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  • 1
    Electronic Resource
    Electronic Resource
    Quantum, many-body, finite-temperature perturbation theory for an electron–ion system (2000)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 7 (2000), S. 68-72 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The expansion in powers of the electron charge, e, for a neutral system of electrons (fermions) and ions (Maxwell–Boltzmann particles) is extended to order e4 for arbitrary values of temperature and density. The methods of calculation of the series terms will be illustrated, and some of the consequences of these results will be discussed. The ionization profile so derived, at least at high temperatures, will be contrasted with Saha theory. Some special features of hydrogen related to the possible plasma phase transition will be noted. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.873819
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  • 2
    Electronic Resource
    Electronic Resource
    Two-point quasifractional approximant in physics. Truncation error (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1470-1477 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The quasifractional approximation method is developed in a systematic manner. This method uses simultaneously the power series, and at a second point, the asymptotic expansion. The usual form of the approximants is two or more rational fractions, in terms of a suitable variable, combined with auxiliary nonfractional functions. Coincidence in the singularities in the region of interest is pursued. Equal denominators in the rational fractions is required so that the solution of only linear algebraic equations is needed to determine the parameters of the approximant. An upper bound is obtained for the truncation error for a certain class of functions, which contains most of the functions for which this method has been applied so far. It is shown that quasifractional approximants can be derived as a mixed German and Latin polynomial problem in the context of Hermite–Padé approximation theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529304
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  • 3
    Electronic Resource
    Electronic Resource
    Four-dimensional boson field theory. II. Existence (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 2379-2393 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The existence of the continuum, quantum field theory found by Baker and Johnson [G. A. Baker, Jr. and J. D. Johnson, J. Phys. A 18, L261 (1985)] to be nontrivial is proved rigorously. It is proved to satisfy all usual requirements of such a field theory, except rotational invariance. Currently known information is consistent with rotational invariance however. Most of the usual properties of other known Euclidean boson quantum field theories hold here, in a somewhat weakened form. Summability of the sufficiently strongly ultraviolet cutoff bare coupling constant perturbation series is proved as well as a nonzero radius of convergence for high-temperature expansions of the corresponding continuous-spin Ising model. The description of the theory by these two series methods is shown to be equivalent. The field theory is probably not asymptotically free.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527009
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  • 4
    Electronic Resource
    Electronic Resource
    Four-dimensional boson field theory. III. Nontriviality (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 1146-1158 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The results of numerical investigations based on series analysis indicate clearly that the method of phantom fields constructs nontrivial, self-interacting scalar Euclidean boson field theories. It is found that these continuum theories arise as the scaling limit to normal critical points of lattice statistical mechanical models. The character of these theories is numerically indistinguishable from that of a classical theory on the lambda line near the tricritical point.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527818
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