共查询到20条相似文献,搜索用时 46 毫秒
1.
G. Tauber 《General Relativity and Gravitation》1980,12(12):1043-1054
The spin-two particle is described by a symmetric tensorh
subject to the subsidiary conditionsh
=
h
=0. Their covariant generalization and the wave equation have been obtained directly from the Eulerian variational equations by algebraic methods only. In addition to the tensor fieldh
a symmetric third-rank tensor
=
as well as a vector fieldA
have been added, neither of which enter in the final result. The Lagrangian function is taken as a linear sum of all combinations which can be constructed from these functions, as well as terms involving the curvature tensor and its two possible contractions. Variation with respect toh
,
andA
independently gives the Euler equations. Combining the various trace equations and choice of arbitrary constants yields the subsidiary conditions, while the Euler equations themselves give the connection between the auxiliary functions and the tensorh
as well as the generalization of the wave equationD
D
h
+ 2R
h
-R
h
-R
h
+g
R
h
+Rh
=m
2
h
Finally, variation with respect tog
yields the energy-momentum tensor. 相似文献
2.
Christian Schindler 《International Journal of Theoretical Physics》1991,30(11):1409-1430
Every convex subset of a locally convex Hausdorff space (X, ) is equipped with the (-algebra generated by its-relatively open subsets. Within the set () of probability measures on two particular convex subsets are considered: (a) the set
s
() of probability measures with a separable support, and (b) the set
c
() of probability measures with a compact convex support. If is the base of a cone inX, then there exists an affine barycenter map from
c
() onto whose composition with the natural embedding of in
c
() yields the identity map on , and every-continuous affine transformation of can be represented by an affine transformation of
c
() that is induced by a Markov kernel. If (X, ) is a Banach space and is a closed, bounded, generating cone base inX that is contained in a hyperplane, then analogous results are obtained with respect to
s
(). Since the state spaces considered in noncommutative measure theory are cone bases and every change in time of an empirical system can be thought of as an affine transformation of the associated state space (Schrödinger picture), the existence of these representation theorems implies that the time evolution of general empirical systems can be described by dynamical concepts borrowed from classical probability theory. 相似文献
3.
Giampiero Esposito Hugo Morales-Técotl Giuseppe Pollifrone 《Foundations of Physics Letters》1994,7(3):303-308
Local supersymmetry leads to boundary conditions for fermionic fields in one-loop quantum cosmology involving the Euclidean normal
e
n
A/A
to the boundary and a pair of independent spinor fields
A
and
. This paper studies the corresponding classical properties, i.e., the classical boundary-value problem and boundary terms in the variational problem. If
is set to zero on a 3-sphere bounding flat Euclidean 4-space, the modes of the massless spin–1/2 field multiplying harmonics having positive eigenvalues for the intrinsic 3-dimensional Dirac operator onS
3 should vanish onS
3. Remarkably, this coincides with the property of the classical boundary-value problem when spectral boundary conditions are imposed onS
3 in the massless case. Moreover, the boundary term in the action functional is proportional to the integral on the boundary of
A
e
n
AA
A
. 相似文献
4.
Kazimierz Bragiel 《Letters in Mathematical Physics》1989,17(1):37-44
Irreducible *-representations of C(SU(3)) are constructed for ]0, 1[. It is proved that C(SU(3)) is a type-I C
*-algebra. 相似文献
5.
Let H be a semibounded perturbation of the Laplacian H
0 in L
2(
d
). For an admissible function sufficient conditions are given for the completeness of the scattering system (H), (H
0). If is the exponential function and if e– H
is an integral operator we denote the kernel of the difference D
= e– H
– e– H
0 by D
(x, y), > 0. The singularly continuous spectrum of H is empty ifd dx
d dy |D(x,y)| (1 + |y|2)< for some > 1. This result is applied to potential perturbations and to perturbations by imposing Dirichlet boundary conditions. 相似文献
6.
Michael B. Mensky 《Foundations of Physics》1992,22(9):1173-1193
The path-integral approach to quantum theory of continuous measurements has been developed in preceding works of the author. According to this approach the measurement amplitude determining probabilities of different outputs of the measurement can be evaluated in the form of a restricted path integral (a path integral in finite limits). With the help of the measurement amplitude, maximum deviation of measurement outputs from the classical one can be easily determined. The aim of the present paper is to express this variance in a simpler and transparent form of a specific uncertainty principle (called the action uncertainty principle, AUP). The most simple (but weak) form of AUP is S, whereS is the action functional. It can be applied for simple derivation of the Bohr-Rosenfeld inequality for measurability of gravitational field. A stronger (and having wider application) form of AUP (for ideal measurements performed in the quantum regime) is |
t
(S[q]/q(t))q(t)dt|, where the paths [q] and [q] stand correspondingly for the measurement output and for the measurement error. It can also be presented in symbolic form as (Equation) (Path) . This means that deviation of the observed (measured) motion from that obeying the classical equation of motion is reciprocally proportional to the uncertainty in a path (the latter uncertainty resulting from the measurement error). The consequence of AUP is that improving the measurement precision beyond the threshold of the quantum regime leads to decreasing information resulting from the measurement. 相似文献
7.
