F.E. Low

Bio: F.E. Low is an academic researcher from University of Illinois at Urbana–Champaign. The author has contributed to research in topics: Coupling & Electron. The author has an hindex of 7, co-authored 8 publications receiving 3585 citations.

Quantum electrodynamics at small distances

Abstract: The renormalized propagation functions DFC and SFC for photons and electrons, respectively, are investigated for momenta much greater than the mass of the electron. It is found that in this region the individual terms of the perturbation series to all orders in the coupling constant take on very simple asymptotic forms. An attempt to sum the entire series is only partially successful. It is found that the series satisfy certain functional equations by virtue of the renormalizability of the theory. If photon self-energy parts are omitted from the series, so that D_(FC)=D_F, then S_(FC) has the asymptotic form A[p^2m^2]^n[iγ⋅p]^(−1), where A=A(e_1^2) and n=n(e_1^2). When all diagrams are included, less specific results are found. One conclusion is that the shape of the charge distribution surrounding a test charge in the vacuum does not, at small distances, depend on the coupling constant except through a scale factor. The behavior of the propagation functions for large momenta is related to the magnitude of the renormalization constants in the theory. Thus it is shown that the unrenormalized coupling constant e_0^2/4πℏc, which appears in perturbation theory as a power series in the renormalized coupling constant e_1^2/4πℏc with divergent coefficients, may behave in either of two ways: (a) It may really be infinite as perturbation theory indicates; (b) It may be a finite number independent of e_1^2/4πℏc.

The Motion of Slow Electrons in a Polar Crystal

Abstract: A variational technique is developed to investigate the low-lying energy levels of a conduction electron in a polar crystal. Because of the strong interaction between the electron and the longitudinal optical mode of the lattice vibrations, perturbation-theoretic methods are inapplicable. Our variational technique, which is closely related to the "intermediate coupling" method introduced by Tomonaga, is equivalent to a simple canonical transformation. The use of this transformation enables us to obtain the wave functions and energy levels quite simply. Because the recoil of the electron introduces a correlation between the emission of successive virtual phonons by the electron, our approximation, in which this correlation is neglected, breaks down for very strong electron-phonon coupling. The validity of our approximation is investigated and corrections are found to be small for coupling strengths occurring in typical polar crystals.

The Motion of Slow Electrons in a Polar Crystal

Abstract: A variational technique is developed to investigate the low-lying energy levels of a conduction electron in a polar crystal. Because of the strong interaction between the electron and the longitudinal optical mode of the lattice vibrations, perturbation-theoretic methods are inapplicable. Our variational technique, which is closely related to the "intermediate coupling" method introduced by Tomonaga, is equivalent to a simple canonical transformation. The use of this transformation enables us to obtain the wave functions and energy levels quite simply. Because the recoil of the electron introduces a correlation between the emission of successive virtual phonons by the electron, our approximation, in which this correlation is neglected, breaks down for very strong electron-phonon coupling. The validity of our approximation is investigated and corrections are found to be small for coupling strengths occurring in typical polar crystals.

Scattering of light of very low frequency by systems of spin 1/2

Abstract: It is shown that the first two terms in the expansion of the scattering amplitude of light by a system of spin \textonehalf{} in powers of the frequency can be simply expressed in terms of the macroscopic properties of the system. The first term is the well known Thomson amplitude, and depends only on the total charge and mass. The second term is found to depend only on the charge, mass, and magnetic moment of the system.

Effective range approach to the low-energy p wave pion - nucleon interaction

Abstract: The theory of $p$-wave pion-nucleon scattering is reexamined using the formalism recently proposed by one of the authors (F.E.L.). On the basis of the cut-off Yukawa theory without nuclear recoil it is found, for not too high values of the coupling constant, that: (a) For each $p$-wave phase shift a certain function of the cotangent should be approximately linear at low energies and should extrapolate to the Born approximation at zero total energy. The value of the renormalized unrationalized coupling constant determined in this way from experiment is ${f}^{2}=0.08$. A special feature of the predicted energy dependence of the phase shifts is that ${\ensuremath{\delta}}_{33}$ is positive and the other $p$ phase shifts are negative. (b) The so-called "crossing theorem" requires a relation between the four $p$ phase shifts, so that in addition to the coupling constant only two further constants are needed to completely specify the low-energy behavior. (c) The direction of the energy variation in the (3,3) state is such that a resonance will occur for a sufficiently large cut-off ${\ensuremath{\omega}}_{max}$. Rough estimates indicate that ${\ensuremath{\omega}}_{max}\ensuremath{\approx}6$ will produce a resonance at the energy required by experiment. It is argued that the results (a) and (b) are very probably also consequences of a relativistic theory but that (c) may not be.

Weak decays beyond leading logarithms

Abstract: We review the present status of QCD corrections to weak decays beyond the leading-logarithmic approximation, including particle-antiparticle mixing and rare and $\mathrm{CP}$-violating decays. After presenting the basic formalism for these calculations we discuss in detail the effective Hamiltonians of all decays for which the next-to-leading-order corrections are known. Subsequently, we present the phenomenological implications of these calculations. The values of various parameters are updated, in particular the mass of the newly discovered top quark. One of the central issues in this review are the theoretical uncertainties related to renormalization-scale ambiguities, which are substantially reduced by including next-to-leading-order corrections. The impact of this theoretical improvement on the determination of the Cabibbo-Kobayashi-Maskawa matrix is then illustrated. [S0034-6861(96)00304-2]

Semiconducting and other major properties of gallium arsenide

Abstract: This review provides numerical and graphical information about many (but by no means all) of the physical and electronic properties of GaAs that are useful to those engaged in experimental research and development on this material. The emphasis is on properties of GaAs itself, and the host of effects associated with the presence of specific impurities and defects is excluded from coverage. The geometry of the sphalerite lattice and of the first Brillouin zone of reciprocal space are used to pave the way for material concerning elastic moduli, speeds of sound, and phonon dispersion curves. A section on thermal properties includes material on the phase diagram and liquidus curve, thermal expansion coefficient as a function of temperature, specific heat and equivalent Debye temperature behavior, and thermal conduction. The discussion of optical properties focusses on dispersion of the dielectric constant from low frequencies [κ0(300)=12.85] through the reststrahlen range to the intrinsic edge, and on the ass...

Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture

Abstract: The Kadanoff theory of scaling near the critical point for an Ising ferromagnet is cast in differential form. The resulting differential equations are an example of the differential equations of the renormalization group. It is shown that the Widom-Kadanoff scaling laws arise naturally from these differential equations if the coefficients in the equations are analytic at the critical point. A generalization of the Kadanoff scaling picture involving an "irrelevant" variable is considered; in this case the scaling laws result from the renormalization-group equations only if the solution of the equations goes asymptotically to a fixed point.

The renormalization group and critical phenomena

Abstract: 1. Introduction This paper has three parts. The first part is a simplified presentation of the basic ideas of the renormalization group and the ε expansion applied to critical phenomena , following roughly a summary exposition given in 1972 1. The second part is an account of the history (as I remember it) of work leading up to the papers in I971-1972 on the renormalization group. Finally, some of the developments since 197 1 will be summarized, and an assessment for the future given.