Irreducible Green Functions Research Articles

The self-consistent theory of elementary excitations in systems with many-branch quasiparticle spectra (ferromagnetic semiconductors)

A unified self-consistent theory of the mutual influence of the electronic and spin subsystems in the s-f model approximation for ferromagnetic semiconductors is developed. The calculations are based on the novel approach of the two-time Green function method. It consists in the introduction of irreducible Green functions (IGF) and the derivation of the exact Dyson equation and the exact self-energy operator. It is shown that the IGF method gives a unified and natural approach for the calculation of the elementary excitation spectrum and damping. The full electronic and magnetic quasiparticle spectra of the s-f model are derived by taking explicitly into account magnon-magnon, electron-magnon and electron-electron scattering processes. The recent Babcenco and Cottam results (1981) follow from this theory in the lowest-order approximation.

Magnetic polaron in a ferromagnetic semiconductor. A new self-consistent finite temperature solution

A complete self-consistent finite temperature theory of magnetic polaron states with damping in a ferromagnetic semiconductor is developed using the irreducible Green function (IGF) method.

Decoupling renormalization and hierarchies

We introduce the decoupling renormalization scheme for the one-particle irreducible Green's functions of a theory that has a mass hierarchy. The decoupling-subtraction renormalization-group equations respect a tree-level hierarchy. Thus, fine tuning is to be done only at the tree level.

Decoupling Subtraction Conserving Full Gauge Symmetries

A new subtraction scheme (DṠ) which realizes the decoupling and conserves the symmetries of full gauge group simultaneously, is proposed. One particle irreducible Green's functions subtracted by DṠ reveal the effective low energy symmetries at -p2 ≪M2 and the full symmetries at -p2 ≫M2 where M denotes a heavy mass. Also discussed are conditions in order to carry out DṠ under two-loop approximation.

Metal-insulator transition in the Hubbard model by the irreducible Green functions method

The irreducible Green functions method is developed to obtain an interpolational Green function for the Hubbard model that is appropriate both in the band limit and in the atomic limit. The metal-insulator transition occurs due to the collapse of the electron and hole Fermi surfaces and it is a very smooth transition of the 2.5 kind. The quasiparticle damping is zero on the Fermi surface in the metallic phase.

Local existence of the borel transform in the Φ24 quantum field theory: A fixed point method

A fixed point argument is applied to the system of equations B = M ( B) to be satisfied by the set of Borel transformed euclidean Green functions B = { B 2 N ( p 1,…, p 2 N ; μ)} of Φ 2 4 in a neighbourhood of μ = 0, μ being the Borel variable associated with the coupling λ. We show (for small μ) the existence in an appropriate Banach space, of a unique set B = { B 2 N } of functions B 2 N satisfying these equations, to which the Borel-transformed perturbative series converge for each N (the convergence of the latter is obtained here as a by-product). An analogous application of this method to the set of one-particle irreducible Green functions of Φ 2 4, which yields improved results, is also presented.

The electronic spectrum and the metal-insulator transition in the Hubbard model

Calculations of quasiparticle spectra including high-order terms in the irreducible Green function method are presented. The metal-insulator transition of the 2.5-kind is connected with Fermi-surface collapse. In the band limit Fermi-liquid behaviour is obtained for the whole k-space except a small region near the Fermi surface where two quasibands exist which obey Gibbs statistics.

Exact and approximate differential renormalization-group generators. II. The equation of state

We apply an approximate form of the exact one-particle-irreducible renormalization-group generator to the calculation of the equation of state. Several approaches are explored. (i) Global nonlinear trajectories for the Hamiltonian parameters are exploited to give nonlinear crossover equations of state. Logarithms of the reduced temperature $t\ensuremath{\equiv}\frac{(T\ensuremath{-}{T}_{c})}{{T}_{c}}$ are automatically exponentiated to give power-law behavior. (ii) The form and asymptotic properties of the equation of state are described for those systems whose complete nonlinear trajectories cannot be explicitly obtained. (iii) Nonlinear trajectories for the irreducible Green's functions are solved to give a fully exponentiated equation of state containing no logarithmic terms. (iv) Simple critical (noncrossover) equations of state are obtained by iteration of the generator with linear and quasilinear trajectories. (v) Operator nonlinear equations are solved to give the crossover equation of state for an arbitrary order $\ensuremath{\theta}$ critical system, both in an $\ensuremath{\epsilon}$ expansion and at the borderline dimension. (vi) Combination of the Green's functions are formed into Green's eigenfunctions or operators and their nonlinear trajectories used to calculate fully exponentiated equations of state for order $\ensuremath{\theta}$ Ising systems. Systems considered include the usual Wilson-Fisher Hamiltonian [methods (i)-(iv)], the Sak-model compressible ferromagnet [(i)-(ii)], the $\mathrm{nm}$-hypercubical model (of which the dilute quenched random ferromagnet forms the $n\ensuremath{\rightarrow}0$ limit) [(ii)], and the isotropic $n$-component order $\ensuremath{\theta}$ ferromagnet [(iv)-(vi)]. The tricritical ($\ensuremath{\theta}=3$) case is given explicitly as an example of the general formalism of methods (iv)-(vi). Throughout, we use a bare critical propagator which is an arbitrary generalized homogeneous function of the components of the wave vector. This allows us to simultaneously describe ordinary critical systems and anisotropic Lifschitz points as well as certain structural and spin-reorientation phase transitions.

Generating functional approach to the Green's functions diagrammatic technique for spin and pseudospin lattice systems II. Diagrammatic method for generalized Pauli operators

Abstract A diagrammatic technique for spin and pseudospin lattice systems with complicated single- body levels is developed using the generalized Pauli operators. Rules for the construction and evaluation of the diagrams, representing the zeroth-order many-point irreducible Green's functions are given. The diagrams are constructed with only seven types of vertices and they are considerably simpler than those used up to now. The method formulated in this paper is a continuation of the approach to the spin and pseudospin lattice systems, developed in a previous paper.

Functional methods and perturbation theory

The framework of functional integrals in field theory is convenient for presenting a unified view of the perturbation expansion according to the number of loops. We review the calculation of the generating functional for irreducible Green functions and its renormalization properties. Calculations of the effective potential and $Z$-function are carried up to the order of two loops for the self-coupled scalar field. This is applied to compute the coefficients of the Callan-Symanzik equation which describes the short distance behavior of the theory. In conclusion, we present some speculations concerning the positivity of the coupling constant, and its relation to the on -shell two-particle scattering amplitude.