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1.
Yi Lin 《Communications in Mathematical Physics》2008,281(2):469-497
It has been shown recently by Kapustin and Tomasiello that the mathematical notion of Hamiltonian actions on twisted generalized Kähler manifolds is in perfect agreement with the physical notion of general (2, 2) gauged sigma models with three-form fluxes. In this article, we study the twisted equivariant cohomology theory of Hamiltonian actions on H-twisted generalized complex manifolds. If the manifold satisfies the ${\overline{\partial} \partial}It has been shown recently by Kapustin and Tomasiello that the mathematical notion of Hamiltonian actions on twisted generalized
K?hler manifolds is in perfect agreement with the physical notion of general (2, 2) gauged sigma models with three-form fluxes.
In this article, we study the twisted equivariant cohomology theory of Hamiltonian actions on H-twisted generalized complex manifolds. If the manifold satisfies the -lemma, we establish the equivariant formality theorem. If in addition, the manifold satisfies the generalized K?hler condition,
we prove the Kirwan injectivity in this setting. We then consider the Hamiltonian action of a torus on an H-twisted generalized Calabi-Yau manifold and extend to this case the Duistermaat-Heckman theorem for the push-forward measure.
As a side result, we show in this paper that the generalized K?hler quotient of a generalized K?hler vector space can never
have a (cohomologically) non-trivial twisting. This gives a negative answer to a question asked by physicists whether one
can construct (2, 2) gauged linear sigma models with non-trivial fluxes. 相似文献
2.
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
3.
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
4.
Leszek Pysiak 《International Journal of Theoretical Physics》2007,46(1):16-30
We develop an approach to dynamical and probabilistic properties of the model unifying general relativity and quantum mechanics,
initiated in the paper (Heller et al. (2005) International Journal Theoretical Physics
44, 671). We construct the von Neumann algebra of random operators on a groupoid, which now is not related to a finite group G, but is the pair groupoid of the Lorentzian frame bundle E over spacetime M. We consider the time flow on depending on the state . The state defining the noncommutative dynamics is assumed to be normal and faithful. Then the pair is a noncommutative probabilistic space and can also be interpreted as an equilibrium thermal state, satisfying the Kubo-Martin-Schwinger condition. We argue that both
the “time flow” and thermodynamics have their common roots in the noncommutative unification of dynamics and probability. 相似文献
5.
In this Letter, we show the existence of a natural and projectively equivariant quantization map depending on a linear torsion-free connection for the spaces
of differential operators mapping p-forms into functions on an arbitrary smooth manifold M. We show how this result implies the existence over
of an sl
m+1-equivariant quantization for the spaces
.This revised version was published online in March 2005 with corrections to the cover date. 相似文献
6.
Ruqian Lu 《International Journal of Theoretical Physics》2005,44(9):1495-1530
We propose the concept of finite stop quantum automata (ftqa) based on Hilbert space and compare it with the finite state
quantum automata (fsqa) proposed by Moore and Crutchfield (Theoretical Computer Science 237(1–2), 2000, 275–306). The languages accepted by fsqa form a proper subset of the languages accepted by ftqa. In addition,
the fsqa form an infinite hierarchy of language inclusion with respect to the dimensionality of unitary matrices. We introduce
complex-valued acceptance degrees and two types of finite stop quantum automata based on them: the invariant ftqa (icftq)
and the variant ftqa (vcftq). The languages accepted by icftq form a proper subset of the languages accepted by vcftq. In
addition, the icftq form an infinite hierarchy of language inclusion with respect to the dimensionality of unitary matrices.
In this way, we establish two proper inclusion relations
(fsqa) ⊂
(ftqa) and
(icftq) ⊂
(vcftq), where the symbol
means languages, and two infinite language hierarchies
(fsqa) ⊂
(fsqa),
(icftq)
(icftq). 相似文献
7.
For a (co)monad T
l
on a category , an object X in , and a functor , there is a (co)simplex in . The aim of this paper is to find criteria for para-(co)cyclicity of Z
*. Our construction is built on a distributive law of T
l
with a second (co)monad T
r
on , a natural transformation , and a morphism in . The (symmetrical) relations i and w need to satisfy are categorical versions of Kaygun’s axioms of a transposition map. Motivation comes from the observation
that a (co)ring T over an algebra R determines a distributive law of two (co)monads and on the category of R-bimodules. The functor Π can be chosen such that is the cyclic R-module tensor product. A natural transformation is given by the flip map and a morphism is constructed whenever T is a (co)module algebra or coring of an R-bialgebroid. The notion of a stable anti-Yetter-Drinfel’d module over certain bialgebroids, the so-called ×
R
-Hopf algebras, is introduced. In the particular example when T is a module coring of a ×
R
-Hopf algebra and X is a stable anti-Yetter-Drinfel’d -module, the para-cyclic object Z
* is shown to project to a cyclic structure on . For a -Galois extension , a stable anti-Yetter-Drinfel’d -module T
S
is constructed, such that the cyclic objects and are isomorphic. This extends a theorem by Jara and Ştefan for Hopf Galois extensions. As an application, we compute Hochschild
and cyclic homologies of a groupoid with coefficients in a stable anti-Yetter-Drinfel’d module, by tracing it back to the
group case. In particular, we obtain explicit expressions for (coinciding relative and ordinary) Hochschild and cyclic homologies
of a groupoid. The latter extends results of Burghelea on cyclic homology of groups. 相似文献
8.
