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1.
S. L. Woronowicz 《Communications in Mathematical Physics》1972,28(3):221-235
Let
be aC*-algebra and
be an opposite algebra. Notions of exact andj-positive states of
are introduced. It is shown, that any factor state of
can be extended to a pure exactj-positive state
of
. The correspondence
generalizes the notion of the purifications map introduced by Powers and Størmer. The factor states 1 and 2 are quasi-equivalent if and only if their purifications
and
are equivalent. 相似文献
2.
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
3.
G. Date T. R. Govindarajan P. Sankaran R. Shankar 《Communications in Mathematical Physics》1990,132(2):293-313
We compute the homotopy groups
0 and
1 of the classical configuration space of anO(3) invariant field theory on
×, where
is a compact two dimensional manifold for arbitrary genusg and- denotes the time coordinate. We also present the finite dimensional, unitary, irreducible, inequivalent representations of the appropriate fundamental groups and comment on some of their implications. 相似文献
4.
Richard L. Liboff 《International Journal of Theoretical Physics》2002,41(10):1957-1970
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
5.
K. Závěta 《Czechoslovak Journal of Physics》1961,11(6):424-438
. , .
c
. , , .
c
; .
[1].
., ., . . . , . . , . . . . . 相似文献
The magnetoresistance in zinc-manganese ferrites in the vicinity of the Curie point
The paper describes an exact method for measuring the adiabatic and isothermal magnetoresistant effects in ferrites. It gives the results of studying the temperature dependence of the magnetoresistant effect, which is negative near the Curie point in ferrites and the temperature dependence of which has a maximum of absolute values inT c . It is also shown that the pronounced maximum of the adiabatic magnetoresistant effect is to a certain extent caused by the magnetocaloric effect. When measuring the dependence of the magnetoresistant effect on the field strength for a temperature equal toT c , certain small deviations from the theoretically assumed dependence were found; the influence of different factors on these deviations is discussed and a proposal for their explanation is given in analogy to the results known for metals.
[1].
., ., . . . , . . , . . . . . 相似文献
6.
Karl Kraus 《Communications in Mathematical Physics》1967,7(2):99-111
Concrete C*-algebras, interpreted physically as algebras of observables, are defined for quantum mechanics and local quantum field theory.Aquantum mechanical system is characterized formally by a continuous unitary representation up to a factorU
g
of a symmetry group
in Hilbert space and a von Neumann algebra on invariant with respect toU
g
. The set
of all operatorsX such thatU
g
X U
g
–1
, as a function ofg
, is continuous with respect to the uniform operator topology, is aC*-algebra called thealgebra of observables. The algebra is shown to be the weak (or strong) closure of
.Infield theory, a unitary representation up to a factorU(a, ) of the proper inhomogeneous Lorentz group
and local von Neumann algebras C for finite open space-time regionsC are assumed, with the usual transformation properties of
underU(a, ). The collection of allXC giving uniformly continuous functionsU (a, )X U
–1 (a, ) on
is then a localC*-algebra
, called thealgebra of local observables. The algebra
is again weakly (or strongly) dense in
c
. The norm-closed union
of the
for allC is calledalgebra of quasilocal observables (or quasilocal algebra).In either case, the group
is represented by automorphisms V
g
resp. V(a, ) — with V
g
X=U
g
X U
g
–1
— of theC*-algebra
, and this is astrongly continuous representation of
on the Banach space
. Conditions for V (a, ) can then be formulated which correspond to the usualspectrum condition forU (a, ) in field theory.Work supported in part by the Deutsche Forschungsgemeinschaft. 相似文献
7.
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
8.
The emissivity in the 2.7 m range is examined with a spectrometer having 25 cm–1 for 2.5,
,7.5 cm·atm,4
8cm·atm, 400T1000° K; 150P730 mm Hg. It is found that relation (1) is obeyed to within /0.1, though the calculated transmission is usually less than the measured value. It is shown that the relation is obeyed on account of the mutual position of the CO2 and H2O lines in the band, i.e., one gas may be considered as unselective relative to the other. 相似文献
9.
Let X be a Riemann surface equipped with a projective structure. Let
be a square-root of the holomorphic cotangent bundle K
X
. Consider the symplectic form on the complement of the zero section of
obtained by pulling back the symplectic form on K
X
using the map 2. We show that this symplectic form admits a natural quantization. This quantization also gives a quantization of the complement of the zero section in K
X
equipped with the natural symplectic form. 相似文献
10.
Monte Carlo simulations of the bond fluctuation model of symmetrical polymer blends confined between two neutral repulsive walls are presented for chain lengthN
A=N
B=32 and a wide range of film thicknessD (fromD=8 toD=48 in units of the lattice spacing). The critical temperaturesT
c
(D) of unmixing are located by finite-size scaling methods, and it is shown that
, wherev
30.63 is the correlation length exponent of the three-dimensional Ising model universality class. Contrary to this result, it is argued that the critical behavior of the films is ruled by two-dimensional exponents, e.g., the coexistence curve (difference in volume fraction of A-rich and A-poor phases) scales as
, where
2 is the critical exponent of the two-dimensional Ising universality class (
2=1/8). Since for largeD this asymptotic critical behavior is confined to an extremely narrow vicinity ofT
c
(D), one observes in practice effective exponents which gradually cross over from
2 to
3 with increasing film thickness. This anomalous flattening of the coexistence curve should be observable experimentally. 相似文献
11.
