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1.
Type O pure radiation metrics with a cosmological constant 总被引:1,自引:1,他引:0
In this paper we complete the integration of the conformally flat pure radiation spacetimes with a non-zero cosmological constant
Λ, and , by considering the case . This is a further demonstration of the power and suitability of the generalised invariant formalism (GIF) for spacetimes
where only one null direction is picked out by the Riemann tensor. For these spacetimes, the GIF picks out a second null direction
(from the second derivative of the Riemann tensor) and once this spinor has been identified the calculations are transferred
to the simpler GHP formalism, where the tetrad and metric are determined. The whole class of conformally flat pure radiation
spacetimes with a non-zero cosmological constant (those found in this paper, together with those found earlier for the case
) have a rich variety of subclasses with zero, one, two, three, four or five Killing vectors. 相似文献
2.
A zero modes’ Fock space is constructed for the extended chiral WZNW model. It gives room to a realization of the fusion ring of representations of the restricted quantum universal enveloping
algebra at an even root of unity, and of its infinite dimensional extension by the Lusztig operators We provide a streamlined derivation of the characteristic equation for the Casimir invariant from the defining relations
of A central result is the characterization of the Grothendieck ring of both and in Theorem 3.1. The properties of the fusion ring in are related to the braiding properties of correlation functions of primary fields of the conformal current algebra model.
相似文献
3.
A new parametrization of the 3-metric allows to find explicitly a York map by means of a partial Shanmugadhasan canonical
transformation in canonical ADM tetrad gravity. This allows to identify the two pairs of physical tidal degrees of freedom
(the Dirac observables of the gravitational field have to be built in term of them) and 14 gauge variables. These gauge quantities,
whose role in describing generalized inertial effects is clarified, are all configurational except one, the York time, i.e.
the trace of the extrinsic curvature of the instantaneous 3-spaces (corresponding to a clock synchronization convention) of a non-inertial frame centered on an arbitrary observer. In the Dirac Hamiltonian is the sum of the weak ADM energy (whose density is coordinate-dependent, containing the inertial potentials) and of the first-class constraints. The main results of the
paper, deriving from a coherent use of constraint theory, are: (i) The explicit form of the Hamilton equations for the two
tidal degrees of freedom of the gravitational field in an arbitrary gauge: a deterministic evolution can be defined only in
a completely fixed gauge, i.e. in a non-inertial frame with its pattern of inertial forces. The simplest such gauge is the
3-orthogonal one, but other gauges are discussed and the Hamiltonian interpretation of the harmonic gauges is given. This
frame-dependence derives from the geometrical view of the gravitational field and is lost when the theory is reduced to a
linear spin 2 field on a background space-time. (ii) A general solution of the super-momentum constraints, which shows the
existence of a generalized Gribov ambiguity associated to the 3-diffeomorphism gauge group. It influences: (a) the explicit
form of the solution of the super-momentum constraint and then of the Dirac Hamiltonian; (b) the determination of the shift
functions and then of the lapse one. (iii) The dependence of the Hamilton equations for the two pairs of dynamical gravitational
degrees of freedom (the generalized tidal effects) and for the matter, written in a completely fixed 3-orthogonal Schwinger
time gauge, upon the gauge variable , determining the convention of clock synchronization. The associated relativistic inertial effects, absent in Newtonian
gravity and implying inertial forces changing from attractive to repulsive in regions with different sign of , are completely unexplored and may have astrophysical relevance in the interpretation of the dark side of the universe. 相似文献
4.
Consider in the operator family . P
0 is the quantum harmonic oscillator with diophantine frequency vector ω, F
0 a bounded pseudodifferential operator with symbol decreasing to zero at infinity in phase space, and . Then there exist independent of and an open set such that if and , the quantum normal form near P
0 converges uniformly with respect to . This yields an exact quantization formula for the eigenvalues, and for the classical Cherry theorem on convergence of Birkhoff’s normal form for complex frequencies is recovered.
Partially supported by PAPIIT-UNAM IN106106-2. 相似文献
5.
