Finite-dimensional relativistic quantum mechanics

A finite-dimensional relativistic quantum mechanics is developed by first quantizing Minkowski space. Two-dimensional space-time event observables are defined and quantum microscopic causality is studied. Three-dimensional colored even observables are introduced and second quantized on a representation space of the restricted Poincaré group. Creation, annihilation, and field operators are introduced and a finite-dimensional Dirac theory is presented.     

Quark-Meson Bag Model and Hadron Structure

Based on the assumption that quarks (e.g. up, down quarks) couple with σ, ω and π mesons directly, a quark-meson bag model is-proposed. By adjusting the quark effective mass and quark-meson coupling constants, the nucleon, Δ baryon masses and some observables of proton are calculated.     

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.     

The materialization phase in the colour rope picture

The initial phase of a ultra-relativistic nucleus-nucleus collision where matter in form of quarks and real gluons is created is described in terms of a phenomenological strings with multiple colour charge sources at their ends. Consequences upon different observables are reviewed and discussed.     

On classical representations of finite-dimensional quantum mechanics

In the case of a finite-dimensional Hilbert space, it is shown that quantum mechanics can be embedded into discrete classical probability theory. In particular, states can be represented as stochastic vectors and observables as random variables such that all probabilities and expectation values are given in classical terms.     

Radiative corrections to observables of <Emphasis Type="Italic">W</Emphasis>-boson production in collisions of polarized hadrons

Ascheme is proposed for studying the nucleon spin with the aid of observables in the production of single W bosons in hadron-hadron collisions. Special attention is given to determining the distributions of polarized quarks in the low-x region. Lowest order electroweak radiative corrections to observables are calculated. For the conditions of future experiments at the RHIC facility, the relevant cross sections and single and double asymmetries are estimated numerically with allowance for radiative corrections.     

Top quark production asymmetries A(FB)t and A(FB)ℓ

A large forward-backward asymmetry is seen in both the top quark rapidity distribution A(FB)(t) and in the rapidity distribution of charged leptons A(FB)(?) from top quarks produced at the Tevatron. We study the kinematic and dynamic aspects of the relationship of the two observables arising from the spin correlation between the charged lepton and the top quark with different polarization states. We emphasize the value of both measurements, and we conclude that a new physics model which produces more right-handed than left-handed top quarks is favored by the present data.     

Test of the flavour independence of \alpha_s using next-to-leading order calculations for heavy quarks

We present a test of the flavour independence of the strong coupling constant for charm and bottom quarks with respect to light (uds) quarks, based on a hadronic event sample obtained with the OPAL detector at LEP. Five observables related to global event shapes were used to measure in three flavour tagged samples (uds, c and b). The event shape distributions were fitted by calculations of jet production taking into account mass effects for the c and b quarks. We find: Received: 18 March 1999 / Published online: 14 October 1999     

A chiral soliton model of nucleon and delta

A linear σ-model is used to describe the N and Δ as three quarks interacting via σ and π mesons. The effects of confinement are neglected. Although we solve the mean field equations for a hedgehog baryon we can calculate observables for states of good spin and isospin. These are in resonable agreement with experiment.     

baryon observables in the chiral bag model

Using cranking techniques a variety of baryon observables are calculated within the framework of the chiral bag model. Effects from valence quarks, mesons and the quark Dirac sea are included. Results for the NΔ mass splitting and nucleon magnetic moments are found to be relatively insensitive to the bag radius.     

Nuclear and hadronic reaction mechanisms producing spin asymmetry

We briefly review concept of the quark recombination (QRC) model and a general success of the model. To solve the existing problem, so called anomalous spin observables, in the high energy hyperon spin phenomena, we propose a mechanism; the primarily produced quarks, which are predominantly u and d quarks, act as the leading partons to form the hyperons. Extension of the quark recombination concept with this mechanism is successful in providing a good account of the anomalous spin observables. Another kind of anomaly, the non-zero analysing power and spin depolarization in the Λ hyperon productions, are also discussed and well understood by the presently proposed mechanism. Recently, a further difficulty was observed in an exclusive ΛK ⁺ p production and wel will indicate a possible diagram for resolving it.     