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
12.
John F. Cyranski 《International Journal of Theoretical Physics》1985,24(2):175-178
Recently it has been shown that quantum theory can be viewed as a classical probability theory by treating Hilbert space as a measure space (H, B(H)) of events or hidden states. Each density operator
defines a set
of probability measures such that(E
n
)=w
n
(alln). Coding elements H by subspacesE
n entails distortion. We show that the von Neumann entropyS() = -trInequals the effective rate at which the Hilbert space produces information with zero expected distortion, and comment on the meaning of this. 相似文献
13.
The spaces of linear differential operators
acting on -densities on
and the space
of functions on
which are polynomial on the fibers are not isomorphic as modules over the Lie algebra Vect (n) of vector fields of n. However, these modules are isomorphic as sl(n + 1,)-modules where
is the Lie algebra of infinitesimal projective transformations. In addition, such an
-equivariant bijection is unique (up to normalization). This leads to a notion of projectively equivariant quantization and symbol calculus for a manifold endowed with a (flat) projective structure. We apply the
-equivariant symbol map to study the
of kth-order linear differential operators acting on -densities, for an arbitrary manifold M and classify the quotient-modules
. 相似文献
14.
We study the Leibniz homology of the Poisson algebra of polynomial functions over (2n
,) where is the standard symplectic structure. We identify it with certain highest-weight vectors of some
2n
(
)-modules and obtain some explicit result in low degree. 相似文献
15.
Edward Kissin 《Communications in Mathematical Physics》1994,160(2):333-348
The paper studies unbounded symmetric and dissipative implementations (S,G) of*-superderivations ofC
*-algebras
. It associates with them representations
S
of the domainsD() of on the deficiency spacesN(S) of the symmetric operatorsS. A link is obtained between the deficiency indicesn
±(S) ofS and the dimensions of irreducible representations of
. For the case when (S,G) is a maximal implementation and max(n
±(S))<, some conditions are given for the representation
S
to be semisimple and to extend to a bounded representation of
. 相似文献
16.
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
17.
A moment map
is constructed from the Poisson manifold A of rank-r perturbations of a fixedN×N matrixA to the dual
of the positive part of the formal loop algebra
=gl(r)[[, –1]]. The Adler-Kostant-Symes theorem is used to give hamiltonians which generate commutative isospectral flows on
. The pull-back of these hamiltonians by the moment map gives rise to commutative isospectral hamiltonian flows in A. The latter may be identified with flows on finite dimensional coadjoint orbits in
and linearized on the Jacobi variety of an invariant spectral curveX
r
which, generically, is anr-sheeted Riemann surface. Reductions of A are derived, corresponding to subalgebras ofgl(r, ) andsl(r, ), determined as the fixed point set of automorphism groupes generated by involutions (i.e., all the classical algebras), as well as reductions to twisted subalgebras of
. The theory is illustrated by a number of examples of finite dimensional isospectral flows defining integrable hamiltonian systems and their embeddings as finite gap solutions to integrable systems of PDE's.This research was partially supported by NSF grants MCS-8108814 (A03), DMS-8604189, and DMS-8601995 相似文献
18.
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
19.
Pavel M. Bleher Zheming Cheng Freeman J. Dyson Joel L. Lebowitz 《Communications in Mathematical Physics》1993,154(3):433-469
We investigate the fluctuations inN
(R), the number of lattice pointsnZ
2 inside a circle of radiusR centered at a fixed point [0, 1)2. Assuming thatR is smoothly (e.g., uniformly) distributed on a segment 0RT, we prove that the random variable
has a limit distribution asT (independent of the distribution ofR), which is absolutely continuous with respect to Lebesgue measure. The densityp
(x) is an entire function ofx which decays, for realx, faster than exp(–|x|4–). We also obtain a lower bound on the distribution function
which shows thatP
(–x) and 1–P
(x) decay whenx not faster than exp(–x
4+). Numerical studies show that the profile of the densityp
(x) can be very different for different . For instance, it can be both unimodal and bimodal. We show that
, and the variance
depends continuously on . However, the partial derivatives ofD
are infinite at every rational point Q
2, soD
is analytic nowhere. 相似文献
20.
Couch and Torrence suggest that the vacuum Einstein equations admit a larger class of asymptotically flat solutions than those exhibiting the peeling property. Starting with the assumption that
, (d/dr)
and (/x
A
)
, wherex
A
(A = 2, 3) are angular coordinates, they show that
, where 1 2 and 1<0;
, where 2 1 and 1< 1; and 4 and 3 peel as they would under the stronger peeling conditions. The Winicour-Tamburino energy-momentun and angular momentum integrals for these solutions, in general, diverge. In fact, since Couch and Torrence determine only the radial dependence of the solution, it is not clear that the solutions are well defined. We find that the stronger assumption
, (d/dr)
, and (/x
A
)
does result in well-defined solutions for which both the energy-momentum and angular momentum intergrals are not only finite but result in the same expressions as are obtained for peeling space-times. This assumption appears to be the minimal assumption that is necessary for investigating outgoing radiation at null infinity.In part based on a dissertation by Stephanie Novak and submitted to Syracuse University in partial fulfillment of the requirement for the Ph.D. degree. 相似文献