J. Ponce de Leon 《General Relativity and Gravitation》2006,38(1):61-81
Braneworld theory provides a natural setting to treat, at a classical level, the cosmological effects of vacuum energy. Non-static
extra dimensions can generally lead to a variable vacuum energy, which in turn may explain the present accelerated cosmic
expansion. We concentrate our attention in models where the vacuum energy decreases as an inverse power law of the scale factor.
These models agree with the observed accelerating universe, while fitting simultaneously the observational data for the density
and deceleration parameter. The redshift at which the vacuum energy can start to dominate depends on the mass density of ordinary
matter. For
m
= 0.3, the transition from decelerated to accelerated cosmic expansion occurs at z
T
≈ 0.48 ± 0.20, which is compatible with SNe data. We set a lower bound on the deceleration parameter today, namely > − 1 + 3
m
/2, i.e., > − 0.55 for
m
= 0.3. The future evolution of the universe crucially depends on the time when vacuum starts to dominate over ordinary matter.
If it dominates only recently, at an epoch z < 0.64, then the universe is accelerating today and will continue that way forever. If vacuum dominates earlier, at z > 0.64, then the deceleration comes back and the universe recollapses at some point in the distant future. In the first case,
quintessence and Cardassian expansion can be formally interpreted as the low energy limit of our model, although they are
entirely different in philosophy. In the second case there is no correspondence between these models and ours. 相似文献
6.
Quantum Conjugacy Classes of Simple Matrix Groups 总被引:1,自引:0,他引:1
A. Mudrov 《Communications in Mathematical Physics》2007,272(3):635-660
Let G be a simple complex classical group and its Lie algebra. Let be the Drinfeld-Jimbo quantization of the universal enveloping algebra . We construct an explicit -equivariant quantization of conjugacy classes of G with Levi subgroups as the stabilizers.
Dedicated to the memory of Joseph Donin
This research is partially supported by the Emmy Noether Research Institute for Mathematics, the Minerva Foundation of Germany,
the Excellency Center “Group Theoretic Methods in the study of Algebraic Varieties” of the Israel Science foundation, by the
EPSRC grant C511166, and by the RFBR grant no. 06-01-00451. 相似文献
7.
D. Eriksson S. Hesselbach J. Rathsman 《The European Physical Journal C - Particles and Fields》2008,53(2):267-280
We investigate the viability of observing charged Higgs bosons () produced in association with bosons at the CERN large hadron collider, using the leptonic decay and hadronic decay, within different scenarios of the minimal supersymmetric standard model (MSSM) with both real and complex parameters.
Performing a parton level study we show how the irreducible standard model background from jets can be controlled by applying appropriate cuts and find that the size of a possible signal depends on the cuts needed
to suppress QCD backgrounds and misidentifications. In the standard maximal mixing scenario of the MSSM we find a viable signal
for large and intermediate masses () when using softer cuts (, 50 GeV), whereas for harder cuts (, 100 GeV) we only find a viable signal for very large (). We have also investigated a special class of MSSM scenarios with large mass splittings among the heavy Higgs bosons where
the cross-section can be resonantly enhanced by factors up to one hundred, with a strong dependence on the -violating phases. Even so we find that the signal after cuts remains small except for small masses () when using the softer cuts. Finally, in all the scenarios we have investigated we have only found small -asymmetries. 相似文献
8.
We study rooted self avoiding polygons and self avoiding walks on deterministic fractal lattices of finite ramification index. Different sites on such lattices are not equivalent, and the number of rooted open walks W
n
(S), and rooted self-avoiding polygons P
n
(S) of n steps depend on the root S. We use exact recursion equations on the fractal to determine the generating functions for P
n
(S), and W
n(S) for an arbitrary point S on the lattice. These are used to compute the averages ,, and over different positions of S. We find that the connectivity constant μ, and the radius of gyration exponent are the same for the annealed and quenched averages. However, , and , where the exponents and , take values different from the annealed case. These are expressed as the Lyapunov exponents of random product of finite-dimensional matrices. For the 3-simplex lattice, our numerical estimation gives and , to be compared with the known annealed values and . 相似文献
9.