9.
We calculate the chiral anomaly in the neighborhood of the fixed point space
which is constructed by the group action of a discrete symmetry h on a compact manifold
. The Feynman diagrams approach for the corresponding supersymmetric quantum mechanical system with twisted boundary conditions is used. The result we derive in this way agrees with the generalization of the ordinary index theorem (the G-index theorem) on the spin complex. 相似文献
10.
For a compact connected orientablen-manifoldM, n 3, we study the structure ofclassical superspace
,quantum superspace
,classical conformal superspace
, andquantum conformal superspace
. The study of the structure of these spaces is motivated by questions involving reduction of the usual canonical Hamiltonian formulation of general relativity to a non-degenerate Hamiltonian formulation, and to questions involving the quantization of the gravitational field. We show that if the degree of symmetry ofM is zero, thenS,S
0,C, andC
0 areilh
orbifolds. The case of most importance for general relativity is dimensionn=3. In this case, assuming that the extended Poincaré conjecture is true, we show that quantum superspaceS
0 and quantum conformal superspaceC
0 are in factilh-manifolds. If, moreover,M is a Haken manifold, then quantum superspace and quantum conformal superspace arecontractible
ilh-manifolds. In this case, there are no Gribov ambiguities for the configuration spacesS
0 andC
0. Our results are applicable to questions involving the problem of thereduction of Einstein's vacuum equations and to problems involving quantization of the gravitational field. For the problem of reduction, one searches for a way to reduce the canonical Hamiltonian formulation together with its constraint equations to an unconstrained Hamiltonian system on a reduced phase space. For the problem of quantum gravity, the spaceC
0 will play a natural role in any quantization procedure based on the use of conformal methods and the reduced Hamiltonian formulation. 相似文献
11.
It has been maintained that the physical content of a model of a system is completely contained in the C∗-algebra of quasi-local observables
that is associated with the system. The reason given for this is that the unitarily inequivalent representations of
are physically equivalent. But, this view is dubious for at least two reasons. First, it is not clear why the physical content
does not extend to the elements of the von Neumann algebras that are generated by representations of
. It is shown here that although the unitarily inequivalent representations of
are physically equivalent, the extended representations are not. Second, this view detracts from special global features
of physical systems such as temperature and chemical potential by effectively relegating them to the status of fixed parameters.
It is desirable to characterize such observables theoretically as elements of the algebra that is associated with a system
rather than as parameters, and thereby give a uniform treatment to all observables. This can be accomplished by going to larger
algebras. One such algebra is the universal enveloping von Neumann algebra, which is generated by the universal representation
of
; another is the direct integral of factor representations that are associated with the set of values of the global features.
Placing interpretive significance on the von Neumann algebras mentioned earlier sheds light on the significance of unitarily
inequivalent representations of
, and it serves to show the limitations of the notion of physical equivalence. 相似文献
12.
We construct a five-parameter family of gauge-nonequivalent SU (2) instantons on a noncommutative four sphere and of topological charge equal to 1. These instantons are critical points of a gauge functional and satisfy self-duality
equations with respect to a Hodge star operator on forms on . They are obtained by acting with a twisted conformal symmetry on a basic instanton canonically associated with a noncommutative
instanton bundle on the sphere. A completeness argument for this family is obtained by means of index theorems. The dimension
of the “tangent space” to the moduli space is computed as the index of a twisted Dirac operator and turns out to be equal
to five, a number that survives deformation. 相似文献
13.
It is shown that the correlations predicted by relativistic quantum field theory in locally normal states between projections
in local von Neumann algebras (V
1),(V
2) associated with spacelike separated spacetime regions V
1,V
2 have a (Reichenbachian) common cause located in the union of the backward light cones of V
1 and V
2. Further comments on causality and independence in quantum field theory are made.
Originally published in International Journal of Theoretical Physics, Vol. 44, No. 7, 2005,Due to a publishing error, authorship
of the article was credited incorrectly. The corrected article is reprinted in its entirety here. The online version of the
original article can be found at 相似文献
14.
