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1.
James D. Edmonds Jr. 《Foundations of Physics》1978,8(5-6):439-444
The 2-by-2 Pauli matrix algebra is used to write the 1-by-4 Dirac field in anequivalent 2-by-2 matrix . The current 4-vectors
and *µ are then compared and the latter is shown to not be easily interpretable as a probability density, and also tocontain
. 相似文献
2.
Using the Godement mean of positive-type functions over a groupG, we study -abelian systems {
, } of aC*-algebra
and a homomorphic mapping of a groupG into the homomorphism group of
. Consideration of the Godement mean off(g)U
g
withf a positive-type function overG andU a unitary representation ofG first yields a generalized mean-ergodic theorem. We then define the Godement mean off(g) (
g
(A)) withA
and a covariant representation of the system {
, } for which theG-invariant Hilbert space vectors are cyclic and study its properties, notably in relation with ergodic and weakly mixing states over
. Finally we investigate the discrete spectrum of covariant representations of {
, } (i.e. the direct sum of the finite-dimensional subrepresentations of the associated representations ofG).On leave of absence from Istituto di Fisica G. Marconi Piazzale delle Scienze 5 — Roma. 相似文献
3.
C. W. Rietdijk 《Foundations of Physics》1978,8(7-8):615-628
Quantum theory predicts that, e.g., in a Stern-Gerlach experiment with electrons the measured spin component
does not come about by an adjustment at the last moment, a forced flipping or tilting of the spin (vector), which would imply z-angular momentum exchange between particle and instrument, but will afterward appear to have had the value
already before the measurement. Because an electron spin cannot have components
in all directions at the same time, the measuring direction has a privileged status before the measurement, however we choose that direction, which implies a retroactive effect. A second proof of retroactivity is derived from a special case of the paradox of Einstein, Podolsky, and Rosen. It is strongly suggested by our result that, in essential respects, both Bohr and Einstein were right in their famous controversy about determinism and considering microprocesses as a whole. 相似文献
4.
S. Doplicher R. V. Kadison D. Kastler Derek W. Robinson 《Communications in Mathematical Physics》1967,6(2):101-120
We study pairs {
, } for which
is aC*-algebra and is a homomorphism of a locally compact, non-compact groupG into the group of *-automorphisms of
. We examine, especially, those systems {
, } which are (weakly) asymptotically abelian with respect to their invariant states (i.e. |A
g
(B) —
g
(B)A 0 asg for those states such that (
g
(A)) = (A) for allg inG andA in
). For concrete systems (those with
-acting on a Hilbert space andg
g
implemented by a unitary representationg U
g
on this space) we prove, among other results, that the operators commuting with
and {U
g
} form a commuting family when there is a vector cyclic under
and invariant under {U
g
}. We characterize the extremal invariant states, in this case, in terms of weak clustering properties and also in terms of factor and irreducibility properties of {
,U
g
}. Specializing to amenable groups, we describe operator means arising from invariant group means; and we study systems which are asymptotically abelian in mean. Our interest in these structures resides in their appearance in the infinite system approach to quantum statistical mechanics. 相似文献
5.
Hans Kummer 《Foundations of Physics》1987,17(1):1-62
An axiomatic theory is formulated which describes a class of yes-no experiments, involving a fixed basic source, a fixed basic detector, and various filters. It is assumed that all filters considered can be constructed from a setP of primitive filters by composition and stochastic selection. Two physically plausible axioms are formulated which allow us to define the concept of asystem in the present context (cf. Definition2.4). To each system we can attach anorder unit module (
) (cf. Definition5.1) whereby (
) is acomplete, separable order unit space. Two additional axioms are proposed which have the effect that the space (
) becomes isomorphic to the order unit space underlying a JB-algebra, at least in the case where
isfinite dimensional (cf. Corollary7.9). 相似文献
6.
André Gleyzal 《Foundations of Physics》1976,6(3):299-303
An analytic gravitational fieldZ
(Z
y
) is shown to include electromagnetic phenomena. In an almost flat and almost static complex geometryds
2
=zdzdz of four complex variables z=t, x, y, x the field equationsR
Rz
= –(U
U
– Z
) imply the conventional equations of motion and the conventional electromagnetic field equations to first order if =(Z
v) and =(z
) are expressed in terms of the conventional mass density function
, the conventional charge density function
, and a pressurep as follows:
v=const=p/c
2–10–29 gm/cm3. 相似文献
7.
We examine the BRS cohomology of chiral matter inN=1,D=4 supersymmetry to determine a general form of composite superfield operators which can suffer from supersymmetry anomalies. Composite superfield operators (a, b) are products of the elementary chiral superfieldsS and
and the derivative operatorsD
,
and
. Such superfields (a, b) can be chosen to have a symmetrized undotted indices
i
and b symmetrized dotted indices
. The result derived here is that each composite superfield (a,b) is subject to potential supersymmetry anomalies ifa–b is an odd number, which means that (a,b) is a fermionic superfield. 相似文献
8.
