Simplicial gauge theory and quantum gauge theory simulation

We propose a general formulation of simplicial lattice gauge theory inspired by the finite element method. Numerical tests of convergence towards continuum results are performed for several SU(2) gauge fields. Additionally, we perform simplicial Monte Carlo quantum gauge field simulations involving measurements of the action as well as differently sized Wilson loops as functions of β.     

O(n) tricriticality in two dimensions

We present exact results for several universal parameters of the tricritical O(n) model in two dimensions. The results apply to the range −2⩽n⩽3/2, and include the central charge and three scaling dimensions, associated with temperature, magnetic field and the introduction of an interface. Since these results are based on an extrapolation of known relations between the O(n) and the Potts model, they cannot be considered as rigorous. For this reason, we perform an accurate numerical analysis of the central charge and the critical exponents. This analysis, which is based on transfer-matrix calculations on the honeycomb lattice, is in a full and precise agreement with the theoretical predictions.      

The β function,scaling, and improved action forSU(3) lattice gauge theory

We present a detailed analysis of the nonperturbativeβ function along the Wilson axis for theSU(3) pure gauge theory using the Monte Carlo renormalization group method. The scaling behavior of the string tension, the deconfinement transition temperature, and the O⁺⁺ glueball mass obtained from published data is compared. The results show that there is no asymptotic scaling forK _F=(6/g ²)<6.1. We also estimate the renormalized action generated by the √3 block transformation for use in future calculations.     

An algorithm for detecting abelian monopoles inSU 2-valued lattice gauge-Higgs systems

We present an algorithm which calculates the monopole number of anSU ₂-valued lattice gauge field, together with a lattice Higgs field, on a simplicial lattice of dimension ≧3. The calculation is gauge invariant. The expected value of the monopole density (for a fixed Higgs field) does not depend on the Higgs field. Partially supported by NSF grants DMS 8607168 and DMS 8907753 Partially supported by PSC-CUNY and by NSF grant DMS 8805485     

Measurement of K β K /α values using proton beamvalues using proton beam

The Measurement of K _β K _/α intensity ratios are measured in some 3d shell elements by using a 2 MeV proton beam along with a high resolution Si(Li) detector. The present Measurement of K _β K _/α intensity ratios are in good agreement with Scofield modified theoretical values, thus supporting the basic assumptions in that theory. From the present Measurement of K _β K _/α intensity ratios, it is evident that due to chemical effects, the experimental Measurement of K _β K _/α intensity ratios will be increased while they will be decreased due to the presence of simultaneous M-shell vacancies which are produced due to proton excitation.     

Scaling and string tension in pureSU(2) lattice gauge theory

Wilson loops inSU(2) lattice gauge theory without fermions are determined on lattices of size 12⁴, 16⁴ and 24⁴ at β=2.4, 2.5 and 2.6. At β=2.6 the static quark-antiquark potential is extracted for distances up to 8 lattice units. A string tension smaller by a factor 2 than in previous investigations is found. Deviations from asymptotic scaling for multiplicatively improved Creutz ratios are certain, and their magnitude depends on the geometrical size of the ratios. This implies deviations from scaling.     

Multifractal behaviour of n-simplex lattice

We study the asymptotic behaviour of resistance scaling and fluctuation of resistance that give rise to flicker noise in an n-simplex lattice. We propose a simple method to calculate the resistance scaling and give a closed-form formula to calculate the exponent, β _L, associated with resistance scaling, for any n. Using current cumulant method we calculate the exact noise exponent for n-simplex lattices.     

