Evaluation of a class of diagrams useful in many-body calculations

A recent functional approach to the many-body theory has put in evidence the relevance of the diagrams containing one fermion loop only. We shall prove here a relevant theorem which shows that all (but one) of the γ-functions are irrelevant, the contained information being transferred to analyticity properties. The simplest diagrams are explicitly evaluated and some useful limits are discussed. However, some of these diagrams have been considered also in different approaches to the many-body problem, so their evaluation is of general interest. The low-density behaviour is also considered.     

Field-induced spin-orientational phase transitions in Néel ferrimagnets. I

The breakdown of the aligned states of Néel ferrimagnets in an applied magnetic field is considered. The behaviour of isotropic two-and three-sublattice ferrimagnets is treated in the framework of the mean-field approximation. A phenomenological method also limited by the mean-field approximation is used to analyse the behaviour of the anisotropic ferrimagnet. Particular emphasis is placed on the vicinity of the compensation temperature. Approximate analytical expressions which are valid near the compensation temperature are given for the phase-boundary positions, typical magnetic fields, and temperature ranges of the phase diagrams.     

Green's function equations of motion for a many-fermion system: II. Inhomogeneous system at finite temperature

The equations of motion for many-time causal Green's functions are extended to an inhomogeneous many-fermion system at finite temperature. The boundary condition that the perturbation vanishes in the remote past and distant future (adiabatic hypothesis) is used to determine the unperturbed propagator. The temperature enters the theory only as a parameter. Thus there is no need for analytic continuations in the complex temperature-time plane. The theory is used to derive thermal Hartree-Fock theory and Wick's theorem at finite temperature. A linked cluster perturbation expansion at finite temperature is obtained by iterating the equations of motion, without unlinked disconnected diagrams even appearing. After integration over frequency, the present theory gives the perturbation theory rules in terms of global propagators that Baym and Sessler obtained from the imaginary-time theory.     

热场动力学中的切割图方法及热格林函数的虚部

在热场动力学的框架下,依据有限温度下的切割定理提出了一套直观的费曼图切割方法及其相应的费曼规则,从而给出了一条计算热格林函数应部的方便途径.作为应用的例子我们分别讨论了二点、三点和四点格林函数的虚部.     

The equivalence theorem for the heavy-Higgs Standard Model and the gauged nonlinear σ-model

The equivalence theorem states that the leading part of the amplitude for a process with external longitudinally polarized vector bosons is given by the amplitude in which the longitudinal vector bosons are replaced by the corresponding pseudo-Goldstone bosons. The validity of this theorem within the standard model with a heavy Higgs boson and within the gauged nonlinear -model (in which the Higgs boson is absent) is shown. Furthermore it is examined to what extent also internal lines other than scalar lines can be neglected. A simple power-counting method is developed which determines the leading diagrams for a given process at an arbitrary loop order. This method is also applied to effective Lagrangians with additional nonstandard interaction terms of higher dimension (chiral Lagrangians).     

Critical behaviours and magnetic properties of three-dimensional bond and anisotropy dilution Blume——Capel model in the presence of an applied field

This paper studies the critical behaviours and magnetic properties of three-dimensional bond and anisotropy dilution Blume--Capel model (BCM) in the presence of an applied field within the effective field theory. The trajectory of tricritical point, reentrant transitions and degenerate patterns of anisotropy are obtained both for the bond and the anisotropy dilutions. The global phase diagrams demonstrate unusually reentrant phenomena. The temperature dependences of magnetization curves undergo remarkable spin glass behaviour at low temperatures, and transform from ferromagnetism to paramagnetism at high temperature in applied fields. Temperature dependence of magnetic susceptibility curve is in qualitative agreement with experimental result.     

Processes at high energy and large momentum transfer: the momentum-space approach to the asymptotics ofφ 3 ladder diagrams

The Sudakov method is extended to study the scattering amplitudes in the high-energy and large-momentum-transfer limit. The behaviour of arbitraryφ ³ ladder diagrams in the leading logarithm approximation is reconsidered. This leads to a simple physical picture of the asymptotic behaviour: the leading-term contributions are related to the different paths along which the large momentum is transferred through the ladder diagrams.     

