共查询到20条相似文献,搜索用时 31 毫秒
1.
Ingrid Daubechies 《Letters in Mathematical Physics》1978,2(6):459-469
We use a hyperdifferential operator approach to study holomorphic quantization. We explicitly construct the Hilbert space operator which corresponds to a given holomorphic function. We further construct the adjoint and products of such operators and we discuss some special cases of selfadjointness.Wetenschappelijk medewerker bij het Interuniversitair Instituut voor Kernwetenschappen (in het kader van havorsingsprogramma 21 EN) 相似文献
2.
Dieter H. Mayer 《Letters in Mathematical Physics》1987,14(2):105-115
We discuss examples of one-dimensional lattice spin systems of classical statistical mechanics whose generalized zeta function has all its poles and zeros on the real axis. The close relation between certain hyperbolic dynamical systems and these spin systems lets one expect that this is also true for some of the dynamical systems. In fact, we have found several one-dimensional expansive systems, among them the Gauss map whose zeta functions have their zeros, respectively their poles, on the real axis. Such a behaviour is closely related to the spectral properties of the sytems transfer operator which in the cases considered is a positive nuclear operator in a Banach space of holomorphic functions. We formulate a general conjecture concerning the spectrum of this class of operators. 相似文献
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4.
We consider the coherent states of a singular oscillator; these states are defined to be the characteristic states of an operator
that reduces the number of basis functions for a discrete spectrum to one. We use the Darboux transform to study the coherent
states of a transformed Hamiltonian. We obtain an expression for measures that can be used to decompose unity. We construct
a holomorphic representation for the state vectors in the space of functions holomorphic everywhere in the complex plane,
including vectors for discrete spectra and coherent states. We obtain a holomorphic representation of the Darboux transformation
operators.
Tomsk State University. Institute of High-Energy Electronics. Siberian Division of the Russian Academy of Sciences. Translated
from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 46–53, February, 1998. 相似文献
5.
We obtain the normally ordered form of the general multimode exponential operator by means of parameter differentiation method and its antinormally ordered form by virtue of the technique of integration within an ordered product of operators.As an application,we obtain a new comp[leteness relation in n-mode Fock space. 相似文献
6.
We investigate the location of zeros and poles of a dynamical zeta function for a family of subshifts of finite type with
an interaction function depending on the parameters . The system corresponds to the well known Kac-Baker lattice spin model in statistical mechanics. Its dynamical zeta function
can be expressed in terms of the Fredholm determinants of two transfer operators and with the Ruelle operator acting in a Banach space of holomorphic functions, and an integral operator introduced originally by Kac, which acts in the space with a kernel which is symmetric and positive definite for positive β. By relating via the Segal-Bargmann transform to an operator closely related to the Kac operator we can prove equality of their spectra and hence reality, respectively positivity, for the eigenvalues of the operator for real, respectively positive, β. For a restricted range of parameters we can determine the asymptotic behavior of the eigenvalues of for large positive and negative values of β and deduce from this the existence of infinitely many non-trivial zeros and poles
of the dynamical zeta functions on the real β line at least for generic . For the special choice , we find a family of eigenfunctions and eigenvalues of leading to an infinite sequence of equally spaced ``trivial' zeros and poles of the zeta function on a line parallel to
the imaginary β-axis. Hence there seems to hold some generalized Riemann hypothesis also for this kind of dynamical zeta functions.
Received: 14 March 2002 / Accepted: 24 June 2002 Published online: 14 November 2002 相似文献
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9.
Indranil Biswas 《Journal of Geometry and Physics》2002,41(4):286-295
We consider equivariant holomorphic immersions of a universal cover
of a compact Riemann surface X into a Grassmannian
satisfying a nondegeneracy condition. The equivariance condition says that there is a homomorphism ρ of the Galois group to
that takes the natural action of the Galois group on
to the action of the Galois group on
defined using ρ. We prove that the space of such embeddings are in bijective correspondence with the space of all holomorphic differential operators of order two on a rank n vector bundle over X with the property that the symbol of the operator is an isomorphism. 相似文献
10.
