共查询到20条相似文献,搜索用时 31 毫秒
1.
Yasuyuki Kawahigashi Roberto Longo Michael Müger 《Communications in Mathematical Physics》2001,219(3):631-669
We describe the structure of the inclusions of factors ?(E)⊂?(E′)′ associated with multi-intervals E⊂ℝ for a local irreducible net ? of von Neumann algebras on the real line satisfying the split property and Haag duality.
In particular, if the net is conformal and the subfactor has finite index, the inclusion associated with two separated intervals
is isomorphic to the Longo–Rehren inclusion, which provides a quantum double construction of the tensor category of superselection
sectors of ?. As a consequence, the index of ?(E)⊂?(E′)′ coincides with the global index associated with all irreducible sectors, the braiding symmetry associated with all sectors
is non-degenerate, namely the representations of ? form a modular tensor category, and every sector is a direct sum of sectors
with finite dimension. The superselection structure is generated by local data.
The same results hold true if conformal invariance is replaced by strong additivity and there exists a modular PCT symmetry.
Received: 7 July 1999 / Accepted: 13 January 2001 相似文献
2.
Ekaterina Turilova 《International Journal of Theoretical Physics》2009,48(11):3083-3091
Let ℳ be a von Neumann algebra acting on a Hilbert space H and let S be a dense lineal in H that is affiliated with a von Neumann algebra ℳ. The “topological” definition of measures on the classes of orthoclosed and
splitting subspaces of S affiliated with a von Neumann algebra ℳ is given and results on the relationships of these measures to measures on orthoprojections
of the algebra ℳ are presented. 相似文献
3.
Let ℱ be a local net of von Neumann algebras in four spacetime dimensions satisfying certain natural structural assumptions.
We prove that if ℱ has trivial superselection structure then every covariant, Haag-dual subsystem ℬ is of the form ℱ1
G
⊗I for a suitable decomposition ℱ=ℱ1⊗ℱ2 and a compact group action. Then we discuss some application of our result, including free field models and certain theories
with at most countably many sectors.
Received: 26 January 2000 / Accepted: 28 September 2000 相似文献
4.
In this paper we give a complete characterization of Morita equivalent star products on symplectic manifolds in terms of
their characteristic classes: two star products ⋆ and ⋆' on (M,ω) are Morita equivalent if and only if there exists a symplectomorphism ψ\colon M
M such that the relative class t(⋆, ψ⋆(⋆')) is 2 π i-integral. For star products on cotangent bundles, we show that this integrality condition is related to Dirac's
quantization condition for magnetic charges.
Received: 19 July 2001 / Accepted: 23 January 2002 相似文献
5.
John A. Toth 《Communications in Mathematical Physics》2003,238(1-2):225-256
Let (M,g) be a C
∞
compact Riemann manifold with classical Hamiltonian, HC
∞
(T
*
M). Assume that the corresponding -quantization P
1
:=Op
(H) is quantum completely integrable. We establish an -microlocal Weyl law on short spectral intervals of size 2−ε;∀ε>0 for various families of operators P
1
u
;uI containing P
1
, both in the mean and pointwise a.e. for uI. The -microlocalization refers to a small tubular neighbourhood of a non-degenerate, stable periodic bicharacteristic γ⊂T
*
M−0.
Received: 10 December 2001 / Accepted: 23 January 2003
Published online: 2 April 2003
RID="⋆"
ID="⋆" Supported in part by an Alfred P. Sloan Research Fellowship and NSERC grant OGP01720280
Communicated by P. Sarnak 相似文献
6.
W. A. Majewski 《Letters in Mathematical Physics》1982,6(6):437-440
Let ℳ be a von Neumann algebra with a cyclic and separating vector Ω and let ω(·) denote the corresponding vector state, i.e.,
ω(A)=(Ω, AΩ) A ∈ ℳ. We have proved that a positive semigroup τ on ℳ can induce the dynamical semigroup in the GNS representation associated
with ω if the state ω is a τ-invariant one. Some applications are given. 相似文献
7.
Yasuyuki Kawahigashi 《Communications in Mathematical Physics》2002,226(2):269-287
We study the recent construction of subfactors by Rehren which generalizes the Longo–Rehren subfactors. We prove that if
we apply this construction to a non-degenerately braided subfactor N⊂M and α±-induction, then the resulting subfactor is dual to the Longo–Rehren subfactor M⊗M
opp⊂R arising from the entire system of irreducible endomorphisms of M resulting from αplusmn;-induction. As a corollary, we solve a problem on existence of braiding raised by Rehren negatively. Furthermore, we generalize
our previous study with Longo and Müger on multi-interval subfactors arising from a completely rational conformal net of factors
on S
1 to a net of subfactors and show that the (generalized) Longo–Rehren subfactors and α-induction naturally appear in this context.
Received: 11 September 2001 / Accepted: 7 October 2001 相似文献
8.
9.