Janusz Grabowski 《Letters in Mathematical Physics》1994,32(4):307-313
Starting from the Gelfand-Fuks-Virasoro cocycle on the Lie algebraX(S
1) of the vector fields on the circleS
1 and applying the standard procedure described by Drinfel'd in a finite dimension, we obtain a classicalr-matrix (i.e. an elementr
X(S
1) X(S
1) satisfying the classical Yang-Baxter equation), a Lie bialgebra structure onX(S
1), and a sort of Poisson-Lie structure on the group
of diffeomorphisms. Quantizations of such Lie bialgebra structures may lead to quantum diffeomorphism groups.Research supported by the Erwin Schrödinger International Institute for Mathematical Physics. 相似文献
8.
E. Duering R. Blumenfeld D. J. Bergman A. Aharony M. Murat 《Journal of statistical physics》1992,67(1-2):113-121
The current and logarithm-of-the-current distributionsn(i) andn(ln i) on bond diluted two-dimensional random-resistor networks at the percolation threshold are studied by a modified transfer matrix method. Thek th moment (–9k8) of n(ln i) i.e., ln i&k, is found to scale with the linear sizeL as (InL)(k). The exponents (k) are not inconsistent with the recent theoretical prediction (k)=k, with deviations which may be attributed to severe finitesize effects. For small currents, ln n(y)–, yielding information on the threshold below which the multifractality of
(i) breaks down. Our numerical results for the moments of the currents are consistent with other available results. 相似文献
9.
We establish an analogue of Weyl's classical theorem for the asymptotics of eigenvalues of Laplacians on a finitely ramified (i.e., p.c.f.) self-similar fractalK, such as, for example, the Sierpinski gasket. We consider both Dirichlet and Neumann boundary conditions, as well as Laplacians associated with Bernoulli-type (multifractal) measures onK. From a physical point of view, we study the density of states for diffusions or for wave propagation in fractal media. More precisely, let (x) be the number of eigenvalues less thanx. Then we show that (x) is of the order ofx
d
S/2 asx+, where the spectral exponentd
S
is computed in terms of the geometric as well as analytic structures ofK. Further, we give an effective condition that guarantees the existence of the limit ofx
–d
S/2(x) asx+; this condition is, in some sense, generic. In addition, we define in terms of the above spectral exponents and calculate explicitly the spectral dimension ofK.The research of Michel L. Lapidus was partially supported by the National Science Foundation under Grant DMS-8904389 (transferred to the University of California as grant DMS-9196085) and Grant DMS-9207098, as well as by Yale University 相似文献
10.
John Dauns 《International Journal of Theoretical Physics》1988,27(2):183-192
Four-dimensional space-time, all relevant inner products, and some of the groups leaving these inner products invariant are manufactured from more basic algebraic ingredients, all inside the 8-dimensional Pauli algebra : (1) Euclidean 3-spaceE
3, (2) Minkowski 4-spaceM
4, (3) complex 4-space 4, and all three metrics and all three inner products. The groupsSO(3;) SO(3; 1;) SO (4;) are obtained as images of twofold covering maps of subgroups of or their direct product. A method of embedding in the Clifford algebraC(1;n–1) ofn-dimensional Minkowski space is given for anyn4. Furthermore, all three groups act not only on the relevant vector spaces, but on all ofC(1;n–1), leaving setwise invariant. 相似文献
11.
Yoel Tikochinsky 《International Journal of Theoretical Physics》1988,27(5):543-549
Starting with very simple assumptions, Feynman rules for the quantum mechanical amplitudes and the associated probabilities are derived. These rules emerge as the only consistent rules for manipulating complex amplitudes assigned to processes. The probability of a process to which an amplitudex has been assigned is determined asp(x)=|x|
, 0<2. If virtual processes are allowed,=2. 相似文献
12.
We present an example of a generalized Brownian motion. It is given by creation and annihilation operators on a twisted Fock space ofL
2(). These operators fulfill (for a fixed –11) the relationsc(f)c
*
(g)–c
*
(g)c(f)=f,g1 (f, g L
2()). We show that the distribution of these operators with respect to the vacuum expectation is a generalized Gaussian distribution, in the sense that all moments can be calculated from the second moments with the help of a combinatorial formula. We also indicate that our Brownian motion is one component of ann-dimensional Brownian motion which is invariant under the quantum groupS
U(n) of Woronowicz (with =v
2). 相似文献
13.
J. Schnakenberg 《Zeitschrift für Physik B Condensed Matter》1980,38(4):341-349
The fluctuations in limit cycles of second-order bifurcation (transition from a stable to an unstable focus) are investigated near the bifurcation point c, being an external control parameter. Two different methods are applied: a time- and space-dependent Fokker-Planck equation obtained from an 1/2-expansion of the master equation ( being the volume) and a time- and space-dependent Langevin equation. Both methods give the same results. It is shown that the dependence of the radial correlation on 2 = | – c| and the time-behaviour of the phase correlation (ensemble dephasing) are determined by the dimensionality of space. 相似文献
14.
