Origin and phenomenology of weak-doublet spin-1 bosons

We study phenomenological consequences of the Standard Model extension by the new spin-1 fields with the internal quantum numbers of the electroweak Higgs doublets. We show, that there are at least three different classes of theories, all motivated by the hierarchy problem, which predict appearance of such vector weak-doublets not far from the weak scale. The common feature for all the models is the existence of an SUW(3) gauge extension of the weak SUW(2) group, which is broken down to the latter at some energy scale around TeV. The Higgs doublet then emerges as either a pseudo-Nambu-Goldstone boson of a global remnant of SUW(3), or as a symmetry partner of the true eaten-up Goldstone boson. In the third class, the Higgs is a scalar component of a high-dimensional SUW(3) gauge field. The common phenomenological feature of these theories is the existence of the electroweak doublet vectors (Z^?,W^?), which in contrast to well-known Z^′ and W^′ bosons posses only anomalous (magnetic moment type) couplings with ordinary light fermions. This fact leads to some unique signatures for their detection at the hadron colliders.     

Theory of spin-3/2 particles

A new class of P-invariant equations for vector-bispinors is obtained. It is shown that it is more convenient to classify the equations only with respect to their general covariant form.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 89–93, November, 1987.     

Dynamical model of spin-1 and spin-0 particles (II)

Equations are proposed that completely describe $\text{s = 0,}\text{1}\text{2}\text{, 1}$ particles, i.e. specify 2s+2 limiting states in the E → ∞ limit. A set of states closed with respect to the E → ∞ limiting procedure is considered, whence follows the necessity for the introduction of a λ-state corresponding to one-dimensional unitary representation of the Lorentz group. It is shown further, that a cosmological term proportional to the square of the λ-state strength should be introduced in gravitation theory. On the basis of the Lorentz group, a table of fundamental interactions is proposed and a dual transformation for the interacting system is introduced. Appendices deal with a generalisation of the Duffin-Kemmer formalism and a new method for the introduction of interactions.     

Effective chiral lagrangians for spin-1 mesons

The commonly used types of effective theory for vector mesons are reviewed and their relationships clarified. They are shown to correspond to different choices of field for spin-1 particles and the rules for transforming between them are described. The importance of respecting chiral symmetry is stressed. The choice of fields that transform homogeneously under the nonlinear realisation of chiral symmetry imposes no preconceptions about the types of coupling for the mesons. This representation thus provides a convenient framework for relating different theories. It is also used to elucidate the nature of the assumptions in specific hiddengauge and massive Yang-Mills models that have been widely used.     

Effective chiral Lagrangians for spin-1 mesons

The commonly used types of effective theory for vector mesons are reviewed and their relationships clarified. They are shown to correspond to different choices of field for spin-1 particles and the rules for transforming between them are described. The importance of respecting chiral symmetry is stressed. The choice of fields that transform homogeneously under the nonlinear realisation of chiral symmetry imposes no preconceptions about the types of coupling for the mesons. This representation thus provides a convenient framework for relating different theories. It is also used to elucidate the nature of the assumptions in specific hidden-gauge and massive Yang-Mills models that have been widely used.     

Weak localization in disordered spin-1 chiral fermions

We theoretically investigate the quantum interference theory of magnetotransport of the three-component or spin-1 chiral fermions, which possess two linear Dirac bands and a flat band. For isotropic scalar impurities, the correction of conductivity from the coherent backscatter and non-coherent backscatter contributions cancel out in the intravalley scattering, leading to a weak localization correction to the Drude conductivity from the intervalley scattering. For the anisotropic impurities, the above cancelation is removed, we find the approximative quantum interference conductivity in the weak anisotropy case. The contributions from the chiral anomaly and classical Lorentz force are also discussed. Our work reveals some intriguing and detectable transport signatures of the novel spin-1 chiral fermions.     

Stable particles in anisotropic spin-1 chains

Motivated by field-theoretic predictions we investigate the stable excitations that exist in two characteristic gapped phases of a spin-1 model with Ising-like and single-ion anisotropies. The sine-Gordon theory indicates a region close to the phase boundary where a stable breather exists besides the stable particles, that form the Haldane triplet at the Heisenberg isotropic point. The numerical data, obtained by means of the Density Matrix Renormalization Group, confirm this picture in the so-called large-D phase for which we give also a quantitative analysis of the bound states using standard perturbation theory. However, the situation turns out to be considerably more intricate in the Haldane phase where, to the best of our data, we do not observe stable breathers contrarily to what could be expected from the sine-Gordon model, but rather only the three modes predicted by a novel anisotropic extension of the Non-Linear Sigma Model studied here by means of a saddle-point approximation.     

