共查询到20条相似文献,搜索用时 15 毫秒
1.
Joseph C. Várilly 《Communications in Mathematical Physics》2001,221(3):511-523
We show that the noncommutative spheres of Connes and Landi are quantum homogeneous spaces for certain compact quantum groups.
We give a general construction of homogeneous spaces which support noncommutative spin geometries.
Received: 28 February 2001 / Accepted: 12 March 2001 相似文献
2.
Debashish Goswami 《Communications in Mathematical Physics》2009,285(1):141-160
We formulate a quantum generalization of the notion of the group of Riemannian isometries for a compact Riemannian manifold,
by introducing a natural notion of smooth and isometric action by a compact quantum group on a classical or noncommutative
manifold described by spectral triples, and then proving the existence of a universal object (called the quantum isometry
group) in the category of compact quantum groups acting smoothly and isometrically on a given (possibly noncommutative) manifold
satisfying certain regularity assumptions. The idea of ‘quantum families’ (due to Woronowicz and Soltan) are relevant to our
construction. A number of explicit examples are given and possible applications of our results to the problem of constructing
quantum group equivariant spectral triples are discussed.
Supported in part by the Indian National Academy of Sciences. 相似文献
3.
Jyotishman Bhowmick Francesco D’Andrea Ludwik Dąbrowski 《Communications in Mathematical Physics》2011,307(1):101-131
We compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine
quantum symmetries of the spectral triple corresponding to M × F, where M is a compact spin manifold. We also prove that the bosonic and fermionic part of the spectral action are preserved by these
symmetries. 相似文献
4.
We introduce a family of noncommutative 4-spheres, such that the instanton projector has its first Chern class trivial: ch
1(e)=B+b. We construct for them a 4-dimensional cycle and calculate explicitly the Chern-Connes pairing for the instanton projector.Supported by Marie Curie Fellowship HPMF-CT-1999-00053, at Laboratoire de Physique Theórique, Université Paris-Sud, Bat. 210, 91405 Orsay, Cedex, France 相似文献
5.
We construct noncommutative principal fibrations Sθ7→Sθ4 which are deformations of the classical SU(2) Hopf fibration over the four sphere. We realize the noncommutative vector bundles associated to the irreducible representations of SU(2) as modules of coequivariant maps and construct corresponding projections. The index of Dirac operators with coefficients in the associated bundles is computed with the Connes-Moscovici local index formula. “The algebra inclusion is an example of a not-trivial quantum principal bundle.” 相似文献
6.
We describe noncommutative geometric aspects of twisted deformations, in particular of the spheres of Connes and Landi and of Connes and Dubois Violette, by using the differential and integral calculus on these spaces that is covariant under the action of their corresponding quantum symmetry groups. We start from multiparametric deformations of the orthogonal groups and related planes and spheres. We show that only in the twisted limit of these multiparametric deformations the covariant calculus on the plane gives, by a quotient procedure, a meaningful calculus on the sphere. In this calculus, the external algebra has the same dimension as the classical one. We develop the Haar functional on spheres and use it to define an integral of forms. In the twisted limit (differently from the general multiparametric case), the Haar functional is a trace and we thus obtain a cycle on the algebra. Moreover, we explicitly construct the *-Hodge operator on the space of forms on the plane and then by quotient on the sphere. We apply our results to even spheres and compute the Chern–Connes pairing between the character of this cycle, i.e. a cyclic 2n-cocycle, and the instanton projector defined in math.QA/0107070. 相似文献
7.
P. Busch 《Mathematical Physics, Analysis and Geometry》1999,2(1):83-106
The class of stochastic maps, that is, linear, trace-preserving, positive maps between the self-adjoint trace class operators of complex separable Hilbert spaces plays an important role in the representation of reversible dynamics and symmetry transformations. Here a characterization of the isometric stochastic maps is given and possible physical applications are indicated. 相似文献
8.
In this work, we develop a general framework in which Noncommutative Quantum Mechanics (NCQM), characterized by a space noncommutativity matrix parameter θ=εijk
θk and a momentum noncommutativity matrix parameter
β=εijk
βk, is shown to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS). Imposing some constraints
on this particular transformation, we firstly find that the product of the two parameters θ and β possesses a
lower bound in direct relation with Heisenberg incertitude relations, and secondly that the two parameters are equivalent but with opposite sign, up to a dimension factor depending on the
physical system under study. This means that noncommutativity is represented by a unique parameter which may play the role of a fundamental constant
characterizing the whole NCQPS. Within our framework, we treat some physical systems on NCQPS : free particle, harmonic oscillator, system of two-charged particles, Hydrogen atom. Among
the obtained results, we discover a new phenomenon which consists of a free particle on NCQPS viewed as equivalent to a harmonic oscillator with Larmor frequency depending on β,
representing the same particle in presence of a magnetic field
$\vec{B}=q^{-1}\vec{\beta}$. For the other examples, additional
correction terms depending on β appear in the expression of the energy spectrum. Finally, in the two-particle system case, we emphasize the fact that for two opposite charges noncommutativity is effectively feeled with opposite sign. 相似文献
9.
We present computer simulation and theoretical results for a system of N Quantum Hard Spheres (QHS) particles of diameter and mass m at temperature T, confined between parallel hard walls separated by a distance , within the range . Semiclassical Monte Carlo computer simulations were performed adapted to a confined space, considering effects in terms of the density of particles , where V is the accessible volume, the inverse length and the de Broglie’s thermal wavelength , where k and h are the Boltzmann’s and Planck’s constants, respectively. For the case of extreme and maximum confinement, and , respectively, analytical results can be given based on an extension for quantum systems of the Helmholtz free energies for the corresponding classical systems. 相似文献
10.
