共查询到20条相似文献,搜索用时 15 毫秒
1.
A. L. Carey K. C. Hannabuss V. Mathai P. McCann 《Communications in Mathematical Physics》1998,190(3):629-673
In this paper, we study both the continuous model and the discrete model of the Quantum Hall Effect (QHE) on the hyperbolic
plane. The Hall conductivity is identified as a geometric invariant associated to an imprimitivity algebra of observables.
We define a twisted analogue of the Kasparov map, which enables us to use the pairing between K-theory and cyclic cohomology theory, to identify this geometric invariant with a topological index, thereby proving the integrality
of the Hall conductivity in this case.
Received: 17 March 1997 / Accepted: 24 April 1997 相似文献
2.
We study both classical and quantum relation between two Hamiltonian systems which are mutually connected by time-dependent canonical transformation. One is ordinary conservative system and the other is timedependent Hamiltonian system. The quantum unitary operator relevant to classical canonical transformation between the two systems are obtained through rigorous evaluation. With the aid of the unitary operator, we have derived quantum states of the time-dependent Hamiltonian system through transforming the quantum states of the conservative system. The invariant operators of the two systems are presented and the relation between them are addressed. We showed that there exist numerous Hamiltonians, which gives the same classical equation of motion. Though it is impossible to distinguish the systems described by these Hamiltonians within the realm of classical mechanics, they can be distinguishable quantum mechanically. 相似文献
3.
Arthur Jaffe 《Communications in Mathematical Physics》2000,209(1):1-12
In earlier work, we derived an expression for a partition function ?(λ), and gave a set of analytic hypotheses under which ?(λ) does not depend on a parameter λ. The proof that ?(λ) is invariant involved entire cyclic cohomology and K-theory. Here we give a direct proof that . The considerations apply to non-commutative geometry, to super-symmetric quantum theory, to string theory, and to generalizations
of these theories to underlying quantum spaces.
Received: 12 January 1998 / Accepted: 1 May 1999 相似文献
4.
José A. Zapata 《General Relativity and Gravitation》1998,30(8):1229-1245
The canonical quantization of diffeomorphism invariant theories of connections in terms of loop variables is revisited. Such theories include general relativity described in terms of Ashtekar-Barbero variables and extension to Yang-Mills fields (with or without fermions) coupled to gravity. It is argued that the operators induced by classical diffeomorphism invariant or covariant functions are respectively invariant or covariant under a suitable completion of the diffeomorphism group. The canonical quantization in terms of loop variables described here, yields a representation of the algebra of observables in a separable Hilbert space. Furthermore, the resulting quantum theory is equivalent to a model for diffeomorphism invariant gauge theories which replaces space with a manifestly combinatorial object. 相似文献
5.
D. Bahns S. Doplicher K. Fredenhagen G. Piacitelli 《Communications in Mathematical Physics》2003,237(1-2):221-241
We discuss a formulation of quantum field theory on quantum space time where the perturbation expansion of the S-matrix is term by term ultraviolet finite.
The characteristic feature of our approach is a quantum version of the Wick product at coinciding points: the differences
of coordinates q
j
−q
k
are not set equal to zero, which would violate the commutation relation between their components. We show that the optimal
degree of approximate coincidence can be defined by the evaluation of a conditional expectation which replaces each function
of q
j
−q
k
by its expectation value in optimally localized states, while leaving the mean coordinates invariant.
The resulting procedure is to a large extent unique, and is invariant under translations and rotations, but violates Lorentz
invariance. Indeed, optimal localization refers to a specific Lorentz frame, where the electric and magnetic parts of the
commutator of the coordinates have to coincide [11].
Employing an adiabatic switching, we show that the S-matrix is term by term finite. The matrix elements of the transfer matrix
are determined, at each order in the perturbative expansion, by kernels with Gaussian decay in the Planck scale. The adiabatic
limit and the large scale limit of this theory will be studied elsewhere.
Received: 15 January 2003 / Accepted: 20 March 2003
Published online: 5 May 2003
RID="*"
ID="*" Research supported by MIUR and GNAMPA-INDAM
RID="*"
ID="*" Research supported by MIUR and GNAMPA-INDAM
Communicated by H. Araki and D. Buchholz 相似文献
6.