Entirety of Quantum Uncertainty and Its Experimental Verification

As a foundation of quantum physics, uncertainty relations describe ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertainty relations are formulated by mathematical bounds for a specific state. Here we present a method for geometrically characterizing uncertainty relations as an entire area of variances of the observables, ranging over all possible input states. We find that for the pair of position and momentum operators, Heisenberg's uncertainty principle points exactly to the attainable area of the variances of position and momentum. Moreover, for finite-dimensional systems, we prove that the corresponding area is necessarily semialgebraic; in other words, this set can be represented via finite polynomial equations and inequalities, or any finite union of such sets. In particular, we give the analytical characterization of the areas of variances of(a) a pair of one-qubit observables and(b) a pair of projective observables for arbitrary dimension,and give the first experimental observation of such areas in a photonic system.     

Quantum thermodynamics of nonequilibrium. Onsager reciprocity and dispersion-dissipation relations

A generalized Onsager reciprocity theorem emerges as an exact consequence of the structure of the nonlinear equation of motion of quantum thermodynamics and is valid for all the dissipative nonequilibrium states, close and far from stable thermodynamic equilibrium, of an isolated system composed of a single constituent of matter with a finite-dimensional Hilbert space. In addition, a dispersion-dissipation theorem results in a precise relation between the generalized dissipative conductivity that describes the mutual interrelation between dissipative rates of a pair of observables and the codispersions of the same observables and the generators of the motion. These results are presented together with a review of quantum thermodynamic postulates and general results.     

Characterizing entanglement via uncertainty relations

We derive a family of necessary separability criteria for finite-dimensional systems based on inequalities for variances of observables. We show that every pure bipartite entangled state violates some of these inequalities. Furthermore, a family of bound entangled states and true multipartite entangled states can be detected. The inequalities also allow us to distinguish between different classes of true tripartite entanglement for qubits. We formulate an equivalent criterion in terms of covariance matrices. This allows us to apply criteria known from the regime of continuous variables to finite-dimensional systems.     

Fedosov observables on constant curvature manifolds and the Klein–Gordon equation

In this paper we construct the Fedosov star-algebra of observables on the phase–space of a single particle in the case of all (finite-dimensional) constant curvature manifolds imbeddable in a flat space with codimension one. This set of spaces includes the two-sphere and de Sitter (dS)/Anti-de Sitter (AdS) space–times. The algebra of observables was constructed by DQ techniques using, in particular, the algorithm provided by Fedosov.     

CP-violating correlations in the reactione + e −»hadrons

We investigateCP-violating observables involving jets in the processe ⁺ e ^–»hadrons. These observables are sensitive to sources ofCP-violation beyond the standard model. We use an effective Lagrangian approach to parametrize possible newCP-violating interactions. Bounds on electric and weak diple moments of leptons and quarks are discussed.     

Non-standard physics and nucleon strangeness in low-energy PV electron scattering

Contributions from physics beyond the Standard Model, strange quarks in the nucleon, and nuclear structure effects to the left-right asymmetry measured in parity-violating (PV) electron scattering from¹²C and the proton are discussed. It is shown how lack of knowledge of the distribution of strange quarks in the nucleon, as well as theoretical uncertainties associated with higher-order dispersion amplitudes and nuclear isospin-mixing, enter the extraction of new limits on the electroweak parametersS andT from these PV observables. It is found that a series of elastic PV electron scattering measurements using⁴He could significantly constrain thes-quark electric form factor if other theoretical issues are resolved. Such constraints would reduce the associated form factor uncertainty in the carbon and proton asymmetries below a level needed to permit extraction of interesting low-energy constraints onS andT from these observables. For comparison, the much smaller scale ofs-quark contributions to the weak charge measured in atomic PV is quantified. It is likely that only in the case of heavy muonic atoms could nucleon strangeness enter the weak charge at an observable level.     

Integrated spin structure function of the nucleon using extended Fock space approach

We study the effect of sea quarks on the integrated spin structure functions, the F/D ratio and the total quark polarization, ∑, of the nucleon. The extended Fock space approach is used to incorporate the sea quarks and its wavefunction is properly antisymmetrized. These configurations give significant contributions to the integrated spin structure functions. In particular, antisymmetrization is found to play an important role in the case of the integrated spin structure function of the neutron and the F/D ratio. We find good agreement with experimental values for all four spin polarization observables.