The Bethe-Salpeter equation for spin-1 particles

We develop here the general treatment of the Bethe—Salpeter equation for the bound state of two spin-l particles interacting through an electromagnetic interaction. The treatment here, which can be generalized to strong interactions, combines the two-component approach utilized previously by the author in conjunction with spontaneous symmetry breaking. This is done by using a Lagrangian having SU(2)×U(1) symmetry (without fermions) and then choosing the ′t Hooft gauge. In this way, a renormalizable theory for the interaction of two spin-l particles via an electromagnetic interaction is ensured.     

Geometric phase and entanglement for massive spin-1 particles

The cyclic evolution of a spin-1 system is studied under the spin-spin interaction between the transverse and the longitudinal states. The eigenstates of the systems are obtained by generalized and extended Jordan-Wigner transformation with an angle described the path of particle propagation. According to the wave functions of time evaluation for many-particle systems, the entanglement effects and geometric phase are observed. The systems with more than two particles, in contrast to the two particle system, evolve in time with two parameters.     

Quasi-probability distribution for spin-1/2 particles

Quantum distribution functions for spin-1/2 systems are derived for various characteristic functions corresponding to different operator orderings.O. Scully wishes to express his personal thanks to Professor Henry Margenau for sage advice which he offered to his students, namely: Don't spend too much time and effort on the philosophical aspects of quantum mehanics until you have applied quantum mechanics to several laboratory problems and have thereby mastered the subject. This is certainly the approach Professor Margenau has followed, and he provides an excellent role model in matters combining physics and philosophy.     

Lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments in chiral perturbation theory

We review some recent progress in our understanding of the lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments （MMs） in terms of Chiral Perturbation Theory （ChPT）.In particular,we show that at next-to-leading-order ChPT can describe the MMs of the octet baryons quite well.We also make predictions for the decuplet MMs at the same chiral order.Among them,the MMs of the Δ＋＋ and Δ ＋ are found to agree well with data within the experimental uncertainties.     

Lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments in chiral perturbation theory

We review some recent progress in our understanding of the lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments (MMs) in terms of Chiral Perturbation Theory (ChPT).In particular,we show that at next-to-leading-order ChPT can describe the MMs of the octet baryons quite well.We also make predictions for the decuplet MMs at the same chiral order.Among them,the MMs of the Δ++ and Δ + are found to agree well with data within the experimental uncertainties.     

Joint Wigner distribution for spin-1/2 particles

The Wigner distribution has proven to be a useful tool in many quantum problems requiring a joint distribution of position and momentum. In the present paper we develop a joint distribution for spin components within the spirit of the Wigner distribution. This distribution provides an insight into the quantum theory of measurement. We also discuss how one may write joint distributions for two arbitrary noncommuting operators.It is a pleasure to dedicate this paper to Professor John A. Wheeler—physicist, philosopher, poet—an inspiration to us all.Work supported by the Office of Naval Research.     

Electric and magnetic polarizabilities of pointlike spin-1/2 particles

The electric and magnetic polarizabilities of pointlike spin-1/2 particles with an anomalous magnetic moment (AMM) are calculated by the transformation of an initial Hamiltonian into the Foldy-Wouthuysen (FW) representation. Corresponding results for spin-1/2 and spin-1 particles are compared.     

The scattering of spin-1 particles by quantum gravitational bubbles

Quantum gravitational bubbles may be used to obtain a non-perturbative approximation to the path integral of quantum gravity. There are three basic types of bubblesCP ²,S ² ×S ², andK3, and in this paper the propagation of elementary spin-1 particles inCP ² is investigated. To date information about the propagation of particles other than scalars has been obtained by making approximations to the basic bubble types. The work presented here represents the first exact calculation. It is found that spin-1 particles scatter very strongly, particularly at low energies, which is at odds with both physical observation and the earlier work on this subject. Possible explanations for this discrepancy are offered.     

Polarization of spin-1 particles in a uniform magnetic field

The exact solution of the Corben–Schwinger equations is obtained for spin-1 particles without an anomalous magnetic moment in a uniform magnetic field. The exact Hamiltonian in the Foldy–Wouthuysen representation is derived. The conservation of projections of the polarization operator onto four directions is proved. The approximate conservation of projections of this operator onto the horizontal axes of the cylindrical coordinate system is established. For spin-1 particles with the anomalous magnetic moment, the Hamiltonian in the Foldy–Wouthuysen representation is deduced within first order terms in the Planck constant. Dynamics of spin-1 particles with the anomalous magnetic moment and their spins in the strong uniform magnetic field are calculated.     

The He--McKellar--Wilkens effect for spin-1 particles on non-commutative space

By using star product method, the He-McKellar-Wilkens （HMW） effect for spin-one neutral particle on noncommutative （NC） space is studied. After solving the Kemmer-like equations on NC space, we obtain the topological HMW phase on NC space where the additional terms related to the space-space non-commutativity are given explicitly.