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1.
A post-Newtonian analysis of the theory of gravity based on the metric g
ij( x,y)=
ij( x)+ /c
2(1–1 n
2) y
iy j with the index of refraction n(x, y) is given. A generalized Lagrange space endowed with this metric is used for the study of gravitational phenomena. The index of refraction n(x, y) is expanded in integer powers of the gravitational potential U= GM/rc
2 and v
2/ c
2. It is shown that solar system tests impose a constraint on a combination of the constant , the post-Newtonian parameters defining the index of refraction n(x, y), and the post-Newtonian parameter associated to the Riemannian metric
ij( x). 相似文献
2.
Some structural considerations are made on the Finslerian gravitational field: A Finslerian metrical structure such as gλχ( x, y) = γ λχ( x) + hλχ( x, y) is proposed, where γ λχ denotes the Riemann metric of Einstein's gravitational field, while hλχ the Finsler metric induced by the Riemann metric hij( y) of the internal field; The intrinsic behaviour of the internal variable y, which is expressed as ? i = K( x, y) yj in the internal field, is grasped by the Finslerian parallelism δ yi (=0), which is reflected in the spatial structure of the external gravitational field by the mapping relation δy χ = e( x) δ yi. The whole metrical Finsler connection D for gλχ(i.e., Dgλχ = 0) is determined by taking account of the intrinsic behaviour δ yχ. 相似文献
3.
This paper demonstrates the existence of non-trivial solutions ( g, k) to the constraint equations of the initial value formulation of the Einstein field equations over 3 with g
ij
–
ij
| x| –1 as | x| . Using the conformal methods of Lichnerowicz and York, this problem is divided into two parts. First, using weighted Sobolev spaces it is shown the set of pairs ( g, k) with g a conformal metric and k transverse-traceless with respect to g forms a smooth vector bundle P with infinite dimensional fiber. Second, it is shown that the elements of a large open set in P uniquely determine a solution to the scalar constraint equation with the appropriate growth at infinity, and thereby determine solution to the constraint equations. 相似文献
4.
It is shown that the charged symplectic form in Hamiltonian dynamics of classical charged particles in electromagnetic fields defines a generalized affine connection on an affine frame bundle associated with spacetime. Conversely, a generalized affine connection can be used to construct a symplectic 2-form if the associated linear connection is torsion-free and the antisymmetric part of the R
4* translational connection is locally derivable from a potential. Hamiltonian dynamics for classical charged particles in combined gravitational and electromagnetic fields can therefore be reformulated as a P(4)= O(1, 3) R
4* geometric theory with phase space the affine cotangent bundle AT
*
M of spacetime. The sourcefree Maxwell equations are reformulated as a pair of geometrical conditions on the 4* curvature that are exactly analogous to the source-free Einstein equations. 相似文献
5.
In this paper we prove results in resonance scattering for the Schrödinger operator P
v=– h
2+ V, V being a smooth, short range potential on R
n
. More precisely, for energy near a trapping energy level 0 for the classical system defined by the Hamiltonian p( x,)=
2+ V( x), we prove that the scattering phase and the scattering cross sections associated to ( P
v, P 0) have the Breit-Wigner form (Lorentzian line shape) in the limit h0. 相似文献
6.
This paper presents a coordinate-dependent 3+ 1 decomposition of the general relativity field equations in terms of a scalar potential c
2[(– g
44) 1/2–1], a vector potential A
icg
4i/(–g 44) 1/2, and the three-space metric
ijg
ij–g 4i
g
4j/ g
44. The equations are exact and the form of the decomposed equations is valid in any coordinate system. 相似文献
7.
We consider percolation on the sites of a graph G, e.g., a regular d-dimensional lattice. All sites of G are occupied (vacant) with probability p (respectively, q=1–p), independently of each other. W denotes the cluster of occupied sites containing a fixed site (which will usually be taken to be the origin) and W the cardinality of W. The percolation probability is the probability that # W=, i.e., (p)=P
p{# W=}. Some critical values of p,p
H and p
T, are defined, respectively, as the smallest value of p for which (p)> 0, and for which the expectation of # W is infinite. Formally, p
H=inf { p(p)>0} and p
T=inf{ p E
p{# W}=}. We show for fairly general graphs Gthat if p
T, thenP
P{#W n} decreases exponentially inn. For the special casesG =G
0= the simple quadratic lattice andG
1= the graph which corresponds to bond-percolation on 2, we obtain upper and lower bounds for(p) of the formC¦p¦-P
H¦, and bounds forEp{#W} of the formC¦p–p
H¦–. We also investigate smoothness properties of (p)=E
p{number of clusters per site} =E
p {(#W)–1; (#W) 1}. This function was introduced by Sykes and Essam, who assumed that (·) has exactly one singularity, namely, atp=p
H. For the graphsG
0 andG
1, (i.e., site or bond percolation on 2) we show that (p) is analytic atp p
H and has two continuous derivatives atp=p
H. The emphasis is on rigorous proofs.Research supported by the NSF through a grant to Cornell University. 相似文献
8.
