The U(1) problem and instantons on a lattice

Taking Wilson fermions for quarks, we derive the spectral representation of the quark propagator and investigate the relation between the spectrum and the topological charge of gauge configuration. Then we calculate the η and π propagators on an 8³ × 16 lattice and show that topologically non-trivial gauge configurations make the η meson much heavier than the π meson, when the hopping parameter is very close to the critical value.     

Fermions as U(1) instantons

Anomalous quantization of the electromagnetic field allows non-trivial (anti) self-dual configurations to exist in four-dimensional Euclidian space-time. These instanton-like objects are described as massless spinor particles.      

Instantons and the U(1) problem

If instantons spontaneously break the chiral SU(N) × SU(N) symmetry of a non-abelian gauge theory, they break U(1) symmetry in a manner consistent with the chiral Ward identities of the theory. Excitations of the fermion vacuum play a crucial role in this process. A model calculation of the symmetry breaking effect shows a phenomenological structure which differs from that provided by models with many color degrees of freedom.     

How to solve the measurement problem of quantum mechanics

A solution to the measurement problem of quantum mechanics is proposed within the framework of an intepretation according to which only quantum systems with an infinite number of degrees of freedom have determinate properties, i.e., determinate values for (some) observables of the theory. The important feature of the infinite case is the existence of many inequivalent irreducible Hilbert space representations of the algebra of observables, which leads, in effect, to a restriction on the superposition principle, and hence the possibility of defining (macro-) observables which commute with every observable. Such observables have determinate values which are not subject to quantum interference effects. A measurement process is schematized as an interaction between a microsystem and a macrosystem, idealized as an infinite quantum system, and it is shown that there exists a unitary transformation which transforms the initial pure state of the composite system in a finite time (the duration of the interaction) into the required mixture of disjoint states.     

Chirality selection rules and the U(1) problem

The conventional theory for the lack of U(1) chirality invariance in the presence of topological charge v fails to resolve the U(1) problem: it involves selection rules which forbid chirality changes ± 2 needed to generate the charged-pion decay constant F_π. Possible remedies are considered; if they work. F²_π is proportional to the average value of v² per unit Euclidean volume.     

How to solve the problem of the knee in the cosmic ray spectrum

It is shown that recent experimental data in the region of the knee in the cosmic ray spectrum are somewhat contradictory and new approaches are needed to solve the so-called knee problem. The RRISMA project that we propose is based on the simple idea of giving priority to detecting and studying hadrons as the major EAS component. Special detectors are therefore developed. The experiment should be conducted high in the mountains (the higher the better), where the number of hadrons is higher. We therefore proposed combining PRISMA and the LHAASO (Large High Altitude Air Shower Observatory) now under construction in Tibet 4300 m above sea level.     

Generalized permutation symmetry and the flavour problem inSU(2)L×U(1)

A generalized permutation group is introduced as a possible horizontal symmetry forSU(2)_L×U(1) gauge theories. It leads to the unique two generation quark mass matrices with a correct prediction for the Cabibbo angle. For three generations the model exhibits spontaneousCP violation, correlates the Kobayashi-Maskawa mixing parameterss ₁ ands ₃ and predicts an upper bound for the running top quark mass of approximately 45 GeV. The hierarchy of generations is due to a hierarchy of vacuum expectation values rather than of Yukawa coupling constants.     

Can textures solve the horizon problem?

The possibility of solving the horizon problem in standard cosmology, using textures, is discussed in detail. Analysis of the model with dust, textures and radiation shows that the solution of the problem requires a very specific and relatively large value of the textures energy density. It is also shown that the period of time over which the background radiation is observed to be isotropic is much shorter than it had seemed so far on the basis of rough estimates.     

How well do Monte Carlo simulations distinguish between U(1) and SU(2)?: A study of the string tension in U(1) lattice gauge theory

To investigate how a system with a known deconfining phase transition behaves when studied on finite lattices via Monte Carlo simulations, we have made such studies of compact U(1) lattice gauge theory for 8⁴, 10⁴, and 12⁴ lattices. We have concentrated on the mean plaquette energy and the string tension. The string tension does not vanish on a finite lattice, but using finite size scaling arguments the indications are that it does vanish on an infinite lattice, where we predict the critical coupling β_c = 1.008 and the correlation length exponent $\text{ν =}\text{1}\text{3}$. We compare our results to those for SU(2) and find that although there are differences, they are not yet definitive.     

A minimalSU(2)×U(1)×U(1) electroweak model with mirror fermions

We present a minimal extension of the standard electroweak model, which accommodates mirror fermions, based onSU(2)×U(1)×U(1). Mirror mixing happens through sterile neutrino states and induces radiative mixing for charged leptons. Quarks and mirror quarks are not mixed with each other, consistent with the suppression of flavour changing neutral currents. Higgs sector, fermion masses and neutral currents are discussed. In this scheme there can be a secondZ boson as light as 0.2TeV.     

The Cabibbo angle in an SU(2) × U(1) × U(1) model

In the recently proposed SU(2) × U(1) × U(1) model the requirement that strangeness is naturally conserved in the natural Higgs couplings leads to tan θ_c ～m_dm_s.     

Exact SU(n) instantons with cylindrical symmetry

We construct SO(3) symmetric, irreducible instantons in an SU(n) gauge theory. The solutions are symmetric with respect to J = ?ir × ? + T, where T spans the maximal SO(3) subalgebra of SU(n). Our ansatz as well as the resulting self dual equations are closely related to those for monopoles.     

Distinguishability ofSU(2)×U(1)×U′(1) andSO(10) gauge models from the Weinberg-Salam model

The predictions ofSU(2)×U(1)×U′(1) andSO(10) gauge models for the asymmetry parametersA-,B-,C _L andC _R in the deep inelastic scattering of polarized electrons and positrons by unpolarized protons and deuterons are compared with those calculated in the Weinberg Salam model for different values ofy. The model based on,SU(2)×U(1)×U′(1) group has been found almost indistinguishable from the Weinberg Salam model with regard to the parametersA-,B- andC _L (except forB- in the region 0≦y≦0.2) althoughC _R exhibits marked distinguishability. TheSO(10) model, for certain choice of its model parameters, can be distinguished from the Weinberg Salam model through measurement of the asymmetry parameters for different values ofy.