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1.
This article begins with a review of the framework of fuzzy probability theory. The basic structure is given by the -effect algebra of effects (fuzzy events) and the set of probability measures on a measurable space . An observable is defined, where is the value space of X. It is noted that there exists a one-to-one correspondence between states on and elements of and between observables and -morphisms from to . Various combinations of observables are discussed. These include compositions, products, direct products, and mixtures. Fuzzy stochastic processes are introduced and an application to quantum dynamics is considered. Quantum effects are characterized from among a more general class of effects. An alternative definition of a statistical map is given and it is shown that any statistical map has a unique extension to a statistical operator. Finally, various combinations of statistical maps are discussed and their relationships to the corresponding combinations of observables are derived.  相似文献   

2.
We show that the affine quantum group is isomorphic to a bicross-product central extension of the quantum loop group by a quantum cocycle in R-matrix form.  相似文献   

3.
Weert found a superpotential for the bounded part of the Maxwelltensor associatedto the Lienard–Wiechert field. Here we obtain afourth-rank generator for the superpotential .  相似文献   

4.
There are at most 14 independent real algebraic invariants of the Riemann tensor in a four-dimensional Lorentzian space. In the general case, these invariants can be written in terms of four different types of quantities: R , the real curvature scalar, two complex invariants I and J formed from the Weyl spinor, three real invariants I6, I7 and I8 formed from the trace-free Ricci spinor and three complex mixed invariants K, L and M. Carminati and McLenaghan [5] give some geometrical interpretations of the role played by the mixed invariants in Einstein-Maxwell and perfect fluid cases. They show that 16 invariants are needed to cover certain degenerate cases such as Einstein-Maxwell and perfect fluid and show that previously known sets fail to be complete in the perfect fluid case. In the general case, the invariants I and J essentially determine the components of the Weyl spinor in a canonical tetrad frame; likewise the invariants I6, I7 and I8 essentially determine the components of the trace-free Ricci spinor in a (in general different) canonical tetrad frame. These mixed invariants then give the orientation between the frames of these two spinors. The six real pieces of information in K, L and M are precisely the information needed to do this. A table is given of invariants which give a complete set for each Petrov type of the Weyl spinor and for each Segre type of the trace-free Ricci spinor This table involves 17 real invariants, including one real invariant and one complex invariant involving , and in some degenerate cases.  相似文献   

5.
The product of two real spectral triples and , the first of which is necessarily even, was defined by A.Connes as given by and, in the even-even case, by . Generically it is assumed that the real structure obeys the relations , , , where the -sign table depends on the dimension n modulo 8 of the spectral triple. If both spectral triples obey Connes' >-sign table, it is seen that their product, defined in the straightforward way above, does not necessarily obey this -sign table. In this Letter, we propose an alternative definition of the product real structure such that the -sign table is also satisfied by the product.  相似文献   

6.
We show that there are canonical isomorphisms between Hochschild cohomology spaces , where is the algebra of smooth functions on a manifold M and the space of skew multivector fields over M. This implies that continuous and differential deformation theories of coincide.  相似文献   

7.
The charge exchange reaction of negative muons from the atom to oxygen has been measured in gaseous mixtures of H2 + O2. The measurements were performed at three different relative oxygen concentrations ranging from 0.2% to 0.8% and total pressures 3.5–15 bar. A mean transfer rate of , describing the transfer from the ground state of thermalized atoms to oxygen, was determined. In order to investigate the energy dependence of the transfer rate, Monte Carlo simulations of the thermalization and the muon transfer were carried out. The comparison of measured and simulated time spectra yielded an epithermal transfer rate =3.9 1011 s-1 in the energy interval 0.12–0.22 eV. The analysis with the model of Two components shows that all measured time spectra can be reproduced with the same set of parameters.  相似文献   

8.
The Dirac-type equation on topology is worked out and the complete set of solutions in the particular physical case of the zero-energy modes of the massless field quanta is derived. Unlike the Minkowskian case, the 1/2fermionic vacua on the manifold is made of nontrivial static modes of defined chirality.  相似文献   

9.
Electric field gradient q and quadrupole interaction frequency calculated at 256.7 K in the high pressure phase (orthorhombic) of Ga metal are reported. The results are: q=+0.251 atomic units (au), =5.479 MHz. These are compared with results from experiment and previous calculation available for the monoclinic phase of Ga metal at normal pressure. The results from the previous calculation at 248 K are: q=-0.250 au and =5.318 MHz. The result from experiment extrapolated to 256.7 K is: =4.871 MHz. The sign reversal of the calculated q is attributed mainly to the change of point symmetry of the lattice from the orthorhombic to monoclinic. That the interaction frequency in high pressure phase is higher than experiment may be partly due to the increase of pressure and partly to the structural phase change.  相似文献   

10.
Given a braided vector space , we show that iterated integrals of operator-valued functions satisfying a certain exchange relation give rise to representations of the quantum shuffle algebra built on . Using the quantum shuffle construction of the 'upper triangular part' of a quantum shuffle, this provides a simple proof of the result of Bouwknegt, MacCarthy and Pilch saying that integrals of vertex operators acting on certain Fock modules give rise to representations of .  相似文献   

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