The loop expansion for the effective potential in theP(φ)2 quantum field theory

We study the loop expansion for the effective potential, defined as the Fenchel transform (convex conjugate) of the pressure in an external field, in theP()₂ quantum field theory. For values of the classical fielda for which the classical potentialU ₀(a)=P(a)+1/2m ² a ² equals its convex hull and has nonvanishing curvature we prove that the 1-PI loop expansion is asymptotic as 0. We also give an example of a double well classical potential for which the 1-PI loop expansion fails to be asymptotic, and find the true asymptotics.This paper is a condensed version of the author's Ph.D. thesis for the Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada V6T 1Y4     

A new proof of the existence and nontriviality of the continuum ϕ 2 4 and ϕ 3 4 quantum field theories

We use Schwinger-Dyson equations combined with rigorous “perturbation-theoretic” correlation inequalities to give a new and extremely simple proof of the existence and nontriviality of the weakly-coupled continuum ? ₂ ⁴ and ? ₃ ⁴ quantum field theories, constructed as subsequence limits of lattice theories. We prove an asymptotic expansion to order λ or λ² for the correlation functions and for the mass gap. All Osterwalder-Schrader axioms are satisfied except perhaps Euclidean (rotation) invariance.     

On the effective action and field renormalization for variationalλø4

We perform a study of the effective action within the gaussian variational approach for λλ₃₊₁⁴ with the aim of understanding better field renormalization. The difficulties in obtaining a finite effective action in this approach are made clear.     

Tricritical point in quantum phase transitions of the Coleman–Weinberg model at Higgs mass

The tricritical point, which separates first and second order phase transitions in three-dimensional superconductors, is studied in the four-dimensional Coleman–Weinberg model, and the similarities as well as the differences with respect to the three-dimensional result are exhibited. The position of the tricritical point in the Coleman–Weinberg model is derived and found to be in agreement with the Thomas–Fermi approximation in the three-dimensional Ginzburg–Landau theory. From this we deduce a special role of the tricritical point for the Standard Model Higgs sector in the scope of the latest experimental results, which suggests the unexpected relevance of tricritical behavior in the electroweak interactions.     

One-loop surface tension on a boundary inλφ 4 theory

We calculate quantum corrections to the vacuum energy in ⁴ theory with a tachyonic mass term in a half space, where the scalar field is required to satisfy the Dirichlet boundary condition on the surface. It is found that the one-loop self-energy diagram includes a finite energy portion, representing a repulsive surface tension on the boundary.     

Particles and “bumps” in quantum field configurations

We study an approach to making a precise identification of particles with bumps in quantum field configurations. The problem requires some effort because typical field configurations are distributions and not elements of the classical configuration space at all. We show that the part of a configuration consisting of vacuum fluctuations may be identified and filtered out in a very natural way, leaving a function which is in the classical configuration space. The filtered field configuration depends on the state of the field, and for ann-particle state withn particles well localized and well separated in the Newton-Wigner sense, the filtered field configuration hasn bumps located where the particles are. We close with a discussion of observation in the Schrödinger representation for the free field in terms of our results.This paper is dedicated to the memory of Paola Calderoni.     

Analytic and numerical evidence from quantum field theory for the hyperscaling relation dv = 2Δ−γ in the d=3 ising model

The hyperscaling relationdv = 2 - (d=3) for the Ising model has been shown to follow from a constructive approach proposed by one of the authors (R.S.) of a relativistic theory of self-interacting Bosons in d space-time dimensions. We present evidence that the two assumptions made in this approach are valid: On a finite Euclidean (hyper-) cubical lattice in d dimensions the renormalization map from the bare to the renormalized parameters should have nonvanishing Jacobian everywhere. We show this analytically and numerically on the boundary set of the parameters. The numerical analysis involves Monte Carlo calculations in the region where the bare coupling constantg ₀ is infinite, giving the Ising model. The linear sizen of the lattice (with periodic boundary conditions) was taken to be 5, 6, and 10. There we also checked the second assumption saying that the correlation length for the Ising model is a monotonic function of the temperature. We also comment on the possible numbers of zeros of the Callan-Symanzik function of this theory.     

Legendre's relation and the quantum equivalence osp(4|4)1 = osp(2|2)−2 ⊕ su(2)0

Using explicit results for the four-point correlation functions of the Wess–Zumino–Novikov–Witten (WZNW) model we discuss the conformal embedding osp(4|4)₁ = osp(2|2)₋₂ ⊕ su(2)₀. This embedding has emerged in Bernard and LeClair's recent paper cond-mat/003075. Given that the osp(4|4)₁ WZNW model is a free theory with power law correlation functions, whereas the su(2)₀ and osp(2|2)₋₂ models are CFTs with logarithmic correlation functions, one immediately wonders whether or not it is possible to combine these logarithms and obtain simple power laws. Indeed, this very concern has been raised in a revised version of cond-mat/003075. In this paper we demonstrate how one may recover the free field behaviour from a braiding of the solutions of the su(2)₀ and osp(2|2)₋₂ Knizhnik–Zamolodchikov equations. We do this by implementing a procedure analogous to the conformal bootstrap programme Nucl. Phys. B 241 (1984) 333. Our ability to recover such simple behaviour relies on a remarkable identity in the theory of elliptic integrals known as Legendre's relation.     

