Money and Goldstone modes

Why is ``worthless'' fiat money generally accepted as payment for goods and services? In equilibrium theory, the value of money is generally not determined: the number of equations is one less than the number of unknowns, so only relative prices are determined. In the language of mathematics, the equations are ``homogeneous of order one''. Using the language of physics, this represents a continuous ``Goldstone'' symmetry. However, the continuous symmetry is often broken by the dynamics of the system, thus fixing the value of the otherwise undetermined variable. In economics, the value of money is a strategic variable which each agent must determine at each transaction by estimating the effect of future interactions with other agents. This idea is illustrated by a simple network model of monopolistic vendors and buyers, with bounded rationality. We submit that dynamical, spontaneous symmetry breaking is the fundamental principle for fixing the value of money. Perhaps the continuous symmetry representing the lack of restoring force is also the fundamental reason for large fluctuations in stock markets.Comment: 7 pages, 3 figure

Two-Higgs-Doublet Models with CP violation

We consider the Two-Higgs-Doublet Model and determine the range of parameters for which CP violation and Flavor Changing Neutral Current effects are naturally small. It corresponds to small values of the mass parameter m_{12}^2, describing soft (\phi_1,\phi_2) mixing in the potential. We discuss how, in this approach, some Higgs bosons can be heavy, with mass of the order of 1 TeV. The possibility that at the Tevatron, LHC and an e^+e^- Linear Collider, only one Higgs boson will be found, with properties indistinguishable from those in the Standard Model (SM), we define as the SM-like scenario. While this scenario can be obtained with large \mu^2 \sim \Re m_{12}^2 parameter, in which case there is decoupling, we here discuss the opposite case of small \mu^2, without decoupling.Comment: 5 pages, LaTeX, including figures. Presented at SUSY02, DESY, June 2002 and LCWS02, Jeju, Korea, August 2002. To appear in the proceedings. Version 2: minor changes, additional reference

Distinguishing Higgs models at photon colliders

We consider the two effective couplings hZ\gamma and h\gamma\gamma involving a neutral scalar Higgs boson with a mass around 100 GeV in the Standard Model, in the Two Higgs Doublet Model, and in the Minimal Supersymmetric Standard Model. The couplings can be tested at Photon Colliders, and used to distinguish these models.Comment: 5 pages, LaTeX, using sprocl.sty, including 2 figures. Contribution to the Proceedings of the International Workshop on Linear Colliders, April 28-May 5, 1999, Sitges (Spain). Version 2: minor clarification

Periodic orbit sum rules for billiards: Accelerating cycle expansions

We show that the periodic orbit sums for 2-dimensional billiards satisfy an infinity of exact sum rules. We test such sum rules and demonstrate that they can be used to accelerate the convergence of cycle expansions for averages such as Lyapunov exponents.Comment: 19 pages, 5 postscript figures, submitted to Journal of Physics

Resolving SM-like scenarios via Higgs boson production at a Photon Collider: I. 2HDM versus SM

We consider the possibility that after operations at the LHC and e^+e^- Linear Colliders a Higgs boson will be discovered, but no signal of New Physics will be found (Standard-Model-like scenario). This can occur in the Standard Model (SM) as well as in other models, including the Two-Higgs-Doublet Model (2HDM), the MSSM, etc. Experiments at a Photon Collider can resolve these cases. In this paper we compare the SM and the 2HDM~(II). In the analysis we use as independent quantities the ratios, to the SM values, of couplings of the observed Higgs boson to gauge bosons, and to up and down-type quarks (basic couplings). We derive a relation between these ratios within the 2HDM~(II), a pattern relation. With the aid of this relation, different possible realizations of an SM-like scenario are found. For these realizations, we calculate the loop couplings of the Higgs boson with \gamma\gamma and Z \gamma, and also with gluons, taking into account the expected accuracy in the measurements of the basic couplings. The obtained deviation of the two-photon width from its SM value is generally higher than the expected inaccuracy in the measurement of \Gamma_{\gamma \gamma} at a Photon Collider. The result is sensitive to the parameters of the Higgs self interaction.Comment: 29 pages, LaTeX, including figure

Standard-Model-like scenarios in the 2HDM and Photon Collider potential

After operations at the LHC and e^+e^- Linear Colliders it may be found that a Standard-Model-like scenario is realized. In this scenario no new particle will be discovered, except a single Higgs boson having partial widths or coupling constants with fundamental particles, whose squares are close, within anticipated experimental uncertainty, to those of the SM. Experiments at a Photon Collider can resolve whether the SM or e.g. the Two-Higgs-Doublet Model is realized in Nature. For the SM-like realizations of the 2HDM (II) we study the loop couplings of the Higgs boson with \gamma\gamma and Z \gamma, and also with gluons. The deviation of the two-photon width from its SM value is generally higher than the expected inaccuracy in the measurement of \Gamma_{\gamma \gamma} at a Photon Collider. The deviation is sensitive to the parameters of the Higgs self interaction.Comment: 8 pages, aipproc, including figures. Presented at 5th International Linear Collider Workshop (LCWS 2000), Fermilab, Batavia, Illinois, 24-28 Oct 2000, to appear in proceeding

Split-screen single-camera stereoscopic PIV application to a turbulent confined swirling layer with free surface

An annular liquid wall jet, or vortex tube, generated by helical injection inside a tube is studied experimentally as a possible means of fusion reactor shielding. The hollow confined vortex/swirling layer exhibits simultaneously all the complexities of swirling turbulence, free surface, droplet formation, bubble entrapment; all posing challenging diagnostic issues. The construction of flow apparatus and the choice of working liquid and seeding particles facilitate unimpeded optical access to the flow field. A split-screen, single-camera stereoscopic particle image velocimetry (SPIV) scheme is employed for flow field characterization. Image calibration and free surface identification issues are discussed. The interference in measurements of laser beam reflection at the interface are identified and discussed. Selected velocity measurements and turbulence statistics are presented at Re_λ = 70 (Re = 3500 based on mean layer thickness)

Supersymmetric approximations to the 3D supersymmetric O(N) model

We develop several non-perturbative approximations for studying the dynamics of a supersymmetric O(N) model which preserve supersymmetry. We study the phase structure of the vacuum in both the leading order in large-N approximation as well as in the Hartree approximation, and derive the finite temperature renormalized effective potential. We derive the exact Schwinger-Dyson equations for the superfield Green functions and develop the machinery for going beyond the next to leading order in large-N approximation using a truncation of these equations which can also be derived from a two-particle irreducible effective action.Comment: 16 pages, 3 figure