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We explicitly construct a convergent perturbation series for intrinsically divergent Moller—Plesset cases. The means to accomplish this goal is an explicit reduction of the size of the perturbation. This is achieved by means of a Λ transformation and an unlinked-graph shift. Generic multi-reference cases are treated by single-reference methods after a simple and feasible transformation of the Hamiltonian matrix to a basis comprising a suitable reference zero-order vector. This effectively solves the intruder-state problem. We present the 1Δ state of C2 and the H2 ground state at large bond distance as typical examples.

We show that discontinuities in the vacuum polarisation give rise to charge screening effects which are large and result in a lower bound Δ with − m < Δ < m for the energy levels of an electron bound in a supercritical field.

We recently proposed (parts I and II of this series of publications) a new method of infinite subsummation in the Moller-Plesset perturbation series with the objective of “effecting convergence of otherwise divergent series”. In the present work we undertake to study the importance of a shift of unlinked graphs in the Moller-Plesset renormalization term. We demonstrate that this modification of many-body perturbation theory presents a viable starting point for new approximations devised to obtain a substantial fraction of the correlation energy at low order. We present an explicit investigation of the excited states of LiH in a suitable full-CI model space, using our method to calculate the correlation energy and monitoring convergence up to tenth order.

It is demonstrated that the Kramers-Henneberger transformation is the first step in a systematic construction of Floquet states. For a harmonic oscillator which interacts with a classical monochromatic radiation field, all steps of this construction can be performed explicitly and expressed as a simple renormalization scheme. The particular importance of zero-modes for the calculation of quasienergies becomes obvious already in this explicitly solvable model. The general structure of a Kramers-Henneberger expansion is briefly sketched.

We investigate the dynamics of periodically driven anharmonic oscillators. In particular, we consider values of the coupling strength which are orders of magnitude higher than those required for the overlap of primary resonances. We observe a division of phase space into a regular and a stochastic region. Both regions are separated by a sharp chaos border which sets an upper limit to the stochastic heating of particles; its dependence on the coupling strength is studied. We construct perpetual adiabatic invariants governing regular motion. A bifurcation mechanism leading to the annihilation of resonances is explained.

A ϕ4 theory interacting with a (non-local) external potential strong enough to induce zero-mass modes is considered. Such a theory has served as a model for π condensation and, in solid state physics, to explain giant magnetic moments in metals. We show that such a zero-mass mode, in general, does not induce a phase transition to a condensed state because of temporal fluctuations produced by instantons which tend to restore initially broken symmetries. Numerical order of magnitude estimates for the relaxation time are given.

High-temperature or, equivalently, strong coupling expansions are established by applying heat-kernel techniques to the Green's functional of the Schrodinger picture of quantum field theory. The trace of the Green's functional is considered and a high-temperature expansion for the partition function is derived. It is shown that a simple, physically motivated rescaling of parameters leads to well-defined expressions. A generalized Thomas-Fermi expansion for the density of states is finally obtained.

Non-abelian gauge theories are written as the infinite gaugino mass limit of softly broken supersymmetric Yang-Mills theories. Their supersymmetry is exploited by effecting a Nicolai transformation. The average of gauge-invariant objects is then expressed in terms of abelian, transverse, i.e. physical, gauge fields irrespective of the gauge fixing originally chosen; the resulting perturbation theory is ghost-free. Seen from a practical standpoint the computational effort required in either traditional (with linear gauge) or this newly formulated perturbation theory is comparable.

The mobility of Li in β-LiAl formed by cathodic Li incorporation is drastically reduced by small amounts of Si in the parent Al; this is shown by 7Li NMR and electrochemical experiments. During long term cycling, the detrimental effect of lower Li mobility is compensated by the less spongy morphology of Si-doped electrodes. Addition of a few hundred ppm of 1,2-propanediol or methoxyethanol improves the 1st cycle Li-recovery from Si-doped β-LiAl in propylene carbonate electrolytes; paraffin oil is a nonreactive surfactant which slightly decreases the corrosion of β-LiAl.

Coupling constant flow equations are derived for supersymmetric scalar and gauge theories. Thes equations then serve as a starting point for the construction of Nicolai maps. From the fixed-point properties of the latter we establish a large class of stochastic functionals.

Atiyah-Patodi-Singer spectral η-invariants naturally appear as a polarisation charge in the Dirac theory of electrons in an external field. We propose a physical interpretation and discuss the resulting consequences, in particular for strong Coulomb fields. The η-invariant is seen to be discontinuous where zero-modes appear, for Z = Z0 (Z0 = 137 for pointlike Coulomb sources, Z0 > 137 for sources of nuclear extension). A consequence of this picture is that single electron orbitals should never “see” an effective charge exceeding Z0. We discuss this effect in QED.

The ground state of a (2+1) dimensional Georgi-Glashow model is discussed in a dilute monopole gas approximation. In addition to the Coulomb interaction of the latter, we include a Higgs force which is attractive irrespective of the sign of monopole charges. For (Higgs masses) −1 comparable to the mean free distance of monopoles we find a phase transition which is presumably of first order. Strings of monopoles dominate the clustering behaviour near the critical Higgs mass.

The equilibrium properties of an inhomogeneous gas of interacting fermions are derived using methods of finite temperature quantum field theory. A Landau-type quasiparticle spectrum yielding the exact ground state energy or, at finite temperatures, the exact thermodynamic potential is constructed from the g-Hartree equations. The heat kernel expansion of Schrodinger operators is then used to express the Hohenberg-Kohn density functional as a series in the quasiparticle density which is asymptotic in the Thomas-Fermi limit. This series is systematically derived from the microscopic action and incorporates boundary effects in an unambiguous manner. The methods developed apply to a large class of field-theoretical models encompassing theories with Yukawa interactions.

Multichannel dynamical amplitudes can have CDD poles when viewed as the solution of the appropriate one-channel inelastic problem. Manifestations of this phenomenon are investigated. The technique is to work via the eigenamplitudes, in terms of which the essential many-channel dynamics take a simple form; for them, individual Levinson's theorems are derived. On applying the method, it is found that, for a wide class of cases, the phenomenon always occurs in at least one channel and, in many cases, further analysis enables one to say in which one. A speculative application is made to SU3 bootstraps.

The question of constructing Reggeized amplitudes which can be used for time-liked and space-like momentum transfers is discussed. Several models are given which result in general in quite different bootstrap equations. The model of daughter-like solutions to the problem (Class I in the language of O(3,1) or O(4)) is compared to the usual ansatz in the simple cases of ππ and ηη scattering.

It is shown that in the functional formalism the computation of energy levels in a weak external gauge field calls for a modification of the Faddeev-Popov functional measure. Physical implications are discussed.

Soliton-like solutions of classical spinor electrodynamics with the symmetry of a cylinder of finite or infinite length are described. The solutions have non-vanishing total charge and, contrary to ordinary strings, an azimuthal magnetic and a radial electric field. For finite length, these lumps move with the velocity of light in the direction of the symmetry axis and the total four momentum is light-like. The crucial mechanism is a subtle compensation which prevents the matterfield from recoupling to its own electromagnetic field.