Two-loop parameter relations between dimensional regularization and dimensional reduction applied to SUSY-QCD

The two-loop relations between the running gluino–quark–squark coupling, the gluino and the quark mass defined in dimensional regularization (DREG) and dimensional reduction (DRED) in the framework of SUSY-QCD are presented. Furthermore, we verify with the help of these relations that the three-loop β-functions derived in the minimal subtraction scheme combined with DREG or DRED transform into each other. This result confirms the equivalence of the two schemes at the three-loop order, if applied to SUSY-QCD.     

The Faddeev-Popov procedure and application to bosonic strings: An infinite dimensional point of view

A generalisation of the finite dimensional presentation of the Faddeev-Popov perocedure is derived, in an infinite dimensional framework for gauge theories with finite dimensional moduli space using heat-kernel regularised determinants. It is shown that the infinite dimensional Faddeev-Popov determinant is-up to a finite dimensional determinant determined by a choice of a slice-canonically determined by the geometrical data defining the gauge theory, namely a fibre bundlePP/G with structure groupG and the invariance group of a metric structure given on the total spaceP. The case of (closed) bosonic string theory is discussed.     

The Lamb shift in dimensional regularisation

We present a simple derivation of the Lamb shift using effective field theory techniques and dimensional regularisation.     

Exact results for the dynamics of the classical one dimensional easy plane ferromagnet at low temperatures

The in-plane and out-of-plane dynamical correlation functions for the classical one dimensional easy plane ferromagnet are calculated asymptotically exactly at low temperatures. The results are restricted to temperatures much below the crossover temperature at which spins begin aligning in the plane. The long wavelength behavior of the in-plane fluctuations is consistent with dynamical scaling, in contrast to the isotropic case, and agrees with the results of Villain and of Nelson and Fisher. The linewidths for the in-plane fluctuations at short wavelengths are calculated exactly, and approach those of the isotropic model for small anisotropy. The theory of Villain, the theory of Cieplak and Sjolander, and the simulations of Loveluck, Jauslin, Schneider and Stoll all give incorrect results for these linewidths. The out of plane linewidths show an anomalous temperature dependence due to a singularity in the three spin wave density of states that is characteristic of one dimensional systems. The linewidth is proportional toT ² lnT except at the wavevector for which the second derivative of the spin wave frequency with respect to wavevector vanishes (/2 for CsNiF₃) where the linewidth is proportional toT ^5/3. The linewidth has a strong discontinuity as the wavevector increases as a result of a catastrophe occurring in the calculation of the three spin wave density of states. The position and strength of the discontinuity are temperature dependent. The diffusion coefficient is logarithmically dependent on the anisotropy, and diverges as (T ² lnD)^–1, which is consistent with the (lnT)^–1 behavior predicted for the isotropic ferromagnet in earlier work. The results are derived for the case of single ion anisotropy, using a spin wave theory for static correlations and the spin current damping function, and can be readily extended to the case of anisotropic exchange.     

Bounds on the coupling constant in two dimensional boson models

We consider two dimensional boson field theories with an interaction potentialV (). We show how to define a cut-off, renormalised Hamiltonian for a certain class of non-polynomialV (), which are defined via an integral transform. We formulate precisely a variational argument devised by Coleman, obtaining a constraint on the coupling constant of the theory with generalV (), and illustrate the argument with several examples.     

Generalized spin structures on four dimensional space-times

We discuss various methods for investigating the existence and uniqueness of generalized spin structures. We show that on a four dimensional manifold whole families may be constructed using any internal symmetry group of the formG/₂, whereG is a simply connected Lie group.     

On certain infinite dimensional aspects of Arakelov intersection theory

Letk:YX be an embedding of compact complex manifolds. Bismut and Lebeau have calculated the Quillen norm of the canonical isomorphism identifying the determinant of the cohomology of a holomorphic vector bundle overY and the determinant of the cohomology of a resolution by a complex of holomorhic vector bundles overX. The purpose of this paper is to show that the formula of Bismut-Lebeau can be viewed as an equivariant intersection formula over the loop space of the considered manifolds, in the presence of an infinite dimensional excess normal bundle. This excess normal bundle is responsible for the appearance of the additive genusR of Gillet and Soulé in the formula of Bismut and Lebeau.     

Bethe ansatz study of 1+1 dimensional Hubbard model

A wave function of Bethe ansatz form is used to obtain approximate solutions for a 1+1 dimensional Hubbard model. In this model a helical structure with infinite diameter is constructed to mimic the square lattice. Betheansatz analysis is performed along the helical line. By including the hopping integrals in perpendicular direction, the solutions show some recovery of two dimensional character. At half-filling, the system undergoes Mott transition, the critical value of on-site repulsion obtained by this scheme is smaller than that of the mean-field theory. For a given particle density, the energy level of corresponding one dimensional model is extended to a band. The relation of the results to the properties of two dimensional strong-correlation system is discussed.     