The instability of spin waves at ferromagnetic resonance is discussed. An equation of the stationary state of spin wavesk0 is derived by means of the quantum theory of spin waves. It is shown when discussing this equation that the concept of the critical uniform precession angle may be obtained when using an approximation which neglects the action of spin wavesk0 backward on their own excitation. We believe we are justified in supposing that, due to this effect, a stable stationary state can exist even above the critical amplitude of uniform precession, given by theories up to now.
In conclusion the author thanks G. A. Smolenskij for enabling him to carry out this work in his laboratory. Thanks also go to the theoretical staff of the Institute of Semi-conductors of Acad. Sci. USSR in Leningrad for valuable discussions, especially to A. I. Anselm, V. L. Gurevic and J. A. Firsov. 相似文献
. k0. , , k0 . , , , , .
In conclusion the author thanks G. A. Smolenskij for enabling him to carry out this work in his laboratory. Thanks also go to the theoretical staff of the Institute of Semi-conductors of Acad. Sci. USSR in Leningrad for valuable discussions, especially to A. I. Anselm, V. L. Gurevic and J. A. Firsov. 相似文献
15.
C. Dullemond 《General Relativity and Gravitation》1988,20(2):139-170
A classical, Poincaré invariant dynamical system is developed which contains, besides the natural metric
v
, an induced metricg
v
that is generated by a real scalar dynamical field. It is shown that scalar fields whose dynamics are governed by the induced metric can be consistently introduced. Also, point particles which follow timelike quasi-geodesic trajectories can be introduced. The reaction forces acting ong
v
due to the presence of these fields and particles are computed. A discussion of causality and geometrical confinement is given. 相似文献
16.
E. Leutheusser 《Zeitschrift für Physik B Condensed Matter》1984,55(3):235-240
A nonlinear equation of motion of an overdamped oscillator exhibiting a glass-like transition at a critical coupling constant
c
is presented and solved exactly. Below
c
, in the fluid phase, the oscillator coordinatex(t) decays to zero, while above
c
, in the amorphous phase, it decays to a nonzero infinite time limit. Near
c
the motion is slowed down by a nonlinear feedback mechanism andx(t) decays exponentially to its long time limit with a relaxation time diverging as (1 – /
c
)–3/2 and (/
c
–1)–1 for <
c
and >
c
respectively. At
c
x(t) exhibits a power law decay proportional tot
– with exponent -1/2. 相似文献
17.
Denote byX
q
the reduced space ofSU
2 monopoles of chargeq in 3. In this paper the cohomology ofX
q
, the cohomology with compact supports ofX
q
, and the image of the latter in the former are all calculated as representations of /q which acts onX
2. This provides a non-trivial lower bound for theL
2 cohomology ofX
q
which is compatible with some conjectures of Sen. It is also shown that, granted some assumptions about the metric onX
q
, itsL
2 cohomology does not exceed this bound in the situation referred to in the paper as the coprime case.The work described here was carried out partly at the University of Texas at Austin. 相似文献
18.
Coherent vacuum ultraviolet (VUV) radiation was generated by four-wave difference frequency mixing (VUV=21–2) of pulsed dye laser radiation in carbon monoxide (CO). The frequency 1 was tuned to the C
1+(=0)X
1+(=0) two-photon transition, while the dye laser frequency 2 was scaned around 17650 cm–1 which corresponds to the A
1(=7)«C
1+(=0) transition energy. The VUV intensity was found to be strongly wavelength dependent. The analysis of the spectrum revealed (i) that the VUV intensity was enhanced by the rotational levels of the A
1(=7) state and (ii) that the off-resonance excitation in the C
1+(=0)X
1+(=0) two-photon transition greatly contributed to the present four-wave mixing process. The effects of pumping laser detuning, saturation and foreign gases are briefly discussed. 相似文献
19.
Sergey V. Ershov 《Journal of statistical physics》1992,69(3-4):781-812
A delay-differential equationu(t)+u(t)=f(u(t–1)), 0t < , and its generalization are investigated in the limit 0, when the attractor's dimension increases infinitely. It is shown that a number of statistical characteristics are asymptotically independent of. As for the attractor, it can be regarded as a direct product ofO(1/) equivalent subattractors, their statistical characteristics being asymptotically independent of . The results enable one to predict some characteristics of the attractor with fractal dimensionD 1 for the case 1, when they are inaccessible numerically. The approach developed seems to be applicable for a wide class of spatiotemporal systems. 相似文献
20.
We investigate the time evolution of a model system of interacting particles moving in a d-dimensional torus. The microscopic dynamics is first order in time with velocities set equal to the negative gradient of a potential energy term plus independent Brownian motions: is the sum of pair potentials, V(r)+
d
J(r); the second term has the form of a Kac potential with inverse range . Using diffusive hydrodynamic scaling (spatial scale
–1, temporal scale
–2) we obtain, in the limit 0, a diffusive-type integrodifferential equation describing the time evolution of the macroscopic density profile. 相似文献