Models of particle states

Two different types of particle state models are discussed. In the first type, particles are considered to be dynamically bound systems of a small set of physical constituents. In the second type, particle states are constructed from tensor products of symmetry constituents, i.e., states that are the basis elements of finite irreducible representations of an internal algebra. These states need not represent physical particles. We present three models of the first type. For the second type, we discuss in detail the main thrust of this paper, a new version of the quark-lepton model based on the algebrasu(4)_flaourXsu(6)_flavour. The quark color-triplet and a lepton color-singlet are united by a single irreducible representation of su(4)_colour. Thesu(6)_colour algebra is an extension of the originalsu(3)_flavor. All observed ground-state hadron multiplets are in full accord with the predictions of this model. The numbers of hadron ground states it predicts are 36 spin-0 mesons, 36 spin-1 mesons, 70 spin-1/2 baryons, and 56 spin-3/2 baryons.Professor Barut passed away suddenly on December 5, 1994.     

Bell's Inequality for a System Composed of Particles with Different Spins

For two particles with different spins, we derive the Bell's inequality. The inequality is investigated for two systems combining spin-1 and spin-1/2; spin-1/2 and spin-3/2. We show that for these states Bell's inequality is violated.     

Environment-induced decoherence I. The Stern-Gerlach measurement

A dynamical model for the collapse of the wave function in a quantum measurement process is proposed by considering the interaction of a quantum system (spin -1/2) with a macroscopic quantum apparatus interacting with an environment in a dissipative manner. The dissipative interaction leads to decoherence in the superposition states of the apparatus, making its behaviour classical in the sense that the density matrix becomes diagonal with time. Since the apparatus is also interacting with the system, the probabilities of the diagonal density matrix are determined by the state vector of the system. We consider a Stern-Gerlach type model, where a spin-1/2 particle is in an inhomogeneous magnetic field, the whole set up being in contact with a large environment. Here we find that the density matrix of the combined system and apparatus becomes diagonal and the momentum of the particle becomes correlated with a spin operator, selected by the choice of the system-apparatus interaction. This allows for a measurement of spin via a momentum measurement on the particle with associated probabilities in accordance with quantum principles.     

Geometric Phase for Two Entangled Spin-1/2 Particles in a Magnetic Field

In this paper the geometric phases of two entangled spin-1/2 particles in the presence and absence of spin-spin interaction are calculated. We also discuss the geometric phases when only one of the two particles is affected by the external magnetic field. Our results show that the geometric phase in this case is not equal to that of a single particle under the same evolution condition because of the effect of entanglement. We further study the entanglement dependence of the noncyclic geometric phases in the interacting and noninteracting spins under a time-independent uniform magnetic field. A general entanglement-dependence geometric phase is formulated.     

Exploring the entanglement of free spin-(1/2), spin-1 and spin-2 fields

In this study, we explore the entanglement of free spin-(1/2), spin-1, and spin-2 fields. We start with an example involving Majorana fields in 1+1 and 2+1 dimensions. Subsequently, we perform the Bogoliubov transformation and express the vacuum state with a particle pair state in the configuration space, which is used to calculate the entropy. This clearly demonstrates that the entanglement entropy originates from the particles across the boundary.Finally, we generalize this method to free spin-1 and spin-2 fields. These higher free massless spin fields have wellknown complications owing to gauge redundancy. We deal with the redundancy by gauge-fixing in the light-cone gauge. We show that this gauge provides a natural tensor product structure in the Hilbert space, while surrendering explicit Lorentz invariance. We also use the Bogoliubov transformation to calculate the entropy. The area law emerges naturally by this method.     

Polarized electron scattering on spin zero and polarized spin-1/2 targets: Deep inelastic scattering,elastic electron-muon scattering,and elastic electron-nucleon scattering

A covariant formulation is developed and used to derive cross sections for the analysis of experiments in which polarized electrons (muons) are scattered from spin-zero and from polarized spin-1/2 targets. The analysis is based upon the single virtual photon representation of the electromagnetic interaction, initially, neither high-energy nor low-energy approximations are made so that one may derive results in which the orientation of the polarization vectors of the interacting particles changes as a result of the scattering. The general formulation is valid for all polarization configurations for the electron and nucleon in deep inelastic scattering, and for all polarization configurations for the initial and final state particles in elastic scattering. From the general covariant results, specific cross sections are derived for deep inelastic scattering as well as elastic scattering of electrons on muons, nucleons, and spin zero targets. In the latter case, the actual polarization vector for the scattered electron is determined. In the other cases discussed, this vector may be obtained from the cross sections. In addition, a method is presented for defining covariant cross sections, and this method is used to obtain results in the center-of-mass system as well as the laboratory system. Furthermore, explicit cross sections for virtual photon absorption are derived. Finally, in the appendices, an alternative method for the evaluation of traces is given as well as a discussion of the relativistic limit.     

