Although the equation of motion, recently proposed for the classical radiating electron, is of non-local character in proper time, the Newtonian initial data (position and velocity) are sufficient to guarantee existence and uniqueness of the solutions. The corresponding existence proof is accomplished by the Picard-Lindelöf method of successive approximations. This method indicates the possibil...

The conventional weak-coupling expansion for thermodynamic quantities in hot field theories shows poor convergence unless the coupling constant is tiny. I discuss screened perturbation theory (SPT) which is a way of reorganizing the perturbative expansion for scalar theories and hard-thermal-loop perturbation theory (HTLPT), which is its generalization to gauge theories. I present results for t...

EXAFS (extended X-ray absorption fine structure) investigations are reported concerning the thermal expansion behaviour of silver in an extended range of temperature from 10 K to about 950 K measured in transmission mode. Both the ratio method and an EXAFS fitting procedure were applied to reveal the temperature dependence of EXAFS parameters. Models based on quantum and classical thermodynamic...

Asymptotic solutions for large and small surface tension are developed for the profile of a symmetric sessile drop. The problem for large surface tension (i.e., small Bond number) is a regular perturbation problem, where the solution may be written as a uniformly valid asymptotic expansion. The problem for small surface tension (i.e., large Bond number) is a singular perturbation problem with b...

Working within the linear sigma model at finite temperature, we construct effective one-loop vertices and propagators satisfying the chiral Ward identities, for small pion momentum and mass compared to the sigma mass. We obtain an expansion for the pion dispersion relation up to second order in the parameter mπ/4π f π. At leading order, this expansion reproduces the dispersion curve obtained in...

After a brief survey of effective field theories, the linear σ model is discussed as a prototype of an effective field theory of the standard model below the chiral–symmetry–breaking scale. Although it can serve as a toy model for the pion–nucleon interaction, the linear σ model is not a realistic alternative to chiral perturbation theory. The heavy–baryon approach to chiral perturbation theory...

shows nonuniversal critical behavior in two dimensions in the neighborhood of K4 =0. To see if this behavior persists for N & 2 we perform a first-order-perturbation expansion around the decoupling point in two dimensions. As an aid in interpreting the results of this perturbation expansion we have determined the phase diagram of the system through mean-field theory and Monte Carlo studies in 1...

After revealing difficulties of the standard time-dependent perturbation theory in quantum mechanics mainly from the viewpoint of practical calculation, we propose a new quasi-canonical perturbation theory. In the new theory, the dynamics of physical observables, instead of that of coefficients of wave-function expansion, is formulated so that the gauge-invariance and correspondence principles ...

The origin of symbolic manipulation derives from the sheer magnitude of the work involved in the building of perturbation theories, which made inevitable that scientific community became interested in the possibility of constructing those theories with the help of computers. Perturbation theories for differential equations containing a small parameter are quite old. The small perturbation theor...

Since Moser’s seminal work it is well known that the invariant curves of smooth nearly integrable twist maps of the cylinder with Diophantine rotation number are preserved under perturbation. In this paper we show that, in the analytic class, the result extends to Bryuno rotation numbers. First, we will show that the series expansion for the invariant curves in powers of the perturbation parame...