It is shown that the N = 4 superalgebra of the Dirac theory in Taub-NUT space has different unitary representations related among themselves through unitary U(2) transformations. In particular the SU(2) transformations are generated by the spin-like operators constructed with the help of the same covariantly constant Killing-Yano tensors which generate Dirac-type operators. A parity operator is defined and some explicit transformations which connect the Dirac-type operators among themselves are given. These transformations form a discrete group which is a realization of the quaternion discrete group. The fifth Dirac operator constructed using the non-covariant constant Killing-Yano tensor of the Taub-NUT space is quite special. This non-standard Dirac operator is connected with the hidden symmetry and is not equivalent to the Dirac-type operators of the standard N = 4 supersymmetry. 相似文献
11.
We construct the spaces that the elliptic Ruijsenaars operators act on. It is shown that they are extensible to nonnegative selfadjoint operators on a space of square integrable functions, or preserve a finite dimensional vector space of entire functions. These facts are shown in terms of the R-operators which satisfy the Yang–lBaxter equation. The elliptic Ruijsenaars operators are considered as the elliptic analogues of the Macdonald operators or the difference analogues of the Lamé operators. 相似文献
12.
In this paper, we study (n-1)-order deformations of an n-Lie algebra and introduce the notion of a Nijenhuis operator on an n-Lie algebra, which could give rise to trivial deformations. We prove that a polynomial of a Nijenhuis operator is still a Nijenhuis operator. Finally, we give various constructions of Nijenhuis operators and some examples. 相似文献
13.
J. Kutzner 《Zeitschrift für Physik A Hadrons and Nuclei》1973,259(2):177-188
We start with the definition of two mapping operators, one of them is the projection operator onto coherent spin states. With the help of these operators we derive a mapping theorem which defines a correspondence between the operators in spin space andc-number functions of a certain class. It is shown that this correspondence is one-to-one. The quantum-mechanical expectation value of an operator is found to be expressible in the form of a phase space average of classical statistical mechanics. We also derive a product theorem which allows us to transcribe the equations of motion for operators into equivalent equations for thec-number functions. As an illustration of the theory, some examples are discussed. 相似文献
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15.
借助于粒子数算符的本征态和坐标算符函数的本征方程,把坐标算符的本征矢〈f(x)|表示为一个算符对坐标本征矢〈x|的作用.由此,把不对称的坐标投影算符转换为对称的坐标投影算符,再利用坐标本征矢的完备性,给出不对称坐标投影算符的积分.
关键词:
本征矢
算符的积分
本征方程
完备性 相似文献
16.
FAN Hong-Yi Hai-Liang 《理论物理通讯》2006,46(4):599-602
We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU(1,1) algebra. This is an approach for obtaining the time-dependent Hamiltonian from the preassigned time evolution in classical phase space, an approach which is in contrast to Lewis-Riesenfeld's invariant operator theory of treating timedependent harmonic oscillators. 相似文献
17.
Alberto Chamorro 《Pramana》1978,10(1):83-88
It is shown, by providing a general method for the construction that any Fock space linear operator defined on the dense linear
manifold spanned by the particle number representation basis can be represented in terms of the annihilation and creation
operators. The normal form of the representation is unique. 相似文献
18.
Adam D. Helfer 《General Relativity and Gravitation》1985,17(2):133-147
A holomorphic connection on (1, 0)-vector fields which is intrinsically defined on any curved twistor space is described. Although it is a local operator, it is given in terms of the nonlocal geometry of the twistor space corresponding to the local geometry of the spacetime. The connection is represented in local coordinates by a system ofnonlinear first-order partial differential operators. It has torsion but no curvature. A parallelism is given explicitly, and an example is computed. 相似文献
19.
The character of holomorphic functions on the space of pure spinors in 10, 11 and 12 dimensions is calculated. From this character
formula, we derive in a manifestly covariant way various central charges which appear in the pure spinor formalism for the
superstring. We also derive in a simple way the zero momentum cohomology of the pure spinor BRST operator for the D=10 and D=11 superparticle
Mathematics Subject Classifications (2000): 81T30, 83E30, 83E50 相似文献
20.
It has been common knowledge that the single-mode squeezing operator and the two-mode squeezing operator are independent of each other. However, in this work we find that after using the technique of integration within Ω-ordering and β-ordering, we can detach two single-mode squeezing operators from the two-mode squeezing operator. In other words, we show that the two-mode squeezing operator can be split into a β-ordered two-mode squeezing operator (with a new squeezing parameter) and two single-mode squeezing operators (with another squeezing parameter). This tells us that the two-mode squeezing mechanism also involves some single-mode squeezing. 相似文献