Cooling of SU(3) lattice gauge field configurations and the η' mass

A method is proposed to calculate the topological susceptibility in SU(3) lattice gauge theory by measuring the asymptotic action of cooled configurations for an ensemble of configurations. The results of a pilot study are presenred.     

Critical phenomena in the β-(2×4) → α-(2×4) reconstruction transition on the (001) GaAs surface

The critical exponents of the β-(2×4) → α-(2×4) reconstruction phase transition on the (001) GaAs surface are determined experimentally. It is found that the phase transition is analogous to a van der Waals transition. The critical parameters T _c , P _c , and Θ_c have been measured experimentally. The mean field theory is applied, and three-parameter isotherms are obtained that agree with the experimental results at the following values of the parameters: E_st = 0.36 eV, ΔE = 0.18 eV, and E _i = 0.134 eV. Precision measurements of the critical exponents β and δ are carried out. Their values β = 1/8 and δ = 15 indicate that the phase transition is truly two-dimensional.     

Calculation of the surface tension and the surface energy of Lennard–Jones fluids from the radial distribution function in the interface zone

A detailed study is presented of the calculation of the surface tension and the surface energy of Lennard–Jones fluids from the radial distribution function and the density profile. To do so, a modification is made to Lekner and Henderson's statistical mechanics approach by introducing two simple analytical expressions for the radial distribution function of the interface zone. In these expressions the radial distribution functions of the liquid and vapour phases are weighted via step or exponential variations. The well- known exponential model for the density profile in the interface zone is considered. Finally, results are compared with values from experiment, from computer simulation and from relevant theoretical developments. It is shown that the use of the proposed radial distribution function in the interface zone represents a significant improvement in applying Lekner and Henderson's approach.     

Existence of three phases for aP(ϕ)2 model of quantum field

In the two-dimensional model of the quantum field theory with lagrangean density :()²–(–)^{21/2 4}–⁶: there exist (at least) three different phases for small and some ().     

Fermi surface in the new organic quasi-two-dimensional metal α-(BETS)2TlHg(SeCN)4

Quantum oscillations of de Haas-van Alphen and Shubnikov-de Haas and semiclassical angular oscillations of the magnetoresistance have been observed in the quasi-two-dimensional organic metal α-(BETS)₂TlHg(SeCN)₄. The quantum oscillations are connected with the cylindrical part of the Fermi surface. The angular oscillations are associated with the carrier motion on both the cylindrical part and quasi-planar sheets of the Fermi surface. The values of the Dingle temperature, T _D ≈ 2–3 K, and the effective mass, m* ≈ 1.03m ₀, have been defined. The possibility of the weakening of multibody interactions has been shown in this compound.     

The energy-momentum spectrum in theP(ϕ)2 quantum field theory

TheP()₂ interaction with the periodic boundary conditions is considered. It is shown that the energy-momentum spectrum lies in the forward light cone. As a consequence, this result implies that theP()₂ theory in the infinite volume with the periodic boundary conditions is Lorentz invariant.     

Phenomenology of the hierarchical lepton mass spectrum in the flipped SU(5)×U(1) string model

A detailed phenomenological analysis of the lepton mass matrices and their implications in the low energy theory are discussed, within the recently proposed SU(5)×U(1) string model. The unification scale is highly constrained while the Yukawa couplings lie in a natural region. The flavour changing decays μ→eγ, μ→3e, μ→e are highly suppressed while the depletion in the in the flux of muon neutrinos reported by the Kamiokande is explained through ν_μ↔ν_τ oscillations.     

Spontaneous SU(2) symmetry violation in the SU(2) L × SU(2) R × SU(4) electroweak model

A new approach to electroweak (EW) composite scalars is developed starting from the fundamental gauge interaction on high scale. The latter is assumed to have the group structure SU(2) _L × SU(2) _R × SU(4), where SU(4) is the Pati-Salam color-lepton group. The topological EW vacuum filled by instantons is explicitly constructed and the resulting equations for fermion masses exhibit spontaneous SU(2) flavor symmetry violation with possibility of very large mass ratios.     

(2 + 1) dimensional Hărăgus-Courcelle-Il’ichev model for the liquid surface waves in the presence of sea ice or surface tension: Bäcklund transformation,exact solutions and possibly observable effects

The wave propagation on an ocean or water surface in the presence of sea ice or surface tension is of current importance. In this paper, we investigate the (2 + 1) dimensional 6th-order model proposed recently by Hrgus-Courcelle and Ilichev for such wave propagation. Firstly, we correct some errors in the original derivations of this model. With computerized symbolic computation and truncated Painlevé expansion, we then obtain an auto-Bäcklund transformation and types of the solitonic and other exact analytic solutions to the model, with the solitary waves as a special case, able to be dealt with the powerful Wu method. Based on the results, we later propose some possibly observable effects for the future experiments, and in the end, provide a possible way to explain the regular structure of the open-sea ice break-up observations.Received: 21 July 2004, Published online: 23 December 2004PACS: 47.11. + j Computational methods in fluid dynamics - 05.45.Yvi Solitons - 47.35. + i Hydrodynamic waves - 02.70.Wz Symbolic computation (computer algebra)This revised version was published online in January 2005 with corrections to the sequence of the second authors affiliations.     

HMO model of scalar field in medium and self-focusing

In this paper, the HMO model of scalar field in medium is presented using the general covariant classical theory of scalar field in medium, which is regarded as a curved space-time represented by optical metric model (OMM) and the case of self-focusing is discussed.