Form factors and correlation functions of an interacting spinless fermion model

Introducing the fermionic R-operator and solutions of the inverse scattering problem for local fermion operators, we derive a multiple integral representation for zero-temperature correlation functions of a one-dimensional interacting spinless fermion model. Correlation functions particularly considered are the one-particle Green's function and the density–density correlation function both for any interaction strength and for arbitrary particle densities. In particular for the free fermion model, our formulae reproduce the known exact results. Form factors of local fermion operators are also calculated for a finite system.     

The Shift Operators in Ginocchio Model

In fermion space, the vectors (s⁺|0) and D⁺.D⁺|0) are not orthogonal. The analytic expressions of the wave functions in Ginocchio model are more complicated than those in IBM. Using the shift operator method we can easily construct the wave functions in Ginocchio model. The wave functions of the (0,0) irreducible representations of SO(5) for nucleon number N ≤ 10 are given.     

An extended parton model for the effective w and z approximation

Exact expressions for the effective off-shell IVB distributions of fermions and for fermion decay widths to fermion plus IVB are developed. We consider the simple example of heavy fermion production to one loop in order to display the method and to check the results against an exact Feynman diagram calculation. The correct handling of energy conservation is shown to yield results identical to that of the appropriate Feynman diagram result. The off-shell widths derived are related to observed widths, so that the later may be used in such a calculation. The methods is valid for all angles and all energies. It can be extended to find the off-shell corrections for any other vertices as well. The utilization of these structure functions with appropriate off-shell correction factors at vertices and exact energy conservation will yield results with a much wider range of validity than is obtained from the usual parton model. Furthermore one can use the results of this work to explore the range of validity of the usual parton model calculation. In some cases the procedure may be modified less drastically than is necessary to obtain the usual parton calculation and the validity of the modification will be more clearly understood. The modified procedure will be simpler than the Feynman diagram calculation with a range of validity in energy and angle which is much larger than that of the simple parton model.     

Functional Integrals and Convergence of Partition Function in Sine–Gordon–Thirring Model

The effective action in 1D sine-Gordon-Thirring model with impurities coupling is derived by means of functional integral method. For strong coupling model, the convergence of partition function is proved when coupling constants and wave vector satisfy certain constraint conditions. The fermion condense density in stable phase structure is obtained from the extremum of two-order effective action. The results showed that the non-perturbation method of functional integrals can be applied to study strong coupling rang of fermion system.     

Nature of correlations in the atomic limit of the boson fermion model

Using the equation of motion technique for Green's functions we derive the exact solution of the boson fermion model in the atomic limit. Both (fermion and boson) subsystems are characterised by the effective three level excitation spectra. We compute the spectral weights of these states and analyse them in detail with respect to all possible parameters. Although in the atomic limit there is no true phase transition, we notice that upon decreasing temperature some pairing correlations start to appear. Their intensity is found to be proportional to the depleted amount of the fermion nonbonding state. We notice that pairing correlations behave in a fashion observed for the optimally doped and underdoped high T_c superconductors. We try to identify which parameter of the boson fermion model can possibly correspond to the actual doping level. This study clarifies the origin of pairing correlations within the boson fermion model and may elucidate how to apply it for interpretation of experimental data. Received 31 January 2003 / Received in final form 18 March 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: doman@kft.umcs.lublin.pl     

Gauge Covariant Fermion Propagator in the Presence of Arbitrary External Gauge Field and Its Schwinger--Dyson Equation

Gauge covariance for Green＇s functions of a gauge theory through a fermion propagator in the presence of arbitrary external gauge field is proven and a formalism of gauge and Lorentz covariant Schwinger-Dyson equation for the fermion propagator with external gauge field is built up within ladder approximation.     