We prove bounds on moments of the Smoluchowski coagulation equations with diffusion, in any dimension d ≥ 1. If the collision propensities α(n, m) of mass n and mass m particles grow more slowly than , and the diffusion rate is non-increasing and satisfies for some b
1 and b
2 satisfying 0 ≤ b
2 < b
1 < ∞, then any weak solution satisfies for every and T ∈(0, ∞), (provided that certain moments of the initial data are finite). As a consequence, we infer that these conditions
are sufficient to ensure uniqueness of a weak solution and its conservation of mass.
This work was performed while A.H. held a postdoctoral fellowship in the Department of Mathematics at U.B.C.
This work is supported in part by NSF grant DMS0307021. 相似文献
10.
H. Backe A. Dretzke R. Horn T. Kolb W. Lauth R. Repnow M. Sewtz N. Trautmann 《Hyperfine Interactions》2005,162(1-4):77-84
Drift time measurements of ions in a buffer gas cell filled with argon have been performed from which changes of the ion mobility
and ionic radii for various heavy elements and their compounds were determined. The ionic radius of americium shrinks by (3.1
1.3)% with respect to that of plutonium, and an increase of the radius by (28 2)% of plutonium oxide with respect to plutonium was found. Ion chemical reactions of erbium ions were studied online in
an argon buffer gas cell to which the reaction gases oxygen (O) and methane (CH) were added. The erbium ions were implanted into the buffer gas cell with an energy of 50 MeV. The online measured reaction
constant = (3.2 0.4) 10 cm/(molecule s) for the reaction Er + O
ErO + O agrees with a reference measurement = (3.6 0.4) 10 cm/(molecule s), performed with a Fourier-Transform-Mass-Spectrometer. 相似文献
11.
H. Boos M. Jimbo T. Miwa F. Smirnov Y. Takeyama 《Communications in Mathematical Physics》2007,272(1):263-281
For the critical XXZ model, we consider the space of operators which are products of local operators with a disorder operator. We introduce two anti-commutative families of
operators which act on . These operators are constructed as traces over representations of the q-oscillator algebra, in close analogy with Baxter’s Q-operators. We show that the vacuum expectation values of operators in can be expressed in terms of an exponential of a quadratic form of .
On leave of absence from Skobeltsyn Institute of Nuclear Physics, MSU, 119992, Moscow, Russia
Membre du CNRS 相似文献
12.
Asao Arai 《Letters in Mathematical Physics》2007,80(3):211-221
Let H be a self-adjoint operator on a complex Hilbert space . A symmetric operator T on is called a time operator of H if, for all , (D(T) denotes the domain of T) and . In this paper, spectral properties of T are investigated. The following results are obtained: (i) If H is bounded below, then σ(T), the spectrum of T, is either (the set of complex numbers) or . (ii) If H is bounded above, then is either or . (iii) If H is bounded, then . The spectrum of time operators of free Hamiltonians for both nonrelativistic and relativistic particles is exactly identified.
Moreover spectral analysis is made on a generalized time operator.
This work is supported by the Grant-in-Aid No.17340032 for Scientific Research from the JSPS. 相似文献
13.
O. W. Greenberg 《Foundations of Physics》2006,36(10):1535-1553
Lüders and Pauli proved the theorem based on Lagrangian quantum field theory almost half a century ago. Jost gave a more general proof based on “axiomatic” field theory nearly as long ago. The axiomatic point of view has two advantages over the Lagrangian one. First, the axiomatic point of view makes clear why is fundamental—because it is intimately related to Lorentz invariance. Secondly, the axiomatic proof gives a simple way to calculate the transform of any relativistic field without calculating , and separately and then multiplying them. The purpose of this pedagogical paper is to “deaxiomatize” the theorem by explaining it in a few simple steps. We use theorems of distribution theory and of several complex variables without proof to make the exposition elementary. 相似文献
14.