Specific heat of the two dimensional antiferroelectric squaric acid

The heat capacity of a single crystal of the two dimensional antiferroelectric squaric acid was measured particularly near the phase transition. In a wide temperature range belowT _c a strong temperature dependence of the anomaleous specific heat is found which can be described by a critical exponent=0.5. The behaviour close toT _c is determined by a latent heat thus indicating the phase transition to be of the first order. Near the phase transition the thermal behaviour can be described by a Landau type theory. The smallness of the transition entropy detected may be ascribed possibly to proton tunneling.     

Finite dimensional representations of the quantum Lorentz group

All finite dimensional irreducible representations of the quantum Lorentz group SL _q (2,) are described explicitly and it is proved all finite dimensional representations of SL _q (2,) are completely reducible. The conjecture of Podle and Woronowicz will be answered affirmatively.     

Cross sections for the production of heavy quarks via dimensional analysis

Cross sections for the production ofc, b andt quark states have been obtained by using experimental data for K systems plus dimensional analysis. The cross sections forc andb production are found to agree with available experimental data, andt values are in reasonable accord with other calculations. The implications of using p as incident particles in collider experiments are discussed, and it is suggested that simple anticoincidence techniques may reduce unwanted background in the search for top quarks.     

A note on the boson-fermion correspondence and infinite dimensional groups

We show how to construct irreducible projective representations of the infinite dimensional Lie group Map (S ¹, ), by embedding it into the group of Bogoliubov automorphisms of the CAR. Using techniques of G. Segal for extending certain representations of Map (S ¹, SU(2)) we show that our representations extend to give representations of a certain infinite dimensional superalgebra. We relate our work to the well known boson-fermion correspondence which exists in 1+1 dimensions.     

Hyperbolicity,sinks and measure in one dimensional dynamics

Letf be aC ² map of the circle or the interval and let(f) denote the complement of the basins of attraction of the attracting periodic orbits. We prove that(f) is a hyperbolic expanding set if (and obviously only if) every periodic point is hyperbolic and(f) doesn't contain the critical point. This is the real one dimensional version of Fatou's hyperbolicity criteria for holomorphic endomorphisms of the Riemann sphere. We also explore other applications of the techniques used for the result above, proving, for instance, that for everyC ² immersionf of the circle (i.e. a map of the circle onto itself without critical points), either its Julia set has measure zero or it is the whole circle and thenf is ergodic, i.e. positively invariant Borel sets have zero or full measure.     

Ground-state properties of the one dimensional electron liquid

We present a theory of the pair distribution function g(z) and many-body effective electron-electron interaction for the one dimensional (1D) electron liquid. Our approach involves the solution of a zero-energy scattering Schrödinger equation for where we implemented the Fermi hypernetted-chain approximation including the elementary diagram corrections. We present numerical results for g(z) and the static structure factor S(k) and obtain good agreement with data from diffusion Monte Carlo studies of the 1D system. We calculate the correlation energy and charge excitation spectrum over an extensive range of electron density. Furthermore, we obtain the static correlations in good qualitative agreement with those calculated for the Luttinger liquid model with long-range interactions.     

Dynamics of the one dimensional randomly dilute Ising ferromagnet

The effect of randomly dilute impurities in the percolation limit on the relaxation of magnetization M(t) and on the way the time-dependent correlation function M(t)M(0) decays in a one dimensional Ising ferromagnet is considered, as is the behaviour of the dynamic susceptibility. It is found that the decay of the magnetization is hardly altered except for small faster decaying boundary effects. However, the correlation function is drastically altered, decaying in general faster asymptotically than the pure system. The dynamical susceptibility also changes, showing a breaking in the simple relaxational scaling form of the pure system. Crossover behaviour with non-critical slowing down (apart from the critical slowing down asTT _c=0) is also observed in the transition from the pure ferromagnetic to randomly dilute behaviour.     

Massless and massive one-loop three-point functions in negative dimensional approach

In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive, two massive with the same mass m and three equal masses for the virtual particles. Our results are given in terms of hypergeometric and hypergeometric-type functions of the external momenta (and masses for the massive cases) where the propagators in the Feynman integrals are raised to arbitrary exponents and the dimension of the space-time is D. Our approach reproduces the known results; it produces other solutions as yet unknown in the literature as well. These new solutions occur naturally in the context of NDIM revealing a promising technique to solve Feynman integrals in quantum field theories. Received: 14 April 2002 / Revised version: 18 July 2002 / Published online: 7 October 2002 RID="a" ID="a" e-mail: suzuki@ift.unesp.br RID="b" ID="b" e-mail: esdras@ift.unesp.br RID="c" ID="c" e-mail: schmidt@fisica.ufpr.br