Through an examination of the Bohm-Aharonov experiment intrinsic and complete description electromagnetism in a space-time region is formulated terms nonintegrable phase factor. This concept, its global ramifications, studied through Dirac's magnetic monopole field. Generalizations to non-Abelian groups are carried out, result identification with mathematical concept connections on principal fiber bundles.

We consider the anharmonic oscillator defined by differential equation $(\ensuremath{-}\frac{{d}^{2}}{d{x}^{2}}+\frac{1}{4}{x}^{2}+\frac{1}{4}\ensuremath{\lambda}{x}^{4})\ensuremath{\Phi}(x)=E(\ensuremath{\lambda})\ensuremath{\Phi}(x)$ and boundary condition $limit of\text{}\ensuremath{\Phi}(x)\text{as}x\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}=0$. This model is interesting because perturbation series for ground-state energy diverges. To investigate reason this...

We compute exactly the spin-spin correlation functions $〈{\ensuremath{\sigma}}_{0,0}{\ensuremath{\sigma}}_{M,N}〉$ for two-dimensional Ising model on a square lattice in zero magnetic field $T>{T}_{c}$ and $T<{T}_{c}$. then analyze scaling limit $T\ensuremath{\rightarrow}{T}_{c},{M}^{2}+{N}^{2}\ensuremath{\rightarrow}\ensuremath{\infty}$ such that $(T\ensuremath{-}{T}_{c})$ is fixed. In this...

This paper is concerned with the nature of perturbation theory in very high order. Specifically, we study Rayleigh-Schr\"odinger expansion energy eigenvalues anharmonic oscillator. We have developed two independent mathematical techniques (WKB analysis and difference-equation methods) for determining large-$n$ behavior ${A}_{n}^{K}$, nth coefficient Kth level. are not here placing bounds on growth ${A}_{n}^{K}$ as $n$, order theory, gets large. Rather, consider more delicate problem precise...

The distribution of current along a center-driven cylindrical antenna is obtained when the material forming resistive. particular case considered impedance per unit length function distance from end. A solution specifically represented by an outward traveling wave with no reflected wave. admittance and far-field pattern determined. Field patterns are evaluated for wide range lengths. These characterized single major lobe very small minor structure.

We examine the large-order behavior of perturbation theory for anharmonic oscillator, a simple quantum-field-theory model. New analytical techniques are exhibited and used to derive formulas giving precise rate divergence all energy levels ${x}^{2N}$ oscillator. compute higher-order corrections these ${x}^{4}$ oscillator with without Wick ordering.

Recent experiments demonstrate that at the Curie temperature specific heat may be a smooth function of temperature. We propose this effect can due to random impurities and substantiate our proposal by study an Ising model containing such impurities. modify usual rectangular lattice allowing each row vertical bonds vary randomly from with prescribed probability function. In case is particular distribution narrow width, we find logarithmic singularity Onsager's smoothed out into which...

At infinite energy, we predict: (1) ${\ensuremath{\sigma}}_{\mathrm{tot}}$ approaches infinity; (2) the ratio of real part to imaginary forward elastic amplitude zero; (3) $\frac{{\ensuremath{\sigma}}_{\mathrm{el}}}{{\ensuremath{\sigma}}_{\mathrm{tot}}}$ \textonehalf{}; (4) width diffraction peak its product with is a constant. We give theoretical evidence based on massive quantum electrodynamics as well experimental in support these predictions, and physical picture for high-energy scattering.

We study in detail the asymptotic behavior, for large separations, of correlation between two spins case two-dimensional Ising model without magnetic field. In limit infinite separation, this is equal to square spontaneous magnetization per spin. This paper devoted answering question how, fixed temperature, approaches limiting value. The investigation restricted situation where under consideration lie on same row lattice. There are three distinct cases temperature above, below, or critical...

It is speculated that the sharp decrease with increasing energy of differential cross sections at large angles due to a mechanism independent method excitation. Some consequences such possibility are discussed.

It is shown that the pseudopotential method can be extended to yield further terms in low-density expansion of ground-state energy a system Boltzmann or Bose particles with hard-sphere interaction. Two beyond known result are found, and no longer power series ${({a}^{3}\ensuremath{\rho})}^{\frac{1}{2}}$. Other related properties discussed.

We explicitly construct the one-parameter family of solutions, η (ϑ;ν,λ), that remain bounded as ϑ→∞ along positive real ϑ axis for Painlevé equation third kind ww′′= (w′)2−ϑ−1ww′+2νϑ−1(w3−w) +w4−1, where, ϑ→∞, ∼ 1−λΓ (ν+1/2)2−2νϑ−ν−1/2e−2ϑ. further a representation ψ (t;ν,λ) =−ln[η (t/2;ν,λ)], where satisfies differential ψ′′+t−1ψ′= (1/2)sinh(2ψ)+2νt−1 sinh(ψ). The small-ϑ behavior (ϑ;ν,λ) is described ‖λ‖<π−1 by 2σBϑσ. parameters σ and B are given explicit functions λ ν. Finally an...

This is the first in a series of papers on large-order behavior perturbation theory for coupled anharmonic oscillators. We exploit previously published dispersion techniques to convert calculation large order into barrier-penetration problem. then introduce new semiclassical methods describing tunneling through nonspherically symmetric, $N$-dimensional potentials. To illustrate our methods, we calculate simple system two equal-mass oscillators with quartic coupling. Our predictions are...

We compute exactly the four coefficients ${C}_{0\ifmmode\pm\else\textpm\fi{}}$ and ${C}_{1\ifmmode\pm\else\textpm\fi{}}$ in expansion ${\ensuremath{\beta}}^{\ensuremath{-}1}\ensuremath{\chi}={C}_{0\ifmmode\pm\else\textpm\fi{}}{|1\ensuremath{-}\frac{{T}_{c}}{T}|}^{\ensuremath{-}\frac{7}{4}}+{C}_{1\ifmmode\pm\else\textpm\fi{}}{|1\ensuremath{-}\frac{{T}_{c}}{T}|}^{\ensuremath{-}\frac{3}{4}}+O(1)$ for susceptibility of rectangular two-dimensional Ising model.

Using two models, we study the relaxation to a Maxwell distribution in context of classical kinetic theory. For first model, an exact solution nonlinear Boltzmann equation is derived. second asymptotic exhibits remarkable feature transient tail population sometimes much larger than equilibrium distribution. This phenomenon may be importance for calculating rates fast chemical reactions and controlled thermonuclear fusion.

We have examined all two-body, elastic-scattering amplitudes in quantum electrodynamics. Aside from the photon-pole contribution, amplitude for any elastic process is imaginary and proportional to $s$ limit $s\ensuremath{\rightarrow}\ensuremath{\infty}$ with $t$ held finite. The coefficients of $s$, lowest nonvanishing orders $e$, can be expressed simply terms "impact factors." results contradict both Regge-pole model droplet their most straightforward interpretations.