Paolo Aschieri Leonardo Castellani Marija Dimitrijević 《Letters in Mathematical Physics》2008,85(1):39-53
A -product is defined via a set of commuting vector fields , and used in a theory coupled to the fields. The -product is dynamical, and the vacuum solution , reproduces the usual Moyal product. The action is invariant under rigid translations and Lorentz rotations, and the conserved
energy–momentum and angular momentum tensors are explicitly derived.
相似文献
15.
Asao Arai 《Letters in Mathematical Physics》2006,77(3):283-290
A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and the total Hamiltonian is unitarily equivalent to the direct integral
of a family of self-adjoint operators
acting in the Hilbert space
, where
is the Hilbert space of the quantum radiation field. The fiber operator
is called the Hamiltonian of the Dirac polaron with total momentum
. The main result of this paper is concerned with the non-relativistic (scaling) limit of
. It is proven that the non-relativistic limit of
yields a self-adjoint extension of a Hamiltonian of a polaron with spin 1/2 in non-relativistic quantum electrodynamics. 相似文献
16.
We exhibit a finitely generated group whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping
class group associated to a surface of infinite genus, and contains all the pure mapping class groups of compact surfaces of genus g with n boundary components, for any g ≥ 0 and n > 0. We construct a representation of into the restricted symplectic group of the real Hilbert space generated by the homology classes of non-separating circles on , which generalizes the classical symplectic representation of the mapping class groups. Moreover, we show that the first
universal Chern class in is the pull-back of the Pressley-Segal class on the restricted linear group via the inclusion .
L. F. was partially supported by the ANR Repsurf:ANR-06-BLAN-0311. 相似文献
17.
Dyson’s Constants in the Asymptotics of the Determinants of Wiener-Hopf-Hankel Operators with the Sine Kernel 总被引:1,自引:1,他引:0
Torsten Ehrhardt 《Communications in Mathematical Physics》2007,272(3):683-698
Let stand for the integral operators with the sine kernels acting on L
2[0,α]. Dyson conjectured that the asymptotics of the Fredholm determinants of are given by
as α→∞. In this paper we are going to give a proof of these two asymptotic formulas. 相似文献
18.
Serguei I. Iakovlev 《Mathematical Physics, Analysis and Geometry》2006,9(2):109-134
In we consider a family of selfadjoint operators of the Friedrichs model: . Here is the operator of multiplication by the corresponding function of the independent variable , and (perturbation) is a trace-class integral operator with a continuous Hermitian kernel satisfying some smoothness condition. These absolute type operators have one singular point of order . Conditions on the kernel are found guaranteeing the absence of the point spectrum and the singular continuous one of such operators near the origin. These conditions are actually necessary and sufficient. They depend on the finiteness of the rank of a perturbation operator and on the order of singularity . The sharpness of these conditions is confirmed by counterexamples. 相似文献
19.
We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres, in the framework of so-called constant normal restitution coefficients
. In the physical regime of a small inelasticity (that is for some constructive ) we prove uniqueness of the self-similar profile for given values of the restitution coefficient , the mass and the momentum; therefore we deduce the uniqueness of the self-similar solution (up to a time translation).
Moreover, if the initial datum lies in , and under some smallness condition on depending on the mass, energy and norm of this initial datum, we prove time asymptotic convergence (with polynomial rate) of the solution towards the self-similar
solution (the so-called homogeneous cooling state).
These uniqueness, stability and convergence results are expressed in the self-similar variables and then translate into corresponding
results for the original Boltzmann equation. The proofs are based on the identification of a suitable elastic limit rescaling,
and the construction of a smooth path of self-similar profiles connecting to a particular Maxwellian equilibrium in the elastic
limit, together with tools from perturbative theory of linear operators. Some universal quantities, such as the “quasi-elastic
self-similar temperature” and the rate of convergence towards self-similarity at first order in terms of (1−α), are obtained
from our study.
These results provide a positive answer and a mathematical proof of the Ernst-Brito conjecture [16] in the case of inelastic
hard spheres with small inelasticity. 相似文献