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1.
Three problems related to the spherical quantum billiard in are considered. In the first, a compact form of the hyperspherical equations leads to their complex contracted representation. Employing these contracted equations, a proof is given of Courant's nodal-symmetry intersection theorem for diagonal eigenstates of spherical-like quantum billiards in . The second topic addresses the first-excited-state theorem for the spherical quantum billiard in . Wavefunctions for this system are given by the product form, ( )Z q+()Y (n) , where is dimensionless displacement, is angular-momentum number, qis an integer function of dimension, Z() is either a spherical Bessel function (nodd) or a Bessel function of the first kind (neven) and represents (n– 1) independent angular components. Generalized spherical harmonics are written . It is found that the first excited state (i.e., the second eigenstate of the Laplacian) for the spherical quantum billiard in is n-fold degenerate and a first excited state for this quantum billiard exists which contains a nodal bisecting hypersurface of mirror symmetry. These findings establish the first-excited-state theorem for the spherical quantum billiard in . In a third study, an expression is derived for the dimension of the th irreducible representation (irrep) of the rotation group O(n) in by enumerating independent degenerate product eigenstates of the Laplacian.  相似文献   

2.
For the SOS model defined by the Hamiltonian , where x , x ,{1,2,...},h>0,x d ,d2 it is shown that in the low-temperature region an infinite sequence of first-order phase transitions takes place whenh»0 and the temperature is fixed.  相似文献   

3.
Periodic nonlinear Schrödinger equation and invariant measures   总被引:1,自引:1,他引:0  
In this paper we continue some investigations on the periodic NLSEiu u +iu xx +u|u| p-2 (p6) started in [LRS]. We prove that the equation is globally wellposed for a set of data of full normalized Gibbs measrue (after suitableL 2-truncation). The set and the measure are invariant under the flow. The proof of a similar result for the KdV and modified KdV equations is outlined. The main ingredients used are some estimates from [B1] on periodic NLS and KdV type equations.  相似文献   

4.
We investigate the dynamics of Einstein equations in the vicinity of the two recently described types of singularity of anisotropic and homogeneous cosmological models described by the action
with general F() and V(). The dynamical nature of each singularity is elucidated, and we show that both are, in general, dynamically unavoidable, reinforcing the unstable character of previous isotropic and homogeneous cosmological results obtained for the conformal coupling case.  相似文献   

5.
The CPT Group of the Dirac Field   总被引:2,自引:2,他引:0  
Using the standard representation of the Dirac equation, we show that, up to signs, there exist only two sets of consistent solutions for the matrices of charge conjugation (C), parity (P), and time reversal (T), which give the transformation of fields , and , where and . These sets are given by , , and , , . Then , and two successive applications of the parity transformation to fermion fields necessarily amount to a 2 rotation. Each of these sets generates a non abelian group of 16 elements, respectively, and , which are non isomorphic subgroups of the Dirac algebra, which, being a Clifford algebra, gives a geometric nature to the generators, in particular to charge conjugation. It turns out that and , where is the dihedral group of eight elements, the group of symmetries of the square, and 16E is a non trivial extension of by , isomorphic to a semidirect product of these groups; S6 and S8 are the symmetric groups of six and eight elements. The matrices are also given in the Weyl representation, suitable for taking the massless limit, and in the Majorana representation, describing self-conjugate fields. Instead, the quantum operators C, P and T, acting on the Hilbert space, generate a unique group , which we call the CPT group of the Dirac field. This group, however, is compatible only with the second of the above two matrix solutions, namely with , which is then called the matrix CPT group. It turns out that , where is the dicyclic group of 8 elements and S10 is the symmetric group of 10 elements. Since , the quaternion group, and , the 0-sphere, then .  相似文献   

6.
We formulate the variational principle of theDirac equation within the noncommutative even space-timesubalgebra, the Clifford -algebra . A fundamental ingredient in ourmultivectorial algebraic formulation is a -complex geometry, . We derive the Lagrangian for theDirac-Hestenes equation and show that it must be mapped on , where denotes an -algebra of functions.  相似文献   

7.
We study the fractional decomposition of the quantum enveloping affine algebras and with vanishing central charge in the limit . This decomposition is based on the bosonic representation and can be related to fractional supersymmetry and k-fermionic spin. The quantum affine algebras and the classical ones are equivalent in the fermionic realization.  相似文献   

8.
It is shown that for normal states ρ and φ of a W *-algebra , where P(.,.) is the transition probability considered by Uhlmann [1], and ζ(ω) is the vector in the natural positive cone of some standard faithful representation of A, associated with the normal state ω. The above inequality is equivalent to: , where d(.,.) is the Bures distance function [5].  相似文献   

9.
It is proved that runaway solutions persist if Abraham's force –m is generalised by adding to it afinite number of terms which are linear in higher derivatives of . The implication of this result to Eliezer's relativistic generalisation of the Lorentz-Dirac equation is discussed.Worked supported by the Minerva Foundation.  相似文献   

10.
Let (M, g) be a pseudo-Riemannian manifold and the space of densities of degree on M. Denote the space of differential operators from to of order k and S k with = – the corresponding space of symbols. We construct (the unique) conformally invariant quantization map . This result generalizes that of Duval and Ovsienko.  相似文献   