SU(N) elastic rescattering in B and D decays

The treatment of elastic final-state interactions (FSIs) under a symmetry group is presented. The proposed model is based on Watson's theorem, i.e. on symmetry properties of the -matrix and on its unitarity. This theorem provides an easy way to introduce rescattering effects by defining final-state interactions mixing matrices. A symmetry group fixes the structure of such mixing matrices, and the passage from one group to another is studied (for example, SU(2) to SU(3)). Mixings among two charmless pseudoscalar decay product states will be systematically analyzed. Finally, these mixing matrices will be used on quark diagram parametrizations of B and D decay amplitudes. This will have some important consequences on the definition of quark diagrams. It will be argued that these diagrams should not contain any FSI effects, i.e. they should be real (except for CKM factors). FSIs are then introduced at the hadronic level, by mixing basic quark diagram topologies. Received: 17 December 1998 / Revised version: 17 February 1999 / Published online: 28 September 1999     

Study of the O(N) linear \sigma model at finite temperature using the 2PPI expansion

We show that a new expansion, which sums seagull and bubble graphs to all orders, can be applied to the O(N) linear -model at finite temperature. We prove that this expansion can be renormalized with the usual counterterms in a mass independent scheme and that Goldstone's theorem is satisfied at each order. At the one loop order of this expansion, the Hartree result for the effective potential (daisy and superdaisy graphs) is recovered. We show that at one loop 2PPI order, the self-energy of the -meson can be calculated exactly and that diagrams are summed beyond the Hartree approximation. Received: 22 March 2001 / Revised version: 3 September 2001 / Published online: 14 December 2001     

Diagrammar in classical scalar field theory

In this paper we analyze perturbatively a g?⁴classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplify the calculations and make the classical perturbative calculations almost “identical” formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem.     

Manifestations of topological effects in graphene

Graphene is a monoatomic layer of graphite with carbon atoms arranged in a two-dimensional honeycomb lattice configuration. It has been known for more than 60 years that the electronic structure of graphene can be modelled by two-dimensional massless relativistic fermions. This property gives rise to numerous applications, both in applied sciences and in theoretical physics. Electronic circuits made out of graphene could take advantage of its high electron mobility that is witnessed even at room temperature. In the theoretical domain the Dirac-like behaviour of graphene can simulate high energy effects, such as the relativistic Klein paradox. Even more surprisingly, topological effects can be encoded in graphene such as the generation of vortices, charge fractionalisation and the emergence of anyons. The impact of the topological effects on graphene's electronic properties can be elegantly described by the Atiyah–Singer index theorem. Here we present a pedagogical encounter of this theorem and review its various applications to graphene. A direct consequence of the index theorem is charge fractionalisation that is usually known from the fractional quantum Hall effect. The charge fractionalisation gives rise to the exciting possibility of realising graphene based anyons that unlike bosons or fermions exhibit fractional statistics. Besides being of theoretical interest, anyons are a strong candidate for performing error free quantum information processing.     

Thermal and superthermal properties of supersymmetric field theories

We discuss the finite-temperature behaviour of supersymmetric field theories. We show that their “superthermal” properties which concern the question of susy breaking at finite temperature and their thermal properties must be considered separately. Susy breaking is determined by the so-called superthermal ensemble, whereas thermodynamical properties follow from the conventional thermal ensemble, leading to the usual statistics for the bosonic and fermionic components of a superfield. We show that superspace techniques can be used in a straightforward way only for superthermal Green functions but not for thermal ones. We also discuss the possibility of finite-temperature susy restoration and the implications of Goldstone's theorem at finite temperature.     

Yukawa fluid at a hard wall: field theory description

We adopt a field-theoretical approach to study the structure and thermodynamics of a spatially confined fluid interacting with the Yukawa potential. We derive analytic expressions for the pressure, the Helmholtz free energy, the correlation function, the density profile, and the adsorption. Different simple analytic expressions of the density profile are compared with the numerical estimation of the mean field results. Beyond the mean field approximation, we show that fluctuations can contribute significantly to the properties of the system. Notably they lead to a desorption phenomenon regardless of the sign of the interaction. As a consequence, a non-monotonous density profile at the wall and adsorption curves as a function of the density are found for some systems. This behaviour rationalizes the ionic depletion phenomenon responsible for the anomalous behaviour of the electric capacitance as a function of temperature. Particular attention is given to the contact theorem condition.     