R. S. Kaushal 《International Journal of Theoretical Physics》2001,40(4):835-847
Based on the multidimensional Ermakov theory, a general result that relates the Schrodinger equation and the Milne equation in terms of a space invariant is established. Using this result not only the role of phase in the Wigner function approach to quantum mechanics is demonstrated but also a better explanation for the Aharonov–Bohm effect is sought in terms of a fundamental phase and the matter-field-coupling current. The existence of a similar space invariant is also emphasized for the nonlinear Schrodinger equation. 相似文献
7.
This is a study of orbifold-quotients of quantum groups (quantum orbifolds \({\Theta } \rightrightarrows G_{q}\)). These structures have been studied extensively in the case of the quantum S U 2 group. A generalized theory of quantum orbifolds over compact simple and simply connected quantum groups is developed. Associated with a quantum orbifold there is an invariant subalgebra and a crossed product algebra. For each spin quantum orbifold, there is a unitary equivalence class of Dirac spectral triples over the invariant subalgebra, and for each effective spin quantum orbifold associated with a finite group action, there is a unitary equivalence class of Dirac spectral triples over the crossed product algebra. A Hopf-equivariant Fredholm index problem is studied as an application. 相似文献
8.
By a transfer principle, Pascal's Theorem is equivalent to a theorem about point pairs on the real line. It appears that Pascal's Theorem is equivalent to the vanishing of a common invariant of six quadratic forms. Using the q-deformed invariant theory of Leitenberger (J. Algebra
222 (1999), 82), we construct corresponding quantum invariants by a computer calculation. 相似文献
9.
Vadim Schechtman 《Communications in Mathematical Physics》1999,208(2):355-379
A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant
pseudo-K?hler structure is proposed. In particular cases we arrive at Berezin's quantization via covariant and contravariant
symbols.
Received: 5 August 1997 / Accepted: 8 July 1998 相似文献
10.
We discuss the role of spin in Poincaré invariant formulations of quantum mechanics. 相似文献
11.
We study the properties of quantum entanglement in moving frames, and show that, because spin and momentum become mixed when viewed by a moving observer, the entanglement between the spins of a pair of particles is not invariant. We give an example of a pair, fully spin entangled in the rest frame, which has its spin entanglement reduced in all other frames. Similarly, we show that there are pairs whose spin entanglement increases from zero to maximal entanglement when boosted. While spin and momentum entanglement separately are not Lorentz invariant, the joint entanglement of the wave function is. 相似文献
12.
John R. Fanchi 《Foundations of Physics》2000,30(8):1161-1189
The experimental confirmation of nonlocality has renewed interest in Bohm's quantum potential. The construction of quantum potentials for relativistic systems has encountered difficulties which do not arise in a parametrized formulation of relativistic quantum mechanics known as Relativistic Dynamics. The purpose of this paper is to show how to construct a quantum potential in the relativistic domain by deriving a relativistically invariant quantum potential using Relativistic Dynamics. The formalism is applied to three relativistic scalar particle models: a single particle interacting with a scalar potential; N particles interacting with a scalar potential; and a single particle interacting with an electromagnetic 4-vector potential. 相似文献
13.
Taku Matsui 《Communications in Mathematical Physics》1997,189(1):127-144
We consider the classification of pure infinite volume ground states and that of soliton sectors for 1+1 dimensional massive
quantum spin models. We obtain a proof that non-translationally invariant ground state cannot exist for a class of translationally
invariant Hamiltonians including the spin 1 AKLT (Affleck Kennedy Lieb Tasaki) antiferromagnetic spin model. We also obtain
a complete classification of soliton sectors (up to unitary equivalence) for certain massive models (e.g. ferromagnetic XXZ
models).
Received: 13 January 1997 / Accepted: 11 March 1997 相似文献
14.
D.V. Boulatov 《Communications in Mathematical Physics》1997,186(2):295-322
A quantum deformation of 3-dimensional lattice gauge theory is defined by applying the Reshetikhin-Turaev functor to a Heegaard
diagram associated to a given cell complex. In the root-of-unity case, the construction is carried out with a modular Hopf
algebra. In the topological (weak-coupling) limit, the gauge theory partition function gives a 3-fold invariant, coinciding
in the simplicial case with the Turaev-Viro one. We discuss bounded manifolds as well as links in manifolds. By a dimensional
reduction, we obtain a q-deformed gauge theory on Riemann surfaces and find a connection with the algebraic Alekseev-Grosse-Schomerus approach.