11.
A locally finite, causal, and quantal substitute for a locally Minkowskian principal fiber bundle of modules of Cartan differential forms over a bounded region X of a curved C -smooth spacetime manifold M with structure group G that of orthochronous Lorentz transformations L + := SO(1,3), is presented. is usually regarded as the kinematical structure of classical Lorentzian gravity when the latter is viewed as a Yang-Mills type of gauge theory of a sl(2, {})-valued connection 1-form . The mathematical structure employed to model this replacement of is a principal finitary spacetime sheaf of quantum causal sets with structure group G n, which is a finitary version of the continuous group G of local symmetries of General Relativity, and a finitary Lie algebra g n-valued connection 1-form on it, which is a section of its subsheaf . is physically interpreted as the dynamical field of a locally finite quantum causality, whereas its associated curvature as some sort of finitary and causal Lorentzian quantum gravity.  相似文献   

12.
The Einstein equations can be written as Fierz-Pauli equations with self-interaction, together with the covariant Hilbert-gauge condition, where W denotes the covariant wave operator and G ik the Einstein tensor of the metric g ik collecting all nonlinear terms of Einstein's equations. As is known, there do not, however, exist plane-wave solutions ik(z)with g ik Z,i Z,k=0of these equations such that what is essential to the introduction of gravitons is not satisfied in general relativity. This nonexistence corresponds with the uncertainty relation,p(g*)2(x)3h hG/ c 3 concerning the total nonlinear gravitational field g *ik =g k + k .  相似文献   

13.
We consider the Dirichlet Laplacian for astrip in with one straight boundary and a width , where $f$ is a smooth function of acompact support with a length 2b. We show that in the criticalcase, , the operator has nobound statesfor small .On the otherhand, a weakly bound state existsprovided . In thatcase, there are positive c 1,c 2 suchthat the corresponding eigenvalue satisfies for all sufficiently small.  相似文献   

14.
In this paper we consider operatorsH(,x) defined onl 2() by
  相似文献   

15.
GLh(n) ×GLh(m)-covariant (hh)-bosonic[or (hh)-fermionic] algebras are built in terms of thecorresponding Rh and -matrices by contracting theGLq(n) × -covariant q-bosonic (or q-fermionic) algebras , = 1, 2.When using a basis of wherein theannihilation operators are contragredient to thecreation ones, this contraction procedure can be carried out for any n, m values. Whenemploying instead a basis wherein the annihilationoperators, like the creation ones, are irreducibletensor operators with respect to the dual quantumalgebra Uq(gl(n)) , a contraction limit only exists forn, m {1, 2, 4, 6, . . .}. For n = 2, m = 1, andn = m = 2, the resulting relations can be expressed interms of coupled (anti)commutators (as in the classical case), by usingUh(sl(2)) [instead of s1(2)] Clebsch-Gordancoefficients. Some Uh(sl(2)) rank-1/2irreducible tensor operators recently constructed byAizawa are shown to provide a realization of (2, 1).  相似文献   

16.
We constrain the possible time variation of the Higgs vacuum expectation value (v) by recent results on the primordial 4He abundance (Y P ). For that, we use an analytic approach which enables us to take important issues into consideration, that have been ignored by previous works, like the v-dependence of the relevant cross sections of deuterium production and photodisintegration, including the full Klein–Nishina cross section. Furthermore, we take a non-equilibrium Ansatz for the freeze-out concentration of neutrons and protons and incorporate the latest results on the neutron decay. Finally, we approximate the key-parameters of the primordial 4He production (the mean lifetime of the free neutron and the binding energy of the deuteron) by terms of (where v 0 denotes the present theoretical estimate). Eventually, we derive the relation and the most stringent limit on a possible time variation of v is given by: .  相似文献   

17.
We consider a family of Hamiltonian systems
and we prove that it is integrable for . To show this we use the normal variational equation.  相似文献   

18.
For the non-compact abelian lattice Higgs model in Landau gauge Kennedy and King (Princeton preprint, 1985) showed that the two point function does not decay in the Higgs phase. We generalize their methods to show that for the same range of parameters there are states parametrized by an angle [0, 2) such that and 0$$ " align="middle" border="0"> .  相似文献   

19.
In this paper we consider the classical Euclidean wormhole solution of the Born—Infeld scalar field. The corresponding classical Euclidean wormhole solution can be obtained analytically for both very small and large . At the extreme limit of small the wormhole solution has the same format as one obtained by Giddings and Strominger (Nuclear Physics B 306, 890, 1988). At the extreme limit of large the wormhole solution is a new one. The wormhole wave functions can also be obtained for both very small and large . These wormhole wave functions are regarded as solutions of quantum-mechanical Wheeler—Dewitt equation with certain boundary conditions.  相似文献   

20.
The charge exchange reaction of negative muons from the atom to oxygen has been measured in gaseous mixtures of H2 + O2. The measurements were performed at three different relative oxygen concentrations ranging from 0.2% to 0.8% and total pressures 3.5–15 bar. A mean transfer rate of , describing the transfer from the ground state of thermalized atoms to oxygen, was determined. In order to investigate the energy dependence of the transfer rate, Monte Carlo simulations of the thermalization and the muon transfer were carried out. The comparison of measured and simulated time spectra yielded an epithermal transfer rate =3.9 1011 s-1 in the energy interval 0.12–0.22 eV. The analysis with the model of Two components shows that all measured time spectra can be reproduced with the same set of parameters.  相似文献   

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