Physical particles of the massive Schwinger model

The massive Schwinger model is considered in the infinite momentum frame. By assuming its physical particles consist of two fermion bound states, we compute a spectrum. For fermions with large bare masses, the method is reliable. For low-mass fermions, we find we must include states of higher fermion number to adequately describe excited states of the fundamental boson of the theory. We do this for the scalar state in the limit of small bare fermion mass. This representation of the theory provides a unified treatment of both the weak and strong coupling limits, remaining in the fermion representation throughout. We have checked our numerical results with exact calculations wherever possible, and find good agreement.     

Magnetic properties of a one-dimensional integrable electron model with correlated hopping

We investigate ground-state properties of a one-dimensional correlated hopping electron model in the presence of an external magnetic field which is solvable by Bethe ansatz. We present a general method of calculating magnetization, susceptibility, and chemical potential in exactly solvable spin-1/2 fermion models by deriving a parametric representation of these functions and the magnetic field in terms of the charge and spin distributions, the dressed charge matrix, and the dressed energy at the Fermi points in parameter space. For the correlated hopping model, we numerically calculate the dressed properties-which are given by sets of coupled integral equations-for general values of the field, the band filling, and the interaction parameter. In the special limits of magnetic saturation or large interaction parameter the results are presented in analytic form.     

强子作为非拓扑孤粒子的SU（5）大统—模型（Ⅰ）

提出一种新的包含三代已知轻子与夸克的ＳＵ（５）大统—模型．按本模型，强子可看作由夸克形成的非拓扑孤粒子；轻子与夸克本质上是相同的，它们之间的差别是由对称性自发破缺造成的；在强子内部，夸克质量很小，其性质与已知夸克相同；在强子外部，夸克的性质与已知轻子相同，只是质量很重，并将很快衰变．本文除了定义严格守恒的电荷Ｑ０、费米子数Ｆ０外，还在孤粒子内部定义了近似守恒的内色荷、内电荷、内费米子数．已知ＳＵ（５）大统—模型的（Ｌ－Ｂ）守恒相应于本模型的Ｆ０守恒。     

Fermion production despite fermion number conservation

Lattice proposals for a nonperturbative formulation of the Standard Model easily lead to a global U(1) symmetry corresponding to exactly conserved fermion number. The absence of an anomaly in the fermion current would then appear to inhibit anomalous processes, such as electroweak baryogenesis in the early universe. One way to circumvent this problem is to formulate the theory such that this U(1) symmetry is explicitly broken. However we argue that in the framework of spectral flow, fermion creation and annihilation still in fact occurs, despite the exact fermion number conservation. The crucial observation is that fermions are excitations relative to the vacuum, at the surface of the Dirac sea. The exact global U(1) symmetry prohibits a state from changing its fermion number during time evolution, however nothing prevents the fermionic ground state from doing so. We illustrate our reasoning with a model in two dimensions which has axial-vector couplings, first using a sharp momentum cutoff, then using the lattice regulator with staggered fermions. The difference in fermion number between the time evolved state and the ground state is indeed in agreement with the anomaly. Both the sharp momentum cutoff and the lattice regulator break gauge invariance. In the case of the lattice model a mass counterterm for the gauge field is sufficient to restore gauge invariance in the perturbative regime. A study of the vacuum energy shows however that the perturbative counterterm is insufficient in a nonperturbative setting and that further quartic counterterms are needed. For reference we also study a closely related model with vector couplings, the Schwinger model, and we examine the emergence of the θ-vacuum structure of both theories.     

