共查询到20条相似文献,搜索用时 31 毫秒
1.
Mircea Puta 《Letters in Mathematical Physics》1984,8(3):189-194
The geometric prequantization of a reduced phase space of a cotangent bundle is described and its relation with the geometric prequantization of the cotangent bundle is pointed out. 相似文献
2.
Mircea Puta 《Letters in Mathematical Physics》1988,15(3):187-192
The geometric prequantization of Poisson manifolds is described using the Weinstein theory of local symplectic groupoids. 相似文献
3.
José M. Figueroa-O'Farrill Takashi Kimura 《Communications in Mathematical Physics》1991,136(2):209-229
This is the first part of a two-part paper dedicated to the definition of BRST quantization in the framework of geometric quantization. After recognizing prequantization as a manifestation of the Poisson module structure of the sections of the prequantum line bundle, we define BRST prequantization and show that it is the homological analog of the symplectic reduction of prequantum data. We define a prequantum BRST cohomology theory and interpret it in terms of geometric objects. We then show that all Poisson structures correspond under homological reduction. This allows to prove, in the BRST context, that prequantization and reduction commute. 相似文献
4.
SHAOMing-Xue ZHUZHONG-Yuan 《理论物理通讯》2001,35(3):263-266
The Weil‘s integrality condition of prequantization is generalized to two-dimensional phase space with boundaries.It is shown that in the prequantization condition a term related to the symplectic potential on the boundary appears.The necessity of the generalized condition is proved by analyzing the isolated singularities of the Hermitian bundle while the sufficiency of the condition is proved via geometric construction on the space of equivalence class. 相似文献
5.
A. Taleshian M. Shaban Nataj B. Pourhassan 《International Journal of Theoretical Physics》2014,53(11):3943-3947
In this paper, we consider effective Hamiltonian of 2D dilatonic black hole adding Axion field and calculate closed 2-form by using geometric prequantization method. It yields to the Schrödinger equation which may be solved to obtain wave function. We obtained a condition on the cosmological constant to obtain appropriate Hamilton equation of motions. 相似文献
6.
In this letter, the effective-one-body Hamiltonian of two spinning black hole considered and prequantization operators obtained by using the closed 2-form. It is indeed an application of prequantization method in a given physical system. Our results may be considered as mathematical tool and is useful to obtain the wave function. 相似文献
7.
Christian Günther 《International Journal of Theoretical Physics》1977,16(6):447-464
Principal circle bundles with connection and symplectic curvature over Banach manifolds are investigated. Using results on contact manifolds alternate proofs for some results of B. Kostant are given and a symplectic structure for the total space of the corresponding principal \ {0} bundle is constructed. As an example, these results are applied to the projective fibration of a complex Hilbert space. This gives close relations between the geometric formulation of classical and quantum dynamical systems. As another application, a functorial construction of the prequantization procedure of B. Kostant is given. 相似文献
8.
Gérard G. Emch 《International Journal of Theoretical Physics》1981,20(12):891-904
The properties of the representations of the canonical commutation relations, obtained in the prequantization program, are investigated with special attention to the relevance of the KMS structures in this context. In particular, we show how these structures provide a natural way to pass from the prequantization representation of the CCR to the Schrödinger representation. 相似文献
9.
Oliver Fabert 《Communications in Mathematical Physics》2011,302(1):113-159
It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that the rich algebraic formalism of symplectic field theory
leads to a natural appearance of quantum and classical integrable systems, at least in the case when the contact manifold
is the prequantization space of a symplectic manifold. In this paper we generalize the definition of gravitational descendants
in SFT from circle bundles in the Morse-Bott case to general contact manifolds. After we have shown using the ideas in Okounkov
and Pandharipande (Ann Math 163(2):517–560, 2006) that for the basic examples of holomorphic curves in SFT, that is, branched covers of cylinders over closed Reeb orbits,
the gravitational descendants have a geometric interpretation in terms of branching conditions, we follow the ideas in Cieliebak
and Latschev ( [math.s6], 2007) to compute the corresponding sequence of Poisson-commuting functions when the contact manifold is the unit cotangent bundle
of a Riemannian manifold. 相似文献
10.
We describe equivariant differential characters (classifying equivariant circle bundles with connections), their prequantization,
and reduction.
Supported in part by NSF grant DMS-0603892.
Supported in part by NSF grant DMS-0456714. 相似文献
11.
