certain conjecture. We propose another -free resolution of A by extending the construction in the classical finite dimensional integrable system associated with a certain family of hyperelliptic
curves to infinite dimension assuming a similar conjecture. The relation between the two constructions is given.
相似文献
13.
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
14.
15.
For a Lie algebra with Lie bracket got by taking commutators in a nonunital associative algebra
, let
be the vector space of tensors over
equipped with the Itô Hopf algebra structure derived from the associative multiplication in
. It is shown that a necessary and sufficient condition that the double product integral
satisfy the quantum Yang–Baxter equation over
is that
satisfy the same equation over the unital associative algebra
got by adjoining a unit element to
. In particular, the first-order coefficient r1 of r[h] satisfies the classical Yang–Baxter equation. Using the fact that the multiplicative inverse of
is
where
is the inverse of
in
we construct a quantisation of an arbitrary quasitriangular Lie bialgebra structure on
in the unital associative subalgebra of
consisting of formal power series whose zero order coefficient lies in the space
of symmetric tensors. The deformation coproduct acts on
by conjugating the undeformed coproduct by
and the coboundary structure r of
is given by
where
is the flip.Mathematical Subject Classification (2000). 53D55, 17B62 相似文献
16.
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
17.
Pierre Flédrich 《Letters in Mathematical Physics》2006,76(2-3):231-247
Nous étudions, quel que soit le réseau , les courbes hyperelliptiques donnant lieu, via le dictionnaire de Krichever et la formule d’Its-Mateev, à des solutions méromorphes Λ-doublement périodiques en t de l’équation de Korteweg-de Vries. Ce sont des revêtements marqués finis particuliers de la courbe elliptique (X,q)=(C /Λ,0) que nous nommons paires osculatrices hyperelliptiques. Nous sommes amenés à définir la classe des polynômes 3-tangentiels symétriques et à considérer une surface algébrique réglée S→ X et la surface obtenue par un éclatement en huit points de S. Nous associons alors aux polynômes 3-tangentiels symétriques des diviseurs sur S et . En étudiant ces diviseurs, nous démontrons que les paires osculatrices non-ramifiées au point marqué se factorisent via et reconstruisons ensuite de telles paires sur sous certaines conditions numériques. 相似文献
18.
Maxim Samsonov 《Letters in Mathematical Physics》2006,75(1):63-77
A problem of defining the quantum analogues for semi-classical twists in U()[[t]] is considered. First, we study specialization at q = 1 of singular coboundary twists defined in Uq ())[[t]] for g being a nonexceptional Lie algebra, then we consider specialization of noncoboundary twists when = and obtain q-deformation of the semiclassical twist introduced by Connes and Moscovici in noncommutative geometry.
Mathematics Subject Classification: 16W30, 17B37, 81R50 相似文献
19.
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
20.
The lowest spectral gap of segments of a periodic waveguide in is proportional to the square of the inverse length.
Dedicated to Pavel Exner on the occasion of his 60th birthday. 相似文献