We investigate the physics potential of the annihilation decays
in the standard model and beyond. In a naive factorization approach, the branching ratios are estimated to be
and
. In the framework of QCD factorization, we compute the non-factorizable corrections and get
,
. Future measurements of these decays would be useful for testing the factorization frameworks. The smallness of these decays in the SM makes them sensitive probes of new physics. As an example, we will consider the possible admixture of the (V + A) charge current to the standard (V-A) current. This admixture will give a significant contribution to the decays.Received: 29 August 2003, Revised: 17 January 2004, Published online: 19 March 2004Corresponding author: Y.D. Yang 相似文献
15.
For the Lie algebra
N we introduce a system of differential operators called the dynamical operators. We prove that the dynamical differential operators commute with the
N rational quantized Knizhnik–Zamolodchikov difference operators. We describe the transformations of the dynamical operators under the natural action of the
N Weyl group.Mathematics Subject Classifications (2000). 17B37, 17B80, 81R10. 相似文献
16.
We have investigated, in the framework of proximity effect theory, the interface transparency
of superconducting/normal metal layered systems which consist of Nb and high paramagnetic Pd deposited by dc magnetron sputtering. The obtained
value is relatively high, as expected by theoretical arguments. This leads to a large value of the ratio
although Pd does not exhibit any magnetic ordering.Received: 12 December 2003, Published online: 20 April 2004PACS:
74.45. + c Proximity effects; Andreev effect; SN and SNS junctions - 74.78.Fk Multilayers, superlattices, heterostructuresS.L. Prischepa: Permanent address: State University of Computer Science and RadioElectronics, P. Brovka street 6, 220600, Minsk, Belarus 相似文献
17.
Omar Mustafa S. Habib Mazharimousavi 《International Journal of Theoretical Physics》2009,48(1):183-193
Non-Hermitian but
-symmetrized spherically-separable Dirac and Schr?dinger Hamiltonians are considered. It is observed that the descendant Hamiltonians
H
r
, H
θ
, and H
φ
play essential roles and offer some “user-feriendly” options as to which one (or ones) of them is (or are) non-Hermitian.
Considering a
-symmetrized H
φ
, we have shown that the conventional Dirac (relativistic) and Schr?dinger (non-relativistic) energy eigenvalues are recoverable.
We have also witnessed an unavoidable change in the azimuthal part of the general wavefunction. Moreover, setting a possible
interaction V(θ)≠0 in the descendant Hamiltonian H
θ
would manifest a change in the angular θ-dependent part of the general solution too. Whilst some
-symmetrized H
φ
Hamiltonians are considered, a recipe to keep the regular magnetic quantum number m, as defined in the regular traditional Hermitian settings, is suggested. Hamiltonians possess properties similar to the
-symmetric ones (here the non-Hermitian
-symmetric Hamiltonians) are nicknamed as pseudo-
-symmetric. 相似文献
18.
In the Fock space semantics, meanings of sentences are identified with density operators of the (unsymmetrized) Fock space
based on the Hilbert space ℂ2. Generally, the meaning of a sentence is smeared over different sectors of
. The standard quantum computational semantics is a limit case of the Fock space semantics, where the meaning of any sentence
α only “lives” in one sector of
, which is determined by the logical complexity of α. We prove that the global Fock space semantics and the standard quantum computational semantics characterize the same logic.
PACS: 03.67.Lx. 相似文献
19.
A new evaluation of the hadronic vacuum polarization contribution to the muon magnetic moment is presented. We take into account the reanalysis of the low-energy e
+
e
-annihilation cross section into hadrons by the CMD-2 Collaboration. The agreement between e
+
e
-and
spectral functions in the
channel is found to be much improved. Nevertheless, significant discrepancies remain in the center-of-mass energy range between 0.85 and
, so that we refrain from averaging the two data sets. The values found for the lowest-order hadronic vacuum polarization contributions are
where the errors have been separated according to their sources: experimental, missing radiative corrections in e
+
e
-data, and isospin breaking. The corresponding Standard Model predictions for the muon magnetic anomaly read
where the errors account for the hadronic, light-by-light (LBL) scattering and electroweak contributions. The deviations from the measurement at BNL are found to be
(1.9
) and
(0.7
) for the e
+
e
-- and
-based estimates, respectively, where the second error is from the LBL contribution and the third one from the BNL measurement.Received: 7 September 2003, Published online: 30 October 2003 相似文献
20.
R. F. Streater 《Communications in Mathematical Physics》1969,12(3):226-232
We construct a Hilbert space , spanned by vectors
, where
is a bounded measurable set in v (=dimension of space), and interpret
as at state where all pointsx
are occupied by an incompressible fluid, andx
unoccupied. is generated by applying unitary filling operatorsU(
) to a cyclic vector |, the completely unoccupied state. The operatorsU(
) generate a commutativec*-algebra, of which the hermitian elements are interpreted as the observables of the theory.All the -divisible representations of the symmetric group of order 2 are found. We give a generalization to a theory with any number of particle types. 相似文献