## Two-Dimensional Model of a Relativistic Quantum Mechanics for the System of n Particles with a Potential Interaction

A potential-theory formalism is described within which exponentialized corrections to simple Glauber theory may be developed. An alternate formalism with direct generalization to relativistic field theory is developed for potential scattering at all angles, and some numerical work is presented to confirm and justify the approximations employed.

It is shown that the energy-momentum tensor of the electromagnetic field, for an electron in a curved space, may be split into two dynamically independent parts. One of them, the radiation tensor, has the following remarkable properties: (i) its covariant divergence vanishes off the electron world line; (ii) it has no flux through light cones with ...

A consistent and complete classical electrodynamics is developed in terms of the directly measured Liénard-Wiechert potentials, instead of the half-retarded and half-advanced potentials. Analytic continuation of the whole equation of motion allows one to obtain in a simple and unambiguous way the Abraham force and the mass renormalization term.

Straightforward algebraic techniques are presented and used to determine the structure of wave equations whose relativistic covariance is governed by two representations of S L (2,C), S 0(Λ) = (1,1/2) ⊕ (1/2,1) ⊕ (1/2,0) ⊕ (0,1/2) and S 1(Λ) = S 0(Λ) ⊕ (1/2,0) ⊕ (0,1/2), subject to the requirements that the equations should be parity preserving, ad...

Proofs have been given that the Bethe-Peierls approximation solves exactly the Ising problem on a Cayley tree. For a tree with coordination number γ>2, the approximation predicts, among other things, a phase transition in zero field at Tc=2J {ln[γ(γ−2)]}−1, with a discontinuity in the specific heat. On the other hand, the partition function in zero...

Operational criteria are presented for determining those bound states and resonances which can approximately be included in the complete set of states in the S-matrix formulation of statistical mechanics. The criteria depend only on the energy dependence of S-matrix elements, as compared to the energy scales determined by the temperature and densit...

Fermion masses resulting from dynamical breakdown of chiral symmetry in a renormalizable field theory are shown to have an essential singularity at vanishing coupling constant, just as does the energy gap in a superconductor.

Relativistic eikonal physics is applied to Coulomb scattering and bound states. It is shown that the eikonal approximation can accommodate the impact factor result as well as the non-relativistic Balmer spectrum. It is argued that relativistic corrections are outside this realm of approximation. This will be confirmed by eikonalizing the high-energ...

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 carrie...