A microwave frequency standard based on buffer gas-cooled 171Yb + ions confined in a linear Paul trap has been demonstrated in prototype form. The standard exhibits a fractional frequency instability characterised by an Allan deviation of ( y() = 2.9 × 10 –13–1/2 for < 2 × 10 4 s. Factors affecting the stability of the standard have been systematically investigated. 相似文献
9.
We have found a static electrically charged solution to the Einstein-Maxwell equations in a (2+1)-dimensional space-time. Studies of general relativity in lower dimensional space-times provide many new insights and a simplified arena for doing quantum mechanics. In (2+1)-dimensional space-time, solutions to the vacuum field equations are locally flat (point masses are conical sigularities), but when electromagnetic fields are present T
ab
O and the solutions are curved. For a static charge Q we find
and ds
2= –( kQ
2
/2)In( r
c
/ r) dt
2 + (2 /kQ
2[ln( r
c
/ r)] –1
dr
2 + r
2
d
2 where r
c
is a constant. There is a horizon at r = r
c
like the inner horizon of the Reisner-Nordström solution. We have produced a Kruskal extension of this metric which shows two static regions (I and III) with r < r
c
and two dynamical regions (II and IV) with r> r
c
. A spacelike slice across regions I and III shows a football-shaped universe with charge Q at one end and – Q at the other. Slices in the dynamical regions (II and IV) show a cylindrical universe that is expanding in region II and contracting in region IV. Electromagnetic solutions to the Einstein-Maxwell field equations in lower dimensional space-times can be used to provide new insights into Kaluza-Klein theories. In terms of the Kaluza-Klein theory, for example, electromagnetic radiation in a (2+1)-dimensional space-time is really gravitational radiation in the associated (3+1)-dimensional Kaluza-Klein space-time. According to Kaluza Klein theory the absence of gravitational radiation in (2+1)-dimensional space-time implies (correctly) the absence of electromagnetic radiation in (1+1)-dimensional space-time. 相似文献
10.
The static energy-density correlation function S
2(0) S
2( x)– S
22 is calculated in the critical region for the S
4 Ginzburg-Landau-Wilson model at short distances and for nonzero field. Short distance expansion is used and its structure for more complex vertex functions is given. Goldstone mode singularities present at the magnetization curve are taken into account. The main application is given in the theory of polymer solutions. Here, S
2(0) S
2( x)– S
22 becomes the Fourier transform of the densitydensity correlation. 相似文献
11.
A method for solving Kirkwood-type equations in Banach spaces E
() and E
S
() is applied to derive spectral properties of Kirkwood-Salsburg and Kirkwood-Ruelle operators in these spaces. For stable interactions these operators are shown to have, besides the point spectrum, a residual one. We establish also that the residual spectrum may disappear if a superstable (singular) interaction between particles is switched on. In this case the bounded Kirkwood-Salsburg operator is proved to have a zero Fredholm radius. 相似文献
12.
The dynamical meaning of the equations T
/j/ij
=0 is derived as a consequence of the mathematical structure of Einstein's equations. A generalization of Lichnerowicz's analysis of the gravitational equations is proposed.Lavoro eseguito nel centro di Matematica e Fisica Teorica del C.N.R. presso l'Università di Genova. 相似文献
13.
This paper deals with space-times that satisfy the Einstein-Maxwell field equations in the presence of a perfect fluid, which may be charged. The electromagnetic field is assumed to be null. It is proved that if the space-time admits a group of isometrics then the fluid velocity u
i, energy density , pressure p, and charge density are invariant under the group. In addition, if the charge density is nonzero, the electromagnetic field tensor f
ij is also invariant. On the other hand, examples of exact solutions are given which establish that if = 0, then F
ij is not necessarily invariant under the group. In the case of spherically symmetric space-times, however, in which the group of isometries acting is SO (3), f
ij is invariant, independently of whether or not is nonzero. This result leads to the conclusion that in a spherically symmetric space-time the field equations in question admit no solutions with non-trivial null electromagnetic field. 相似文献
14.