Sukanta Dutta Ashok Goyal Mamta 《The European Physical Journal C - Particles and Fields》2009,63(2):305-315
We study the one-loop new physics effects to the CP even triple neutral gauge boson vertices γ
⋆
γ
Z, γ
⋆
Z
Z, Z
⋆
Z
γ and Z
⋆
ZZ in the context of Little Higgs models. We compute the contribution of the additional fermions in Little Higgs models in the
framework of direct product groups where [SU(2)×U(1)]2 gauge symmetry is embedded in SU(5) global symmetry and also in the framework of the simple group where SU(N)×U(1) gauge symmetry breaks down to SU(2)
L
×U(1). We calculate the contribution of the fermions to these couplings when T parity is invoked. In addition, we re-examine the MSSM contribution at the chosen point of SPS1a′ and compare with the SM
and Little Higgs models. 相似文献
10.
We study zero-temperature, stochastic Ising models σ
t
on Z
d
with (disordered) nearest-neighbor couplings independently chosen from a distribution μ on R and an initial spin configuration chosen uniformly at random. Given d, call μ type ℐ (resp., type ℱ) if, for every
x in Z
d
, σ
x
t
flips infinitely (resp., only finitely) many times as t→∞ (with probability one) – or else mixed type ℳ. Models of type ℒ and ℳ exhibit a zero-temperature version of “local non-equilibration”.
For d=1, all types occur and the type of any μ is easy to determine. The main result of this paper is a proof that for d=2, ±J models (where μ=αδ
J
+(1-α)δ-
J
) are type ℳ, unlike homogeneous models (type ℐ) or continuous (finite mean) μ's (type ℳ). We also prove that all other noncontinuous
disordered systems are type ℳ for any d≥ 2. The ±J proof is noteworthy in that it is much less “local” than the other (simpler) proof. Homogeneous and ±J models for d≥ 3 remain an open problem.
Received: 3 November 1999 / Accepted: 10 April 2000 相似文献
11.
The original proof of Gleason’s Theorem is very complicated and therefore, any result that can be derived also without the
use of Gleason’s Theorem is welcome both in mathematics and mathematical physics. In this paper we reprove some known results
that had originally been proved by the use of Gleason’s Theorem, e.g. that on the quantum logic ℒ(H) of all closed subspaces of a Hilbert space H, dim H≥3, there is no finitely additive state whose range is countably infinite. In particular, if dim H=n, then on ℒ(H) there is a unique discrete state, namely m(A)=dim A/dim H, A∈ℒ(H).
Dedicated to Pekka J. Lahti on the occasion of his 60th birthday.
The paper has been supported by the Center of Excellence SAS–Physics of Information–I/2/2005, the grant VEGA No. 2/6088/26
SAV, by Science and Technology Assistance Agency under the contract APVV-0071-06, Bratislava, Slovakia. 相似文献
12.
Claudio Garola 《International Journal of Theoretical Physics》2008,47(1):90-103
The word proposition is used in physics with different meanings, which must be distinguished to avoid interpretational problems. We construct
two languages ℒ
*
(x) and ℒ(x) with classical set-theoretical semantics which allow us to illustrate those meanings and to show that the non-Boolean lattice
of propositions of quantum logic (QL) can be obtained by selecting a subset of p-testable propositions within the Boolean lattice of all propositions associated with sentences of ℒ(x). Yet, the aforesaid semantics is incompatible with the standard interpretation of quantum mechanics (QM) because of known
no-go theorems. But if one accepts our criticism of these theorems and the ensuing SR (semantic realism) interpretation of
QM, the incompatibility disappears, and the classical and quantum notions of truth can coexist, since they refer to different
metalinguistic concepts (truth and verifiability according to QM, respectively). Moreover one can construct a quantum language ℒ
TQ
(x) whose Lindenbaum–Tarski algebra is isomorphic to QL, the sentences of which state (testable) properties of individual samples
of physical systems, while standard QL does not bear this interpretation. 相似文献
13.
Alberto Filipuzzi Gino Isidori 《The European Physical Journal C - Particles and Fields》2009,64(1):55-62
We analyse the violations of lepton-flavour universality in the ratios ℬ(P→ℓ
ν)/ℬ(P→ℓ
′
ν) using a general effective theory approach, discussing various flavour-symmetry breaking patterns of physics beyond the SM.
We find that in models with Minimal Lepton Flavour Violation the effects are too small to be observed in the next generations
of experiments in all relevant meson systems (P=π,K,B). In a Grand Unified framework with minimal breaking of the flavour symmetry, the effects remain small in π and K decays, while large violations of lepton-flavour universality are possible in B→ℓ
ν decays. 相似文献
14.
An infinite set of higher spin conserved charges is found for the sp(2M) symmetric dynamical systems in M(M+ 1)/2-dimensional generalized spacetime M. Since the dynamics in M is equivalent to the conformal dynamics of infinite towers of fields in d-dimensional Minkowski spacetime with d = 3, 4, 6, 10, ... for M = 2, 4, 8, 16, ..., respectively, the constructed currents in M generate infinite towers of (mostly new) higher spin conformal currents in Minkowski spacetime. The charges have a form of integrals of M-forms which are bilinear in the field variables and are closed as a consequence of the field equations. Conservation implies independence of a value of charge of a local variation of a M-dimensional integration surface M analogous to Cauchy surface in the usual spacetime. The scalar conserved charge provides an invariant bilinear form on the space of solutions of the field equations that gives rise to a positive-definite norm on the space of quantum states. 相似文献
15.