压缩相干态腔场的类自旋GHZ态的制备

压缩相干态是准粒子空间的相干态,研究大振幅情况下的单模压缩相干态腔场,其特性类似于大振幅下的单模相干态腔场,与自旋1/2的两态粒子同构.文中提出一种方案,利用大失谐的JaynesCummings模型来制备处于压缩相干态的三个腔场的类自旋GreenbergerHorneZeilinger(GHZ)态. 关键词： 压缩相干态 类自旋GHZ态 大失谐JaynesCumminys模型 同构     

Spin-1/2 relativistic particle in a magnetic field in NC phase space

This work provides an accurate study of the spin-l/2 relativistic particle in a magnetic field in NC phase space. By detailed calculation we find that the Dirac equation of the relativistic particle in a magnetic field in noncommutative space has similar behaviour to what happens in the Landau problem in commutative space even if an exact map does not exist. By solving the Dirac equation in NC phase space, we not only obtain the energy level of the spin-1/2 relativistic particle in a magnetic field in NC phase space but also explicitly offer some additional terms related to the momentum-momentum non-commutativity.     

Quantum mechanics of relativistic spinless particles

A relativistic one-particle, quantum theory for spin-zero particles is constructed uponL ²(x, ct), resulting in a positive definite spacetime probability density. A generalized Schrödinger equation having a Hermitian HamiltonianH onL ²(x, ct) for an arbitrary four-vector potential is derived. In this formalism the rest mass is an observable and a scalar particle is described by a wave packet that is a superposition of mass states. The requirements of macroscopic causality are shown to be satisfied by the most probable trajectory of a free tardyon and a nontrivial framework for charged and neutral particles is provided. The Klein paradox is resolved and a link to the free particle field operators of quantum field theory is established. A charged particle interacting with a static magnetic field is discussed as an example of the formalism.     

Gibbsian Stationary Non-equilibrium States

We study the structure of stationary non-equilibrium states for interacting particle systems from a microscopic viewpoint. In particular we discuss two different discrete geometric constructions. We apply both of them to determine non reversible transition rates corresponding to a fixed invariant measure. The first one uses the equivalence of this problem with the construction of divergence free flows on the transition graph. Since divergence free flows are characterized by cyclic decompositions we can generate families of models from elementary cycles on the configuration space. The second construction is a functional discrete Hodge decomposition for translational covariant discrete vector fields. According to this, for example, the instantaneous current of any interacting particle system on a finite torus can be canonically decomposed in a gradient part, a circulation term and an harmonic component. All the three components are associated with functions on the configuration space. This decomposition is unique and constructive. The stationary condition can be interpreted as an orthogonality condition with respect to an harmonic discrete vector field and we use this decomposition to construct models having a fixed invariant measure.     

Spin-1/2 relativistic particle in a magnetic field in NC phase space

This work provides an accurate study of the spin-1/2 relativistic particle in a magnetic field in NC phase space. By detailed calculation we find that the Dirac equation of the relativistic particle in a magnetic field in noncommutative space has similar behaviour to what happens in the Landau problem in commutative space even if an exact map does not exist. By solving the Dirac equation in NC phase space, we not only obtain the energy level of the spin-1/2 relativistic particle in a magnetic field in NC phase space but also explicitly offer some additional terms related to the momentum-momentum non-commutativity.     

Wave functions and mass spectrum for a system of two relativistic spinor quarks coupled by a chromodynamical interaction

Exact solutions of relativistic quasipotential equations in the configuration representation were found for a system of two spin-1/2 quarks interacting via a Coulomb-like chromodynamical potential. Quantization conditions were found for the pseudoscalar, pseudovector, and vector cases. The present analysis was performed within the Hamiltonian formulation of quantum field theory via a transition to the relativistic configuration representation for the case of two relativistic spin-1/2 quarks of equal mass.     