Four-State Quantum Chain as a Model of Sequence Evolution

A variety of selection-mutation models for DNA (or RNA) sequences, well known in molecular evolution, can be translated into a model of coupled Ising quantum chains. This correspondence is used to investigate the genetic variability and error threshold behaviour in dependence of possible fitness landscapes. In contrast to the two-state models treated hitherto, the model explicitly takes the four-state nature of the nucleotide alphabet into account and allows for the distinction of mutation rates for the different base substitutions, as given by standard mutation schemes of molecular phylogeny. As a consequence of this refined treatment, new phase diagrams for the error threshold behaviour are obtained, with appearance of a novel phase in which the nucleotide ordering of the wildtype sequence is only partially conserved. Explicit analytical and numerical results are presented for evolution dynamics and equilibrium behaviour in a number of accessible situations, such as quadratic fitness landscapes and the Kimura 2 parameter mutation scheme.     

The mixed spin-1/2 and spin-1 Ising system on a two-layer Bethe lattice

Two layered magnetic Bethe lattice with varying coordination number q is introduced and numerically studied via exact recursion relations within a pairwise approach. The system is influenced by competing interlayer and intralayer nearest-neighbour (NN) coupling interactions and also by the crystal and external magnetic fields. Cases where both layers are ferromagnetic or one is ferro and the other antiferromagnetic are considered. System configurations’ energy calculations are used to devise some ground state phase diagrams that have proven useful for the investigation of the very low temperature behaviour of the model. Analysis of the thermal behaviours of the total magnetization within the model parameters’ space yield interesting phase diagrams which display fascinating properties, in particular the presence of tricritical points. Increasing negative values of the crystal field strength stabilizes the disordered paramagnetic phase and sometimes gives rise to wavy transition lines.     

Light-Front Momentum Integrals for Fermion Loops in the Massive Schwinger Model

A novel consistent treatment of the light-front momentum integrals is proposed. The actual calculations are performed for the closed fermion loops in (1 + 1) dimensions, including Furry’s theorem. The regularization of Pauli-Villars is employed for the tadpole and two-leg diagrams. The problems with the light-front effective potentials are consistently solved.     

GHZ paradoxes based on an even number of qubits

GHZ paradoxes are presented for all even numbers of qubits from four up. They are obtained from proofs of the Kochen–Specker (KS) theorem by showing how the assumption of noncontextuality can be justified on the basis of locality. The nature of the entangled states involved in our paradoxes is discussed. Some multiqubit proofs of the KS theorem are also presented in the form of diagrams from which they are visually obvious. The implications of our results are discussed.     

Restoring good high energy behaviour in Higgs production via W fusion at the LHC

The W-fusion scattering process for off-shell W bosons is studied, focusing on the issue of its high-energy behaviour which is known to be anomalous. It is shown that the unitarity violating terms can be isolated and extracted in a well-defined and efficient way using the pinch- technique. This restores the good high energy behaviour of the cross section and, in particular, makes possible the identification of the Higgs resonance in the invariant mass distribution of the Z pair. The discarded terms, which are proportional to the off-shellness of the W bosons, cancel against similar terms originating from the remaining diagrams for the full physical process . This cancellation ensures the gauge invariance of our result, which therefore constitutes a meaningful separation between signal andbackground when they both contribute coherently. Equipped with this result, we are able to define a resonant approximation for the process which circumvents the problem of good high energy behaviour without having to resort to the lengthy calculation of the complete set of diagrams. In this approximation only the W- and Z-fusion signal graphs are included, i.e. the ones which contain the Higgs resonance. We have verified that the approximate resonant cross section describes very well the full result not only close to the resonance but also beyond it. Received: 30 January 1999 / Published online: 20 May 1999