In this paper we further develop the theory of α-induction for nets of subfactors, in particular in view of the system of
sectors obtained by mixing the two kinds of induction arising from the two choices of braiding. We construct a relative braiding
between the irreducible subsectors of the two “chiral” induced systems, providing a proper braiding on their intersection.
We also express the principal and dual principal graphs of the local subfactors in terms of the induced sector systems. This
extended theory is again applied to conformal or orbifold embeddings of SU(n WZW models. A simple formula for the corresponding modular invariant matrix is established in terms of the two inductions,
and we show that it holds if and only if the sets of irreducible subsectors of the two chiral induced systems intersect minimally
on the set of marked vertices, i.e. on the “physical spectrum” of the embedding theory,
or if and only if the canonical endomorphism sector of the conformal or orbifold inclusion subfactor is in the full induced
system. We can prove either condition for all simple current extensions of SU
(
n
) and many conformal inclusions, covering in particular all type I modular invariants of SU(2) and SU(3), and we conjecture that it holds also for any other conformal inclusion of SU
(
n
) as well. As a by-product of our calculations, the dual principal graph for the conformal inclusion SU(3)5⊂SU(6)1 is computed for the first time.
Received: 24 December 1998 / Accepted: 22 February 1999 相似文献
16.
Hiroshi Isozaki 《Communications in Mathematical Physics》2001,222(2):371-413
We construct a generalized Fourier transformation ℱ(λ) associated with the 3-body Schr?dinger operator H=−Δ+Σ
a
V
a
(x
a
) and characterize all solutions of (H−λ)u= 0 in the Agmon–H?rmander space ℬ* as the image of ℱ(λ)*. These stationary solutions admit asymptotic expansions in ℬ* in terms of spherical waves associated with scattering channels.
Received: 20 September 2000 / Accepted: 20 May 2001 相似文献
17.
By using the thermo entangled state representation we solve the master equation for a dissipative cavity with Kerr medium
to obtain density operators’ infinite operator-sum representation ρ(t)=∑
m,n,l=0∞
M
m,n,l
ρ
0ℳ
m,n,l
†
. It is noticeable that M
m,n,l
is not Hermite conjugate to ℳ
m,n,l
†
, nevertheless the normalization ∑
m,n,l=0∞ℳ
n,m,l
†
M
m,n,l
=1 still holds, i.e., they are trace-preserving in a general sense. This example may stimulate further studying if general
superoperator theory needs modification. 相似文献
18.
Paolo Bertozzini Roberto Conti Roberto Longo 《Communications in Mathematical Physics》1998,193(2):471-492
Let ? be a local conformal net of von Neumann algebras on S
1 and ρ a M?bius covariant representation of ?, possibly with infinite dimension. If ρ has finite index, ρ has automatically
positive energy. If ρ has infinite index, we show the spectrum of the energy always to contain the positive real line, but,
as seen by an example, it may contain negative values. We then consider nets with Haag duality on ℝ, or equivalently sectors
with non-solitonic extension to the dual net; we give a criterion for irreducible sectors to have positive energy, namely
this is the case iff there exists an unbounded M?bius covariant left inverse. As a consequence the class of sectors with positive
energy is stable under composition, conjugation and direct integral decomposition.
Received: 21 April 1997 / Accepted: 23 September 1997 相似文献
19.
V. D. Lyakhovsky 《Czechoslovak Journal of Physics》2002,52(11):1269-1275
We study the twist deformations of algebras of motiong
H ⊂ sl(N) with the Cartan subalgebraH(gH) equal toH(sl(N)). The proposed deformations are maximal in the sense that their carrier algebrasg
c coincide withg
H. The algebraic properties are demonstrated forg
H ⊂ sl(5).
Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002.
This work has been partially supported by the Russian Foundation for Fundamental Research under the grant N 00-01-00500. 相似文献
20.
Magnus B. Landstad 《Communications in Mathematical Physics》1977,52(2):191-202
One way of generalizing the definition of an action of the dual group of a locally compact abelian group on a von Neumann algebra to non-abelian groups is to consider (G)-comodules, where (G) is the Hopfvon Neumann algebra generated by the left regular representation ofG. To a (G)-comodule we shall associate a dual covariance algebra
and a natural covariant system (
, ,G), and in Theorem 1 the covariant systems coming from (G)-comodules are characterized. In [2] it was shown that the covariance algebra of a covariant system in a natural way is a (G)-comodule. Therefore one can form the dual covariance algebra of a covariance algebra and the covariance algebra of a dual covariance algebra. Theorems 2 and 3 deal with these algebras — generalizing a result by Takesaki. As an application we give a new proof of a theorem by Digernes stating that the commutant of a covariance algebra itself is a covariance algebra and prove the similar result for dual covariance algebras. 相似文献