Fermion gases in magnetic fields: a semiclassical treatment

The study of quantum degenerate gases has received much interest in these last years essentially thanks to the extremely important experimental results of the achievement of Bose-Einstein condensation of atoms and, very recently, of almost complete degeneracy of atomic fermion gases. Here we want to present the results of a semi-analytical method for the study of an interacting degenerate fermion gas based on semiclassical kinetic theory; special care has been devoted to the study of a rotating electron gas, in a cylindrically symmetrical configuration, radially confined by a uniform magnetic field. The model will lead to a particular Thomas-Fermi equation which is generalized to take into account finite temperature and average velocity of the gas, and which is further developed to consider the effects of external fields. Received 10 March 2000     

Superconductivity in chiral-asymmetric matter within the (2 + 1)-dimensional four-fermion model

The phase structure of chiral-asymmetric matter has been studied within the (2 + 1)-dimensional quantum-field theory with the fermion–antifermion and fermion–fermion (or superconducting) channels of four-fermion interaction. For this purpose, the model takes both the chemical potential of the number of particles μ and the chiral chemical potential μ₅ conjugated to the difference between the numbers of right and left fermions into account. A series of phase diagrams was plotted for different chemical potentials. It is shown that the chemical potential μ promotes the appearance of a superconducting phase, while an increase in the chemical potential μ₅ suppresses the effect of the chemical potential μ on a system. The results of this study may be of interest for high-energy physics, condensed matter physics and, in particular, graphene physics.     

Geometric chaoticity leads to ordered spectra for randomly interacting fermions

A rotationally invariant random interaction ensemble was realized in a single- j fermion model. A statistical approach reveals the random coupling of individual angular momenta as a source for the empirically known dominance of ground states with zero and maximum spin. The interpretation is supported by the structure of the ground state wave functions.     

Cumulant approach to dynamical correlation functions at finite temperatures

A new theoretical approach, based on the introduction of cumulants, to calculate thermodynamic averages and dynamical correlation functions at finite temperatures is developed. The method is formulated in Liouville instead of Hilbert space and can be applied to operators which do not require to satisfy fermion or boson commutation relations. The application of the partitioning and projection methods for the dynamical correlation functions is considered. The present method can be applied to weakly as well as to strongly correlated systems.     

Nonstandard magnetic oscillations in the Nambu-Jona-Lasinio model

The Nambu-Jona-Lasinio model at nonzero values of an external magnetic field H and of the chemical potential is considered in the strong-coupling region G>G _c. The phase portrait of the model exhibits an infinitely large number of massless chiral-invariant phases and massive phases resulting from a spontaneous breakdown of chiral invariance. This phase structure is responsible for aperiodic oscillations of some thermodynamic parameters of the system, including the dynamical fermion mass, as functions of H ^?1.     

Virtual quark-quark scattering in the pseudoparticle background

We calculate off-shell four point functions of massless fermions in a pseudoparticle background. The results are exact to lowest order quantum fluctuations about the classical pseudoparticle field. Only pseudoparticle solutions of unit winding number contribute to the calculated correlation functions. The developed technique requires knowledge only of the zero frequency fermion solutions in the pseudoparticle potential.     

带有质量的Wilson费米子的格点Schwinger模型中M_V对m的变化率的计算

用变分法计算带有质量的Ｗｉｌｓｏｎ费米子的格点Ｓｃｈｗｉｎｇｅｒ模型中矢量介子的质量Ｍ，从而求出Ｍ、对费米子质量ｍ的变化率Ｍｖ／ｍ（ｍ＝０处），结果与连续理论的准确解十分接近．     

Realistic Type IIB supersymmetric Minkowski flux vacua

We show that there exist supersymmetric Minkowski vacua on Type IIB toroidal orientifold with general flux compactifications where the RR tadpole cancellation conditions can be relaxed elegantly. Then we present a realistic Pati–Salam like model. At the string scale, the gauge symmetry can be broken down to the Standard Model (SM) gauge symmetry, the gauge coupling unification can be achieved naturally, and all the extra chiral exotic particles can be decoupled so that we have the supersymmetric SMs with/without SM singlet(s) below the string scale. The observed SM fermion masses and mixings can also be obtained. In addition, the unified gauge coupling, the dilaton, the complex structure moduli, the real parts of the Kähler moduli and the sum of the imaginary parts of the Kähler moduli can be determined as functions of the four-dimensional dilaton and fluxes, and can be estimated as well.