Perfect Scalars on the Lattice

We perform renormalization group transformations to construct optimally local perfect lattice actions for free scalar fields of any mass. Their couplings decay exponentially. The spectrum is identical to the continuum spectrum, while thermodynamic quantities have tiny lattice artifacts. To make such actions applicable in simulations, we truncate the couplings to a unit hypercube and observe that spectrum and thermodynamics are still drastically improved compared to the standard lattice action. We show how preconditioning techniques can be applied successfully to this type of action. We also consider a number of variants of the perfect lattice action, such as the use of an anisotropic or triangular lattice, and modifications of the renormalization group transformations motivated by wavelets. Along the way we illuminate the consistent treatment of gauge fields, and we find a new fermionic fixed point action with attractive properties.Comment: 26 pages, 11 figure

Unravelling quantum carpets: a travelling wave approach

Quantum carpets are generic spacetime patterns formed in the probability distributions P(x,t) of one-dimensional quantum particles, first discovered in 1995. For the case of an infinite square well potential, these patterns are shown to have a detailed quantitative explanation in terms of a travelling-wave decomposition of P(x,t). Each wave directly yields the time-averaged structure of P(x,t) along the (quantised)spacetime direction in which the wave propagates. The decomposition leads to new predictions of locations, widths depths and shapes of carpet structures, and results are also applicable to light diffracted by a periodic grating and to the quantum rotator. A simple connection between the waves and the Wigner function of the initial state of the particle is demonstrated, and some results for more general potentials are given.Comment: Latex, 26 pages + 6 figures, submitted to J. Phys. A (connections with prior literature clarified

Constraints on Two-Higgs Doublet Models at Large tan{beta} from W and Z decays

We study constraints on type-II two Higgs doublet models at large tan{beta} from LEP/SLD Z-pole data and from lepton universality violation in W decay. We perform a global fit and find that, in the context of Z decay, the LEP/SLD experimental values for lepton universality violation, R_b, and A_b all somewhat disfavor the model. Contributions from the neutral Higgs sector can be used to constrain the scalar-pseudoscalar Higgs mass splittings. Contributions from the charged Higgs sector allow us to constrain the charged Higgs mass. For tan{beta}=100 we obtain the 1 sigma classical (Bayesian) bounds of m_{H+} > 670 GeV (370 GeV) and 1 > m_{h0}/m_{A0} > 0.68 (0.64). The 2 sigma bounds are weak. Currently, the Tevatron experimental limits on lepton universality violation in W decay provide no significant constraint on the Higgs sector.Comment: 26 pages, 9 postscript figures, REVTe

Interpretations of the NuTeV sin⁡2θW\sin^2 \theta_W

We summarize theoretical explanations of the three $\sigma$ discrepancy between $\sin^2 \theta_W$ measured by NuTeV and predicted by the Standard Model global fit. Possible new physics explanations ({\it e.g.} an unmized $Z'$) are not compelling. The discrepancy would be reduced by a positive momentum asymmetry $s^-$ in the strange sea; present experimental estimates of $s^-$ are unreliable or incomplete. Upgrading the NuTeV analysis to NLO would alleviate concerns that the discrepancy is a QCD effect.Comment: (proceedings for the NuFact'02 Workshop); reference and footnote added, following the NuTeV proceeding

Coherent states of P{\"o}schl-Teller potential and their revival dynamics

A recently developed algebraic approach for constructing coherent states for solvable potentials is used to obtain the displacement operator coherent state of the P\"{o}schl-Teller potential. We establish the connection between this and the annihilation operator coherent state and compare their properties. We study the details of the revival structure arising from different time scales underlying the quadratic energy spectrum of this system.Comment: 13 pages, 6 figure

Recent Developments in Precision Electroweak Physics

Developments in precision electroweak physics in the two years since the symposium are briefly summarized.Comment: Update on recent developments, prepared for the publication of the Proceedings of Alberto Sirlin Symposium, New York University, October 2000. 10 pages, 1 figur

Higgs-Boson Mass Limits and Precise Measurements beyond the Standard Model

The triviality and vacuum stability bounds on the Higgs-boson mass (\mh) were revisited in presence of weakly-coupled new interactions parameterized in a model-independent way by effective operators of dimension 6. The constraints from precision tests of the Standard Model were taken into account. It was shown that for the scale of new physics in the region \Lambda \simeq 2 \div 50 \tev the Standard Model triviality upper bound remains unmodified whereas it is natural to expect that the lower bound derived from the requirement of vacuum stability is substantially modified depending on the scale \La and strength of coefficients of effective operators. A natural generalization of the standard triviality condition leads also to a substantial reduction of the allowed region in the (\Lambda,\mh) space.Comment: 18 pages 3 eps figures. The discussion in the appendix was modified slightly and some typographical errors were correcte

Critical dimensions of the diffusion equation

We study the evolution of a random initial field under pure diffusion in various space dimensions. From numerical calculations we find that the persistence properties of the system show sharp transitions at critical dimensions d1 ~ 26 and d2 ~ 46. We also give refined measurements of the persistence exponents for low dimensions.Comment: 4 pages, 5 figure

Bounds on the Higgs-Boson Mass in the Presence of Non-Standard Interactions

The triviality and vacuum stability bounds on the Higgs-boson mass are revisited in the presence of new interactions parameterized in a model-independent way by an effective lagrangian. When the scale of new physics is below 50 TeV the triviality bound is unchanged but the stability lower bound is increased by 40-60 GeV. Should the Higgs-boson mass be close to its current lower experimental limit, this leads to the possibility of new physics at the scale of a few TeV, even for modest values of the effective lagrangian parameters.Comment: 5 pages, 2 figures, RevTex, submitted to PR

Coherent state of a nonlinear oscillator and its revival dynamics

The coherent state of a nonlinear oscillator having a nonlinear spectrum is constructed using Gazeau Klauder formalism. The weighting distribution and the Mandel parameter are studied. Details of the revival structure arising from different time scales underlying the quadratic energy spectrum are investigated by the phase analysis of the autocorrelation function