Received: 29 April 1996 / Accepted: 24 September 1996 相似文献
15.
We show that nodal points of ground states of some quantum systems with magnetic interactions can be identified in simple
geometric terms. We analyse in detail two different archetypical systems: i) the planar rotor with a non-trivial magnetic
flux Φ and ii) the Hall effect on a torus. In the case of the planar rotor we show that the level repulsion generated by any
reflection invariant potential V is encoded in the nodal structure of the unique vacuum for θ=π. In the second case we prove that the nodes of the first Landau
level for unit magnetic charge appear at the crossing of the two non-contractible circles α−, β− with holonomies h
α-(A)=h
β-(A)=−1 for any reflection invariant potential V. This property illustrates the geometric origin of the quantum translation anomaly.
Received: 6 April 1999 / Accepted: 21 October 2000 相似文献
16.
We consider actions of quantum groups on lattice spin systems. We show that if an action of a quantum group respects the local structure of a lattice system, it has to be an ordinary group. Even allowing weakly delocalized (quasi-local) tails of the action, we find that there are no actions of a properly quantum group commuting with lattice translations. The non-locality arises from the ordering of factors in the quantum groupC
*-algebra, and can be made one-sided, thus allowing semi-local actions on a half chain. Under such actions, localized quantum group invariant elements remain localized. Hence the notion of interactions invariant under the quantum group and also under translations, recently studied by many authors, makes sense even though there is no global action of the quantum group. We consider a class of such quantum group invariant interactions with the property that there is a unique translation invariant ground state. Under weak locality assumptions, its GNS representation carries no unitary representation of the quantum group.Supported in part by NSF Grant # PHY90-19433 A02Copyright © 1995 by the authors. Faithful reproduction of this article by any means is permitted for non-commercial purposes. 相似文献
17.
We consider a single free spin- 1 / 2 particle. The reduced density matrix for its spin is not covariant under Lorentz transformations. The spin entropy is not a relativistic scalar and has no invariant meaning. 相似文献
18.
S. D. Odintsov 《Fortschritte der Physik》1990,38(5):371-391
The review of formulation and methods of calculation of the parametrization and gauge invariant effective actions in quantum field theory is given. As an example the Vilkovisky-De Witt Effective action (EA) is studied (this EA is a natural representative of gauge and parametrization invariant EA's). The examples where the use of the standard EA leads to the ambiguity are demonstrated. This happens as the result of dependence of the standard EA upon the choice of gauge condition. These examples are as follows: Coleman-Weinberg potential in the finite theories and symmetry breaking, EA in quantum gravity with matter and d = 5 gauged supergravity, the possibility of spontaneous supersymmetry breaking in N = 1 supergravity and the spontaneous compactification in the multidimensional R2-gravity. In all these cases the one-loop Vilkovisky-De Witt EA is found and therefore the problem of gauge dependence of EA is solved. The dependence of standard EA of composite fields upon the gauge is studied for the general gauge theories. The class of gauge and parametrization invariant EA's of the composite fields is offered. 相似文献
19.
The invariant of a link in three-sphere, associated with the cyclic quantum dilogarithm, depends on a natural number N. By the analysis of particularexamples, it is argued that, for a hyperbolic knot (link), the absolute valueof this invariant grows exponentially at large N, the hyperbolic volume of the knot (link) complement being the growth rate. 相似文献
20.
We derive an explicit expression for the Haar integral on the quantized algebra of regular functions ℂ
q
[K] on the compact real form K of an arbitrary simply connected complex simple algebraic group G. This is done in terms of the irreducible ✶-representations of the Hopf ✶-algebra ℂ
q
[K]. Quantum analogs of the measures on the symplectic leaves of the standard Poisson structure on K which are (almost) invariant under the dressing action of the dual Poisson algebraic group K
✶ are also obtained. They are related to the notion of quantum traces for representations of Hopf algebras. As an application
we define and compute explicitly quantum analogs of Harish-Chandra c-functions associated to the elements of the Weyl group of G.
Received: 26 January 2001 / Accepted: 31 May 2001 相似文献