Three types of maximally entangled states for a two-particle system

Foratwo-particle(spin1/2)systemthespinstateisdescribedusingavectorinafour-dimensionalHilbertspace.Inangularmomentumcouplingtheory[1],theangularmomentumuncouplingandcouplingrepresentationsareusuallyadopted.WhilethesimultaneouseigenstatesoftheCSCO(s1z,s2z),12,12,12and12,arechosenasthebasisofangularmomentumuncouplingscheme,thesimultaneouseigenstatesoftheCSCO(2,zSS),,SM(12=+Sss),arechosenasthebasisofangularmomentumcouplingscheme,1212100,2轾=-臌1212110,2轾=+臌121211,1,1.=-=Thefo…     

Probability relations involving several subsystems

We consider the question of factorizability in tensor product spaces, and argue that the correlations associated with entangled states are even more problematic in the general case involving any tensor product of Hilbert spaces, than in the Einstein, Podolsky, and Rosen case with only two [1].     

Interpreting Observables in a Quantum World from the Categorial Standpoint

We develop a relativistic perspective on structures of quantum observables, in terms of localization systems of Boolean coordinatizing charts. This perspective implies that the quantum world is comprehended via Boolean reference frames for measurement of observables, pasted together along their overlaps. The scheme is formalized categorically, as an instance of the adjunction concept. The latter is used as a framework for the specification of a categorical equivalence signifying an invariance in the translational code of communication between Boolean localizing contexts and quantum systems. Aspects of the scheme semantics are discussed in relation to logic. The interpretation of coordinatizing localization systems, as structure sheaves, provides the basis for the development of an algebraic differential geometric machinery suited to the quantum regime.     

Model-independent constraints on spin observables

We discuss model-independent constraints on spin observables in exclusive and inclusive reactions, with special attention to the case of photoproduction.     

On Fuzzy Probability Theory

Our main aim from this work is to see which theorems in classical probability theory are still valid in fuzzy probability theory. Following Gudder's approach [Demonestratio Mathematica 31(3), 1998, 235–254; Foundations of Physics, 30, 1663–1678] to fuzzy probability theory, the basic concepts of the theory, that is of fuzzy probability measures and fuzzy random variables (observables), are presented. We show that fuzzy random variables extend the usual ones. Moreover, we prove that for any separable metrizable space, the crisp observables coincide with random variables. Then we prove the existence of a joint observable for any collection of observables, and we prove the weak law of large numbers and the central limit theorem in the fuzzy context. We construct a new definition of almost everywhere convergence. After proving that Gudder's definition implies ours and presenting an example that indicates that the converse is not true, we prove the strong law of large numbers according to this definition.     

Linear response and relaxation in quantum lattice systems

For spin-lattice systems, the Kubo formula, expressing the relaxation function in terms of the linear response function, is found to be exact in the thermodynamic limit. In addition, analyticity properties are obtained.     

Electroweak precision data and gravitino dark matter

Electroweak precision measurements can provide indirect information about the possible scale of supersymmetry already at the present level of accuracy. We review present day sensitivities of precision data in mSUGRA-type models with the gravitino as the lightest supersymmetric particle (LSP). The χ ² fit is based on M _W , sin² θ _eff, (g−2) _μ , BR(b → sγ) and the lightest MSSM Higgs boson mass, M _h . We find indications for relatively light soft supersymmetry-breaking masses, offering good prospects for the LHC and the ILC, and in some cases also for the Tevatron.      

Incoherent pion photoproduction on the deuteron including polarization effects

Incoherent pion photoproduction on the deuteron including polarization effects is studied in the energy region from π-threshold up to the Δ(1232)-resonance with inclusion of all leading πNN effects. For the elementary pion photoproduction operator, a realistic effective Lagrangian approach is used which displays chiral symmetry, gauge invariance, and crossing symmetry, as well as a consistent treatment of the spin-3/2 interaction. The interactions in the final two-body subsystems are taken in separable form. Effects of final state interaction are investigated and their role in unpolarized and polarization observables are found to be significant. The extracted cross sections and spin asymmetries are compared with available experimental data and predictions of other works, and a satisfactory agreement is obtained. In addition, the sensitivity of results to the elementary N(γ, π)N operator is investigated. Considerable dependence of the d(γ, π)NN results on the elementary amplitude is found. This indicates that it can serve as a filter for different elementary operators.     

New observables in topological instantonic field theories

Instantonic theories are quantum field theories where all correlators are determined by integrals over the finite-dimensional space (space of generalized instantons). We consider novel geometrical observables in instantonic topological quantum mechanics that are strikingly different from standard evaluation observables. These observables allow jumps of special type for the trajectory (at the point of insertion of such observables). They do not (anti)commute with evaluation observables and raise the dimension of the space of allowed configurations, while the evaluation observables lower this dimension. We study these observables in geometric and operator formalisms. Simple examples are explicitly computed; they depend on the linking of points.