We consider the assumption that clocks measure proper time-that is, in a gravitational field ideal clocks are governed by the equation ds
2= g
ij
dx i dx j-and give some theoretical and experimental constraints on clock measurements. In particular, we find that if we assume that clocks are governed by an equation of the form ds
4= c
ijkl
dx i dx j dx k dx l, then this equation must reduce to the quadratic equation in a weak, spherically symmetric, static gravitational field (at least to first order in the Newtonian gravitational potential U), otherwise additional contributions to the time-delay effect of radar propagation (that are not observed) are predicted. 相似文献
15.
Using zinc octa(diethoxyphosphenylmethyl)phthalocyanine as an example, we determined experimentally the quantum yield of generation of singlet oxygen ( ) which makes it possible to evaluate quantitatively the efficiency of photogeneration of 1O 2 and the influence of biomolecules on this parameter. It is shown that the efficiency of generation of singlet oxygen by the sensitizers used in photodynamic therapy depends on their state in a solution and increases with disaggregation of the dye and its interaction with biomolecules. It is established that phthalocyanine in an aqueous buffer solution sensitizes the formation of 1O 2 with the quantum yield = 0.16 ± 0.02. On introduction of the detergent Triton X100 into the buffer solution of phthalocyanine, increases up to 0.48 ± 0.07. In a microheterogeneous medium (buffer + albumin) = 0.42. 相似文献
16.
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=0 of 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
17.
We present a consistent set of commutation relations (C.R.) for a quantum system immersed in a classical gravitational field. The gravity field is described by metric tensor g
ik
(x) and g
00( x) with coordinate gauge g
i0=0. The Hamiltonian of the system is found to be a linear function of [– g
00( x)] 1/2. Its properties we define by C.R. avoiding explicit expression in terms of fields, as well as its splitting into free and interaction parts. In this way a consistent set of C.R., which are equally simple for a flat and curvilinear space, can be established. To stress the main idea of our approach, we consider the simple but still nontrivial example of a scalar electrodynamics immersed in a gravity field. The electromagnetic current operator we define by its C.R. and not explicitly. An interesting feature of this approach is that the Poisson equation follows from the consistency of the C.R. The C.R. for the energy and momentum operators of the system in a gravity field are established which generalize the usual Poincare group generators C.R. For example, we find ( i/hc
2)[ H
(x)
, H
(x)
]= P
–
, where H
(x)
is the Hamiltonian of the system, which is a linear functional of ( x)[– g
00( x)] 1/2 and P
s(x)
represents the momentum-density operator [averaged with the classical function s(x)]. 相似文献
18.
Given a curved space-time with a metric tensor g
ij, Maxwell's equations may be written as if they were valid in a flat space-time in which there is an optical medium with a constitutive equation.When optical phenomena are considered, this medium turns out to be equivalent to the gravitational field. Optical phenomena in various gravitational fields are analysed and we find that the language of classical optics for the equivalent medium is as suitable as that of Riemannian geometry.This work was started at the Department of Applied Mathematics and Theoretical Physics, Cambridge, England. 相似文献
19.
We study the Ising and N-vector spin glasses with exchange couplings J=( J
ij
; i, j Z
d
), which are independent random variables with EJ ij=0 and EJ
n
ij
n
n!¦i–j¦
–nd
, for n, some finite constant >0, and >1/2. For sufficiently small , we show that for E-a.a. J there is a weakly unique, extremal, infinite-volume Gibbs measure J for which the expectation of a single (component of) spin vanishes and which has the cluster property in L
2( E) with the same decay as interaction. This work is based on results and methods of Fröhlich and Zegarlinski. 相似文献
20.
The first theorem states that all flat space-time gravitational theories must have a Lagrangian with a first term that is an homogeneous (degree-1) function of the 4-velocity u
i
, plus a functional of
ij
u
i
u
j
. The second theorem states that all gravitational theories, that satisfy the strong equivalence principle have a Lagrangian with a first term g
ij
( x) u
i
u
j
plus an irrelevant term. In both cases the theories must issue from a unique variational principle. Therefore, under this condition it is impossible to find a flat space-time theory that satisfies the strong equivalence principle. 相似文献
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