M. Aguero J. A. S. Aguilar C. Ortiz M. Sabido J. Socorro 《International Journal of Theoretical Physics》2007,46(11):2928-2934
In this paper we present the noncommutative Bianchi Class A cosmological models coupled to barotropic perfect fluid. The commutative
and noncommutative quantum solution to the Wheeler–DeWitt equation for any factor ordering, to the anisotropic Bianchi type
II cosmological model are found, using a stiff fluid (γ=1). In our toy model, we introduce noncommutative scale factors, is say, we consider that all minisuperspace variables q
i
does not commute, so the simplectic structure was modified. 相似文献
11.
We study the properties of quasi-distributions or Wigner measures in the context of noncommutative quantum mechanics. In particular, we obtain necessary and sufficient conditions for a phase-space function to be a noncommutative Wigner measure, for a Gaussian to be a noncommutative Wigner measure, and derive certain properties of the marginal distributions which are not shared by ordinary Wigner measures. Moreover, we derive the Robertson-Schrödinger uncertainty principle. Finally, we show explicitly how the set of noncommutative Wigner measures relates to the sets of Liouville and (commutative) Wigner measures. 相似文献
12.
We sketch our proof that the real Euclidean 4-model on the four-dimensional Moyal plane is renormalisable to all orders. The bare action of relevant and marginal couplings of the model is parametrised by four (divergent) quantities which require normalisation to the experimental data. The corresponding physical parameters are the mass, the field amplitude (to be normalised to 1), the coupling constant and—in addition to the commutative version—the frequency of a harmonic oscillator potential. 相似文献
13.
We propose a mathematical structure, based on anoncommutative geometry, which combines essentialaspects of general relativity with those of quantummechanics, and leads to correct limitingcases of both these physical theories. Thenoncommutative geometry of the fundamental level isnonlocal with no space and no time in the usual sense,which emerge only in the transition process to thecommutative case. It is shown that because of the originalnonlocality, quantum gravitational observables should belooked for among correlations of distant phenomenarather than among local effects. We compute the Einstein–Podolsky–Rosen effect; itcan be regarded as a remnant or a shadowof the noncommutative regime of the fundamental level.A toy model is computed predicting the value of thecosmological constant (in the quantum sector) which vanishes whengoing to the standard spacetime physics. 相似文献
14.
In this paper we study the bilayer quantum Hall (QH) effect on a noncommutative phase space (NCPS). By using perturbation theory, we calculate the energy spectrum, eigenfunction, Hall current, and Hall conductivity of the bilayer QH system, and express them in terms of noncommutative parameters θ and θ^-, respectively. In our calculation, we assume that these parameters vary from laver to laver. 相似文献
15.
We study exactly the solvable noncommutative scalar quantum field models of (2n) or (2n + 1) dimensions. By writing out an equivalent action of the noncommutative field, it is shown that the special condition B. 0 = 4-1 in field theoretic context means the full restoration of the maximal U(∞) gauge symmetries broken due to kinetic term. It is further shown that the model can be obtained by dimensional reduction of a 2n-dimensional exactly solvable noncommutative φ4 quantum field model closely related to the 1+1-dimensional Moyal/matrix-valued nonlinear Schr6dinger (MNLS) equation. The corresponding quantum fundamental commutation relation of the MNLS model is also given explicitly. 相似文献
16.
In this paper we study the bilayer quantum Hall (QH) effect on a noncommutative phase space (NCPS). By using perturbation theory, we calculate the energy spectrum, eigenfunction, Hall current, and Hall conductivity of the bilayer QH system, and express them in terms of noncommutative parameters θ and \bar{θ}, respectively. In our calculation, we assume that these parameters vary from layer to layer. 相似文献
17.
Johannes Aastrup Jesper Møller Grimstrup Mario Paschke Ryszard Nest 《Communications in Mathematical Physics》2011,302(3):675-696
We construct normalizable, semi-classical states for the previously proposed model of quantum gravity which is formulated
as a spectral triple over holonomy loops. The semi-classical limit of the spectral triple gives the Dirac Hamiltonian in 3+1
dimensions. Also, time-independent lapse and shift fields emerge from the semi-classical states. Our analysis shows that the
model might contain fermionic matter degrees of freedom. 相似文献
18.
The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutative space-time, a modified propagator and free energy are derived by means of functional integrals method. Moreover, quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background. 相似文献
19.
Mamatabdulla Hekim Abduwali Anwar Jianhua Wang 《International Journal of Theoretical Physics》2016,55(7):3226-3233
We study the noncommutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric multipole moment, in the presence of an external magnetic field. First, by introducing a shift for the magnetic field we give the Schrödinger equations in the presence of an external magnetic field both on a noncommutative space and a noncommutative phase space, respectively. Then by solving the Schrödinger equations, we obtain quantum phases of the electric multipole moment both on a noncommutative space and a noncommutative phase space. We demonstrate that these phase are geometric and dispersive. 相似文献
20.
The charged Dirac oscillator on a noncommutative plane coupling to a uniform perpendicular magnetic field is studied in this paper. We map the noncommutative plane to a commutative one by means of Bopp shift and study this problem on the commutative plane. We find that this model can be mapped onto a quantum optics model which contains Anti-Jaynes-Cummings (AJC) or Jaynes-Cummings (JC) interactions when a dimensionless parameter ζ (which is the function of the intensity of the magnetic field) takes values in different regimes. Furthermore, this model behaves as experiencing a chirality quantum phase transition when the dimensionless parameter ζ approaches the critical point. Several evidences of the chirality quantum phase transition are presented. We also study the non-relativistic limit of this model and find that a similar chirality quantum phase transition takes place in its non-relativistic limit. 相似文献