Defects within the landau theory: A perturbation approach

We discuss the continuum medium theory that enables us to find the defect contribution to phase transition anomalies with the use of only a few phenomenological parameters. The theory is invalid in the immediate vicinity of the phase transition temperature and for high concentration of defects. The possibilities of interpretation of experimental data on the basis of the theory are also discussed.     

Effective Hamiltonains and degenerate perturbation theory calculations of the mass spectrum in lattice QCD

Hamiltonian quantum chromodynamics has been formulated on a discrete lattice, in an attempt to calculate the hadronspectrum using strong coupling expansions. Previous attempts have involved including an irrelevant four-fermion interaction term in the Hamiltonian. As well as making the quark content of the zeroth order states the same as that of the simple additive quark model, this term splits the infinite zeroth order degeneracies of the original Hamiltonian. In this paper we calculate the masses of low lying states in the absence of such a term, using an effective Hamiltonian method to solve the degeneracy problem. We discuss the problems of continuing our series to the continuum limit in the presence of level repulsion.     

On the perturbation theory in spatially closed background

Recent studies have shown that searches in the mono-photon and missing energy final state can be used to discover dark matter candidates at the ILC. While an excess in this final state over the Standard Model background would indicate the existence of a dark sector, no detailed information about the internal structure of this sector can be inferred. Here, we demonstrate how just a few observables can discriminate between various realisations of dark sectors, including e.g. the spin of mediators.     

On the stationary perturbation theory in quantum mechanics

A simple method is proposed for solving the Shcrödinger equation in the presence of a perturbation. Formally exact expressions are obtained in the form of infinite series for the energies and wave functions without assuming that the perturbation is small. Under the additional assumption that it is small (in accordance with a well-defined criterion of smallness) the obtained results yield directly the results of Schrödinger's perturbation theory. The developed approach contains in compact form various formulations of perturbation theory. The calculations use neither the complex technique of projection operators nor the complicated formalism of Green's functions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 33–36, November, 1980.     

On the perturbation theory of critical phenomena

It is shown how, using the ideas of Brezin, Le Guillou and Zinn-Justin, one may obtain the critical properties of the φ⁴ model from renormalised perturbation theory without the use of the Callan-Symanzik equation and an associated approximation     

On the theory of the collective phenomena in quasi-two-dimensional semiconductors

Results of calculation of the electron-hole liquid ground state energy are presented and their connection with other possible states of a two-dimensional system of electrons and holes is discussed.     

On the theory of collective motion in nuclei. II. Quantum theory

The collective Hamiltonian is assumed to be invariant under the orthogonal group O(A ? 1, $\text{R}$). It is shown that the quantum collective dynamics can be formulated on a coset space of the symplectic group $\text{sp}$(6, $\text{R}$) of dimension 12, 16 or 18. The first case corresponds to the collective dynamics based on closed shells and leads to a Hilbert space of analytic functions in six complex collective quasiparticle variables. Dequantization of this scheme yields the classical dynamics described in I. In the limit A ? 1 one obtains a system of s- and d-bosons with symmetry group $\text{u}$ (6) in the collective state space.     

On the collective excitations and the existence of the gap in the degenerate Bose gas spectrum

Themodel of degenerate weakly nonideal Bose gas is considered without the assumption on the C-number nature of creation and annihilation operators of particles in the zero-momentum state. It was shown that the “density-density” Green’s function pole defines the Bogolyubov spectrum of phonon-roton-type collective excitations. The single-particle excitation spectrum is characterized by the gap whose value is defined by the particle density in the “condensate”.     

On the theory of collective motion in nuclei. I. Classical theory

From the assumption that the collective Hamiltonian be invariant under the orthogonal group O(A ? 1, $\text{R}$) it is concluded that classical collective dynamics can be formulated on a symplectic manifold. This manifold is shown to be a coset space of the symplectic group $\text{L}$h(6, $\text{R}$) of dimension 12, 16 or 18. The first case corresponds to the dequantization of closed-shell collective dynamics and is described in terms of six complex s- and d-quasiparticles. In the limit A ? 1 it is shown that a transformation leads to interacting s- and d-bosons with the symmetry group $\text{u}$ (6) in the collective phase space.     

Derivation of the effective pion-nucleon Lagrangian within heavy baryon chiral perturbation theory

We develop a method for constructing the heavy baryon chiral perturbation theory (HBChPT) Lagrangian, to a given chiral order, within HBChPT. We work within SU(2) theory, with only the pion field interacting with the nucleon. The main difficulties, which are solved, are to develop techniques for implementing charge conjugation invariance, and for taking the nucleon on shell, both within the non-relativistic formalism. We obtain complete lists of independent terms in L_HBChPT through O(q³) for off-shell nucleons. Then, eliminating equation-of-motion (e.o.m.) terms at the relativistic and non-relativistic level (both within HBChPT), we obtain L_HBChPT for on-shell nucleons, through O(q³). The extension of the method (to obtain on-shell L_HBChPT within HBChPT) to higher orders is also discussed.     

η- mixing in U(3) chiral perturbation theory

We investigate η- mixing in infrared regularized U(3) chiral perturbation theory by calculating the η and masses up to one-loop order. From this analysis it becomes obvious that even at leading order η--mixing does not obey the usually assumed one-mixing-angle scheme if large N _c counting rules are not employed. Received: 12 March 2001 / Accepted: 4 July 2001     

Pion-kaon scattering near the threshold in chiral SU(2) perturbation theory

In the context of chiral SU(2) perturbation theory, pion-kaon scattering is analysed near the threshold to fourth chiral order. The scattering amplitude is calculated both in the relativistic framework and by using an approach similar to heavy baryon chiral perturbation theory. Both methods lead to equivalent results. We obtain relations between threshold parameters, valid to fourth chiral order, where all those combinations of low-energy constants which are not associated with chiral-symmetry breaking terms drop out. The remaining low-energy constants can be estimated using chiral SU(3) symmetry. Unfortunately, the experimental information is not precise enough to test our low-energy theorems.     

Magnetic dipole moment of the Δ(1232) in chiral perturbation theory

The magnetic dipole moment of the Δ(1232) is calculated in the framework of manifestly Lorentz-invariant baryon chiral perturbation theory in combination with the extended on-mass-shell renormalization scheme. As in the case of the nucleon, at leading order both isoscalar and isovector anomalous magnetic moments are given in terms of two low-energy constants. In contrast to the nucleon case, at next-to-leading order the isoscalar anomalous magnetic moment receives a (real) loop contribution. Moreover, due to the unstable nature of the Δ(1232), at next-to-leading order the isovector anomalous magnetic moment not only receives a real but also an imaginary loop contribution.     

Thermodynamic perturbation theory for the (12-6-n) fluids

A perturbation method in which attractive forces are taken as perturbation of the repulsive (reference) forces is applied to calculate the thermodynamic properties of (12-6-n) fluids in terms of the properties of hard-sphere fluid. The numerical values of the thermodynamic properties (free energy per particle, compressibility and excess internal energy) for a range of temperature and density are given for (12-6-8) fluids. Further, two perturbation schemes are adopted to evaluate the total radial distribution function using the EXP version of the optimized cluster theory (OCT). The numerical results are reliable as reported at two states (T* = 1·036,ρ* = 0·65 andT* = 0·719ρ* = 0·85) for the (12-6-8) fluid and the Lennard-Jones (12-6) fluid as well.