格点规范理论(Ⅰ)

本文介绍了由Wilson等人发展起来的处理粒子间强相互作用的格点规范理论。由于这个理论是建立在点阵上的规范理论,故首先讨论了点阵上体系的场论性质和统计物理性质之间的联系,介绍了处理粒子禁闭问题的Wilson判据,点阵的哈密顿形式。然后讨论了各种具体模型的计算方法,如规范场的点阵模型、紧致QED模型、费米子模型、阿贝尔Higgs模型等。在此基础上,总结出Wilson定理。本文也讨论了格点规范理论中的实空间重正化群方法,介绍了Heisenberg平面模型的重正化群分析,一维的二维的复现关系及Migdal近似。最后评介了近年来对于Wilson回路算子的一些研究,内容包括’t Hooft代数和Wilson回路算子方程等。     

Low-lying Gamow-Teller transitions in spherical nuclei

The Pyatov Method has been used to study the low-lying Gamow-Teller transitions in the mass region of 98 ⩽ A ⩽ 130. The eigenvalues and eigenfunctions of the total Hamiltonian have been solved within the framework of proton-neutron quasiparticle random-phase approximation. The low-lying β decay log(ft) values have been calculated for the nuclei under consideration.     

A Condensed Matter Interpretation of SM Fermions and Gauge Fields

We present the bundle (Aff(3)⊗ℂ⊗Λ)(ℝ³), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each (ℂ⊗Λ)(ℝ³) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space (Aff(3)⊗ℂ)(ℤ³). This space allows a simple physical interpretation as a phase space of a lattice of cells. We find the SM SU(3) _c ×SU(2) _L ×U(1) _Y action on (Aff(3)⊗ℂ⊗Λ)(ℝ³) to be a maximal anomaly-free gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations. The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with ℤ₂-degenerated vacuum state. We construct anticommuting fermion operators for the resulting ℤ₂-valued (spin) field theory. A metric theory of gravity compatible with this model is presented too.     

Extended Holomorphic Anomaly in Gauge Theory

The partition function of an N=2{\mathcal {N}=2} gauge theory in the Ω-background satisfies, for generic value of the parameter b = -e₁/e₂{\beta=-{\epsilon_1}/{\epsilon_2}} , the, in general extended, but otherwise β-independent, holomorphic anomaly equation of special geometry. Modularity together with the (β-dependent) gap structure at the various singular loci in the moduli space completely fixes the holomorphic ambiguity, also when the extension is non-trivial. In some cases, the theory at the orbifold radius, corresponding to β = 2, can be identified with an “orientifold” of the theory at β = 1. The various connections give hints for embedding the structure into the topological string.     

Hadron masses in QCD with one quark flavour

One-flavour QCD – a gauge theory with SU(3) colour gauge group and a fermion in the fundamental representation – is studied by Monte Carlo simulations. The mass spectrum of the hadronic bound states is investigated in a volume with extensions of L≃4.4r₀ (≃ 2.2 fm) at two different lattice spacings: a≃0.37r₀ (≃ 0.19 fm) and a≃0.27r₀ (≃ 0.13 fm). The lattice action is a Symanzik tree-level improved Wilson action for the gauge field and an (unimproved) Wilson action for the fermion.     

Energy dependence of photon-inducedL shell x-ray intensity ratios in Ta and W

TheL shell x-ray intensity ratios have been measured for the elements Ta and W by photoionization ofL shell electrons in the photon energy region 14⩽E⩽44 keV. The experimental results are compared with those calculated at the photon energies used in the present measurements. The measured values show fairly good agreement with the calculated values within the experimental uncertainties.     

The search for cosmic strangelets with the supersonic concorde and with JACEE's circumpolar balloon flight in Antarctica

The search for cosmic strangelet nuclei was carried out by two experiments with emulsion chambers. A balloon-borne JACEE emulsion chamber was flown at 3.5 g/cm² for 200 h in Antarctica (JACEE-10 experiment) and the Concorde flights were made by ECHOS at an atmospheric depth of 110 g/cm² between Paris and New York. No nuclei withZ⩾30 survived after traversing 60–120 g/cm² of the detector materials in the JACEE instruments. No evidence for a long mean free path were found in the zenith angle distribution forZ/β⩾26 nuclei. The exposure factor used by the JACEE was 72 m²hsr. The intensity upperbounds,I⩽(2.2–9.7)×10⁻²/m²h sr, were obtained for strangelets having an atmospheric attenuation length of 220−50 g/cm², which corresponds to the case for mass numberA=100–10000 andZ/β > 13. Concorde experiments (ECHOS) used both a thin and a thick emulsion chamber. The total exposure was 209 m² h sr and no candidates with chargeZ⩾30 were found. The largest track hadZ/β=28.6±1.29 withβ ∼ 1. Nuclei observed with charge 13⩽Z⩽30 were consistent with the survival intensity of ordinary nuclei. The flux bounds from the ECHOS experiments were I⩽(2.1–5.0) x 10⁻²/m²h for strangelets with mass number 100⩽A⩽1000.     