Recently, a class of
-invariant scalar quantum field theories described by the non-Hermitian Lagrangian
=
()
2
+g
2
(i) was studied. It was found that there are two regions of . For <0 the
-invariance of the Lagrangian is spontaneously broken, and as a consequence, all but the lowest-lying energy levels are complex. For 0 the
-invariance of the Lagrangian is unbroken, and the entire energy spectrum is real and positive. The subtle transition at =0 is not well understood. In this paper we initiate an investigation of this transition by carrying out a detailed numerical study of the effective potential V
eff
(c) in zero-dimensional spacetime. Although this numerical work reveals some differences between the <0 and the >0 regimes, we cannot yet see convincing evidence of the transition at =0 in the structure of the effective potential for
-symmetric quantum field theories. 相似文献
9.
Toshiharu Kawai 《General Relativity and Gravitation》1986,18(10):995-1018
We develop a gauge theory of gravity on the basis of the principal fiber bundle over the four-dimensional space-timeM with the covering groupP¯
0
of the proper orthochronous Poincaré group. The field components
are constructed with the connection coefficients
,
and with a Higgs-type field. A Lorentz metricg is introduced with
, which are then identified with the components of duals of the Vierbein fields. Associated with there is a spinor structure onM. For Lagrangian densityL, which is a function of
,
,, matter field , and oftheir first derivatives, we give the conditions imposed by the requirement of the
gauge invariance. The Lagrangian densityL is restricted to be of the formL =L
tot
(, T
klm
,R
klmn
,
k
, ), in whichT
klm
,R
klmn
are the field strengths of
,
, respectively. Identities and conservation laws following from the
gauge invariance are given. Particularly noteworthy is the fact that the energy momentum conservation law follows from theinternal translational invariance. The field equation of is automatically satisfied, if those of
and of are both satisfied. The possible existence of matter fields with intrinsic energy momentum is pointed out. When is a field with vanishing intrinsic energy momentum, the present theory practically agrees with the conventional Poincaré gauge theory of gravity, except for the seemingly trivial terms in the expression of the spin-angular momentum density. A condition leading to a Riemann-Cartan space-time is given. The field holds a key position in the formulation. 相似文献
10.
The geometro-stochastic quantization of a gauge theory based on the (4,1)-de Sitter group is presented. The theory contains an intrinsic elementary length parameter R of geometric origin taken to be of a size typical for hadron physics. Use is made of a soldered Hilbert bundle over curved spacetime carrying a phase space representation of SO(4, 1) with the Lorentz subgroup related to a vierbein formulation of gravitation. The typical fiber of is a resolution kernel Hilbert space
constructed in terms of generalized coherent states
related to the principal series of unitary irreducible representations of SO(4, 1), namely de Sitter horospherical waves for spinless particles characterized by the parameter . The framework is, finally, extended to a quantum field-theoretical formalism by using bundles with Fock space fibers constructed from
.Supported in part by NSERC Research Grant No. A5206. 相似文献
11.
Domingos H. U. Marchetti Abel Klein J. Fernando Perez 《Journal of statistical physics》1990,60(1-2):137-166
We give a rigorous proof of power-law falloff in the Kosterlitz-Thouless phase of a two-dimensional Coulomb gas in the sense that there exists a critical inverse temperaturegb and a constant >0 such that for all> and all external charges R we have
, whereG
(x) is the two-point external charges correlation function,=dist(, Z), and
for
0$$
" align="middle" border="0">
. In the case of a hard-core or standard Coulomb gas with activityz, we may choose=(z) such that(z)24 asz0. 相似文献
12.
D. Kastler M. Mebkhout G. Loupias L. Michel 《Communications in Mathematical Physics》1972,27(3):195-222
With
aC*-algebra with unit andgG
g
a homomorphic map of a groupG into the automorphism group ofG, the central measure
of a state of
is invariant under the action ofG (in the state space of
) iff is -invariant. Furthermore if the pair {
,G} is asymptotically abelian, is ergodic iff
is ergodic. Transitive ergodic states (corresponding to transitive central measures) are centrally decomposed into primary states whose isotropy groups form a conjugacy class of subgroups. IfG is locally compact and acts continuously on
, the associated covariant representations of {
, } are those induced by such subgroups. Transitive states under time-translations must be primary if required to be stable. The last section offers a complete classification of the isotropy groups of the primary states occurring in the central decomposition of euclidean transitive ergodic invariant states. 相似文献
13.
R. N. Chaudhuri 《Czechoslovak Journal of Physics》1986,36(8):930-932
The Hill determinant method is discussed in the context ofq
confinement power potential of typeV(r)= – V
0–a/r + br, b > 0, which is commonly used for thec
andb
systems. The masses predicted by the potential are in good agreement with the experimental results.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia May 27–June 1, 1985. 相似文献
14.