In this note we use some of the results of [3] to derive a general duality theorem for the cohomologies of foliated structures on a manifold. The result is applied to the special case of a symplectic manifold M on which the foliation is given by a complex polarization F in the sense of geometric quantization. We obtain, for example, a rigorous proof of the fact that for a smooth function ƒ on M whose Hamiltonian vector field leaves F invariant, the spectrum of the corresponding prequantization operator v(ƒ) coincides with the spectrum of its transpose, under the above duality. This latter result was obtained by Simms in [12] under certain hypotheses. Proofs of the validity of those hypotheses are now available in the literature; cf. [3] and [7]. 相似文献
12.
Mark J. Gotay 《International Journal of Theoretical Physics》1980,19(2):139-161
A classical theorem of Van Hove in conjunction with a formalism developed by Weinstein is used to prove that a quantization functor does not exist. In the proof a category of exact transverse Lagrangian submanifolds is introduced which provides a functorial link between Schrödinger quantization and the prequantization/polarization theory of Kostant and Souriau. 相似文献
13.
《Physics letters. [Part B]》1988,205(4):525-529
Geometric quantization is applied to first-class constrained systems. It is shown how certain inconsistencies associated with the prequantization of open gauge algebras and observables can be cured at the quantum level by the introduction of suitable polarizations. Furthermore it is shown a large Poisson subalgebra of the ideal of constrait functions can be consistently implemented at the quantum level and how reparametrization invariance of the constraint surface relates to a partially flat local Kähler structure on phase space. 相似文献
14.
Given a Poisson (or more generally Dirac) manifold P, there are two approaches to its geometric quantization: one involves a circle bundle Q over P endowed with a Jacobi (or Jacobi–Dirac) structure; the other one involves a circle bundle with a (pre)contact groupoid structure over the (pre)symplectic groupoid of P. We study the relation between these two prequantization spaces. We show that the circle bundle over the (pre)symplectic groupoid of P is obtained from the Lie groupoid of Q via an S1 reduction that preserves both the Lie groupoid and the geometric structures. 相似文献
15.
V. A. Lugo 《Letters in Mathematical Physics》1981,5(6):509-516
We introduce an associative bilinear product F * G on the space of Schwartz functions of the coadjoint orbits
of a large family of nilpotent Lie groups. We can then introduce an operator
, for all
. When the nilpotent group is the Heisenberg group N(3), the correspondence
is a canonical prequantization of functions F(q, p) in phase space.
Part of this work was done at the University of California, Los Angeles. 相似文献
16.
Ҧ �� 《核聚变与等离子体物理》2018,38(1):29-33
为了在数值计算中保持哈密顿系统的辛几何结构不变,利用辛几何算法得到了在线性哈密顿系统中射线追踪方程的一般辛差分格式。通过具体算例,利用辛几何算法计算了波在非磁化等离子体中的传播轨迹,并且与传统Runge-Kutta-Fehlberg算法所得结果进行了比较。利用辛几何算法所得传播轨迹与解析解一致,其色散函数值的误差随时间线性增长,能在长时间内保持色散函数值在一个很小的误差范围内。利用传统的Runge-Kutta-Fehlberg算法所得传播轨迹与解析解不一致,其误差随时间做大幅振荡增加。计算结果表明辛几何算法在保持传播轨迹和色散函数值方面具有独特的优势。 相似文献
17.
18.
《Physics letters. A》1997,236(4):296-300
The projective-geometric formulation of geometric phase for any ensemble in the causal quantum theories is given. This formulation generalizes the standard formulation of geometric phase to any causal ensemble including the cases of a single causal trajectory, the experimental geometric phase and the classical geometric phase. 相似文献
19.
A scheme to perfectly preserve an initial qubit state in
geometric quantum computation is proposed for a single-qubit geometric
quantum gate in a nuclear magnetic resonance system. At first, by
adjusting some magnetic field parameters, one can let the dynamic
phase be proportional to the geometric phase. Then, by controlling
the azimuthal angle in the initial state, we may realize a
geometric quantum gate whose fidelity is equal to one under
cyclic evolution. This means that the quantum information is no
distortion in the process of geometric quantum computation. 相似文献
20.
In this paper the geometric phases of two entangled spin-1/2 particles in the presence and absence of spin-spin interaction
are calculated. We also discuss the geometric phases when only one of the two particles is affected by the external magnetic
field. Our results show that the geometric phase in this case is not equal to that of a single particle under the same evolution
condition because of the effect of entanglement. We further study the entanglement dependence of the noncyclic geometric phases
in the interacting and noninteracting spins under a time-independent uniform magnetic field. A general entanglement-dependence
geometric phase is formulated. 相似文献