Infinite nuclear matter model and a new mass formula for atomic nuclei

The ground-state energy of an atomic nucleus with asymmetryβ is considered to be equivalent to the energy of a perfect sphere made up of the infinite nuclear matter of the same asymmetry plus a residual energyη called the local energy,η represents the energy due to shell, deformation, diffuseness and exchange Coulomb effect etc. Using this picture and the generalized Hugenholtz- Van Hove theorem of many-body theory a new mass formula has been developed. Based on this, a mass table containing the mass excesses of 3481 nuclei in the range 18 ⩽A ⩽ 267 has been made. This mass formula is compared with other mass models.     

Estimates of the number of quantal bound states in one and three dimensions

Using the relation between the number of bound states and the number of zeros of the radial eigen-functionψ(r), or equivalently, that ofφ(r)=rψ(r) in the range 0⩽r⩽∞, the upper bounds on the number of bound states generated by potentialV(r) in different angular momentum channels are obtained in three dimension. Using a similar procedure, the upper bound on the number of bound states in one dimension is also deduced. The analysis is restricted to a class of potentials for whichE=0 is the threshold. By taking a number of specific examples, it is demonstrated that both in one and three dimensions, the estimate of the upper bound obtained by this procedure is very close to or equal to the exact number of bound states. The correlation of the present method with the Levison’s theorem and WKB approximation is discussed.     

Finite-size scaling in a microcanonical ensemble

The finite-size scaling technique is extended to a microcanonical ensemble. As an application, equilibrium magnetic properties of anL×L square lattice Ising model are computed using the microcanonical ensemble simulation technique of Creutz, and the results are analyzed using the microcanonical ensemble finite-size scaling. The computations were done on the multitransputer system of the Condensed Matter Theory Group at the University of Mainz.     

Fermilab top mass and modified Fritzsch mass matrices

Fritzsch like mass matrices with non-zero 22-elements both in U sector and D sector have been investigated in the context of latest data regardingm _t ^phys , |V _ub|, |V _cb|, |V _td| and |V _ts|. Unlike several other phenomenological models, the present model not only accommodates the value ofm _t ^phys in the range 150–240 GeV, encompassing the CDF and D0 values, but is also able to reproduce |V _cb| ≊0.040 and |V _ub/V_cb| = 0.08±0.02 and |V _td| is predicted to lie in the range 0.005–0.014. Further, the angles of the unitarity triangle, related to the CP-violating asymmetries, are calculated to be in the ranges −1.0⩽sin2α⩽−0.1, 0.6 ⩽sin2α⩽1.0 and 0.48⩽sin2β⩽0.56, which are in agreement with other recent calculations.     

Scaling behaviour of Creutz ratios inSU(2) lattice gauge theory

An analysis of the scaling behaviour of Creutz ratios on large lattices is given forSU(2) gauge theory. The β-interval is 2.5≦β≦2.8. Under a factor 2 scaling test, after multiplicative corrections for lattice artifacts, the Monte Carlo data show deviations from scaling, which are similar for all values of β. The ratios can be fitted successfully by a sum of three perturbative terms and an exponentially decreasing nonperturbative term. For many ratios the latter turns out to be very small, and its size dependence at fixed β is consistent with that of an area term in the Wilson loops. The deviation of the corresponding exponents from the ones expected for an area term gives a coherent cxplanation of the observed departures from scaling. It is well possible that for fixed spatial extension (in lattice units) nonperturbative contributions vanish so fast that they cannot be interpreted as physical effects.