W. Drechsler 《Foundations of Physics》1989,19(12):1479-1497
To represent extension of objects in particle physics, a modified Weyl theory is used by gauging the curvature radius of the local fibers in a soldered bundle over space-time possessing a homogeneous space G/H of the (4, 1)-de Sitter group G as fiber. Objects with extension determined by a fundamental length parameter R0 appear as islands D(i) in space-time characterized by a geometry of the Cartan-Weyl type (i.e., involving torsion and modified Weyl degrees of freedom). Farther away from the domains D(i), space-time is identified with the pseudo-Riemannian space of general relativity. Extension and symmetry breaking are described by a set of additional fields (
, given as a section on an associated bundle
over space-time B with structural group
= G D(1), where D(1) is the dilation group. Field equations for the quantities defining the underlying bundle geometry and for the fields
are established involving matter source currents derived from a generalized spinor wave function. Einstein's equations for the metric are regarded as the part of the
-gauge theory related to the Lorentz subgroup H of G exhibiting thereby the broken nature of the
-symmetry for regions outside the domains D(i).Talk presented at the International Conference on Field Theory and General Relativity held at Utah State University, Logan, Utah, June 26–July 2, 1988. 相似文献
15.
R. F. Streater 《Communications in Mathematical Physics》1966,2(1):354-374
The dynamical variables of a classical system form a Lie algebra
, where the Lie multiplication is given by the Poisson bracket. Following the ideas ofSouriau andSegal, but with some modifications, we show that it is possible to realize
as a concrete algebra of smooth transformations of the functionals on the manifold
of smooth solutions to the classical equations of motion. It is even possible to do this in such a way that the action of a chosen dynamical variable, say the Hamiltonian, is given by the classical motion on the manifold, so that the quantum and classical motions coincide. In this realization, constant functionals are realized by multiples of the identity operator. For a finite number of degrees of freedom,n, the space of functionals can be made into a Hilbert space using the invariant Liouville volume element; the dynamical variablesF become operators
in this space. We prove that for any hamiltonianH quadratic in the canonical variablesq
1...q
n
,p
1...p
n
there exists a subspace
1 which is invariant under the action of
and
, and such that the restriction of
to
1 form an irreducible set of operators. Therefore,Souriau's quantization rule agrees with the usual one for quadratic hamiltonians. In fact, it gives the Bargmann-Segal holomorphic function realization. For non-linear problems in general, however, the operators
form a reducible set on any subspace of invariant under the action of the Hamiltonian. In particular this happens for
. Therefore,Souriau's rule cannot agree with the usual quantization procedure for general non-linear systems.The method can be applied to the quantization of a non-linear wave equation and differs from the usual attempts in that (1) at any fixed time the field and its conjugate momentum may form a reducible set (2) the theory is less singular than usual.For a particular wave equation
, we show heuristically that the interacting field may be defined as a first order differential operator acting onc
-functions on the manifold of solutions. In order to make this space into a Hilbert space, one must define a suitable method of functional integration on the manifold; this problem is discussed, without, however, arriving at a satisfactory conclusion.On leave from Physics Department, Imperial College, London SW7.Work partly supported by the Office of Scientific Research, U.S. Air Force. 相似文献
16.
O. Costa de Beauregard 《Foundations of Physics》1982,12(9):861-871
We show that particle-antiparticle exchange and covariant motion reversal are two physically different aspects of the same mathematical transformation, either in the prequantal relativistic equation of motion of a charged point particle, in the general scheme of second quantization, or in the spinning wave equations of Dirac and of Petiau-Duffin-Kemmer. While, classically, charge reversal and rest mass reversal are equivalent operations, in the wave mechanical case mass reversal must be supplemented by exchange of the two adjoint equations, implying
.Denoting by M the rest mass reversal, P the parity reversal, T the Racah time reversal, and Z the
exchange, the connection with the usual scheme of charge conjugation, parity reversal, and Wigner motion reversal, is with, of course, 相似文献
17.
We have examined the influence of parametric noise on the solution behavioru(t, x) of a nonlinear initial value() problem arising in cell kinetics. In terms of ensemble statistics, the eventual limiting solution mean
and variance
are well-characterized functions of the noise statistics, and
and
depend on . When noise is continuously present along the trajectory,
and
are independent of the noise statistics and . However, in their evolution toward
and
, both
u
(t, x) and
u
2
(t, x) depend on the noise and. 相似文献
18.
Wang Zheng Dong 《Letters in Mathematical Physics》1996,38(4):377-388
By considering the cohomology of the loop algebraL
, a representation ofL
is constructed. the construction is based on a derivation ofL
and a two-dimensional closed cochain ofl
with coefficients in real numbersR
1. In the case of =0, the differential of the energy representation of the corresponding loop groupLG is derived.This work was supported in part by the National Natural Science Foundation of China. 相似文献
19.
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
20.
S. Ozawa 《Communications in Mathematical Physics》1984,94(4):421-437
Let be a fixed number >1. We remove [m
]-balls of centersw
1, ...,
with the same radius /m from a bounded domain inR
3. We consider the asymptotic behaviour of thek
th eigenvalue of the Laplacian in
under the Dirichlet condition as a random variable on a probability space
, whenm. 相似文献