Measurement of the wave function (of all elements of the density matrix) of a muonium-like system by the μSR method

A system consisting of two interacting particles, one of which has the angular momentum 1/2 and the other of which has an arbitrary angular momentum (a muonium-like system) is considered. The possibility of reconstruction of all the elements of the spin density matrix with the help of the μSR method is shown. For entangled states (Einstein-Podolsky-Rosen and Schrödinger cat states), the time dependence of components of the polarization vector (μSR photographs) is demonstrated. It is shown that, to identify these states, two μSR photographs suffice.     

Quantum Vacuum and the Structure of Empty Space–Time

We have considered the possibility of formation of a massless particles with spin 1 in the region of negative energies, within the framework of the Weyl-type equation for neutrinos. It is proved that the represented approach allows to get a stable structural formation in the ground state, which can be interpreted as a fundamental massless particle. The structure and properties of this vector boson are studied in detail. The problem of entangling two vector bosons with projections of spins +1 and −1 and, accordingly, the formation of a zero-spin boson is studied within the framework of a complex stochastic matrix equations of the Langevin type. The paper discusses the structure of the Bose particle of a scalar field and the space–time properties of an empty space (quantum vacuum).

     

Spinless particles in the field of unequal scalar vector Yukawa potentials

We present analytical bound state solutions of the spin-zero Klein-Gordon (KG) particles in the field of unequal mix- ture of scalar and vector Yukawa potentials within the framework of the approximation scheme to the centrifugal potential term for any arbitrary l-state. The approximate energy eigenvalues and unnormalized wave functions are obtained in closed forms using a simple shortcut of the Nikiforov-Uvarov (NU) method. Further, we solve the KG-Yukawa problem for its exact numerical energy eigenvalues via the amplitude phase (AP) method to test the accuracy of the present solutions found by using the NU method. Our numerical tests using energy calculations demonstrate the existence of inter-dimensional degeneracy amongst the energy states of the KG-Yukawa problem. The dependence of the energy on the dimension D is numerically discussed for spatial dimensions D = 2-6.     

Relative entropy of entanglement of rotationally invariant states

We calculate the relative entropy of entanglement for rotationally invariant states of spin- and arbitrary spin-j particles or of spin-1 particle and spin-j particle with integer j. A lower bound of relative entropy of entanglement and an upper bound of distillable entanglement are presented for rotationally invariant states of spin-1 particle and spin-j particle with half-integer j.     

Relativistic dynamics for spin-zero and spin-half particles

The classical and quantum mechanics of a system of directly interacting relativistic particles is discussed. We first discuss the spin-zero case, where we basically follow Rohrlich in introducing a set of covariant centre of mass (CM) and relative variables. The relation of these to the classic formulation of Bakamjian and Thomas is also discussed. We also discuss the important case of relativistic potentials which may depend on total four-momentum squared. We then consider the quantum mechanical case of spin-half particles. The negative energy difficulty is solved by introducing a number of first class constraints which fix the spinor structure of physical solutions and ensure the existence of proper CM and relative variables. We derive the form of interactions consistent with Lorentz invariance, space inversion, time reversal and charge conjugation and with the above mentioned first class constraints and find that it is analogous to that for the non-relativistic case. Finally the relationship of the present work with some previous work is briefly discussed.     

Particle and antiparticle spectra of hadronic atoms

The problem on the relativistic spinless and spin-1/2 particle motion in the Coulomb field is analyzed. The eigenvalues and eigenfunctions of particle and antiparticle bound states are calculated. The calculated spectra include the deeply bound states with the binding energy approximately equal to the particle rest mass. The antiparticle bound states play an important role in the atomic capture, radiative decay of hadronic atoms, and collision processes accompanied by recharging of reaction fragments.     

Relativistic quantum dynamics of a neutral particle in external electric fields: An approach on effects of spin

The planar quantum dynamics of a spin-1/2 neutral particle interacting with electrical fields is considered. A set of first order differential equations is obtained directly from the planar Dirac equation with nonminimum coupling. New solutions of this system, in particular, for the Aharonov–Casher effect, are found and discussed in detail. Pauli equation is also obtained by studying the motion of the particle when it describes a circular path of constant radius. We also analyze the planar dynamics in the full space, including the r=0$r=0$ region. The self-adjoint extension method is used to obtain the energy levels and wave functions of the particle for two particular values for the self-adjoint extension parameter. The energy levels obtained are analogous to the Landau levels and explicitly depend on the spin projection parameter.