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1.
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
2.
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
3.
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
4.
Given a conditionally completely positive map on a unital *-algebra , we find an interesting connection between the second Hochschild cohomology of with coefficients in the bimodule of adjointable maps, where M is the GNS bimodule of , and the possibility of constructing a quantum random walk [in the sense of (Attal et al. in Ann Henri Poincar 7(1):59–104,
2006; Lindsay and Parthasarathy in Sankhya Ser A 50(2):151–170, 1988; Sahu in Quantum stochastic Dilation of a class of Quantum
dynamical Semigroups and Quantum random walks. Indian Statistical Institute, 2005; Sinha in Banach Center Publ 73:377–390,
2006)] corresponding to .
D. Goswami was supported by a project funded by the Indian National Academy of Sciences.
L. Sahu had research support from the National Board of Higher Mathematics, DAE (India) is gratefully acknowledged. 相似文献
5.
We use the technique of Harish-Chandra bimodules to prove that regular strongly typical blocks of the category for the queer Lie superalgebra are equivalent to the corresponding blocks of the category for the Lie algebra . 相似文献
6.
Vsevolod Eduardovich Adler Alexander Ivanovich Bobenko Yuri Borisovich Suris 《Letters in Mathematical Physics》2009,89(2):131-139
We consider discrete nets in Grassmannians , which generalize Q-nets (maps with planar elementary quadrilaterals) and Darboux nets (-valued maps defined on the edges of such that quadruples of points corresponding to elementary squares are all collinear). We give a geometric proof of integrability
(multidimensional consistency) of these novel nets, and show that they are analytically described by the noncommutative discrete
Darboux system.
相似文献
7.
8.
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
9.
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
10.
Claude Cibils Andrea Solotar Robert Wisbauer 《Communications in Mathematical Physics》2007,272(3):837-849
We consider -complexes as functors over an appropriate linear category in order to show first that the Krull-Schmidt Theorem holds, then
to prove that amplitude cohomology (called generalized cohomology by M. Dubois-Violette) only vanishes on injective functors
providing a well defined functor on the stable category. For left truncated -complexes, we show that amplitude cohomology discriminates the isomorphism class up to a projective functor summand. Moreover
amplitude cohomology of positive -complexes is proved to be isomorphic to an Ext functor of an indecomposable -complex inside the abelian functor category. Finally we show that for the monoidal structure of -complexes a Clebsch-Gordan formula holds, in other words the fusion rules for -complexes can be determined.
This work has been supported by the projects PICT 08280 (ANPCyT), UBACYTX169, PIP-CONICET 5099 and the German Academic Exchange
Service (DAAD). The second author is a research member of CONICET (Argentina) and a Regular Associate of ICTP Associate Scheme. 相似文献
11.
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
12.
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
13.
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
14.
Roberto Paoletti 《Letters in Mathematical Physics》2006,78(2):189-204
Let (M , ω , J) be a compact and connected polarized Hodge manifold, an isodrastic leaf of half-weighted Bohr–Sommerfeld Lagrangian submanifolds. We study the relation between the Weinstein symplectic structure of and the asymptotics of the the pull-back of the Fubini–Study form under the projectivization of the so-called BPU maps on . 相似文献
15.
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
16.
Matthew Szczesny 《Letters in Mathematical Physics》2008,84(1):65-74
We examine the structure of the insertion–elimination Lie algebra on rooted trees introduced in Connes and Kreimer (Ann. Henri
Poincar 3(3):411–433, 2002). It possesses a triangular structure , like the Heisenberg, Virasoro, and affine algebras. We show in particular that it is simple, which in turn implies that
it has no finite-dimensional representations. We consider a category of lowest-weight representations, and show that irreducible
representations are uniquely determined by a “lowest weight” . We show that each irreducible representation is a quotient of a Verma-type object, which is generically irreducible.
相似文献
17.
Roderich Tumulka 《Letters in Mathematical Physics》2008,84(1):41-46
We prove a theorem about positive-operator-valued measures (POVMs) that is an analog of the Kolmogorov extension theorem,
a standard theorem of probability theory. According to our theorem, if a sequence of POVMs G
n
on satisfies the consistency (or projectivity) condition then there is a POVM G on the space of infinite sequences that has G
n
as its marginal for the first n entries of the sequence. We also describe an application in quantum theory.
The main proof in this article was first formulated in my habilitation thesis [6]. 相似文献
18.
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
19.
20.
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