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  • 1
    Electronic Resource
    Electronic Resource
    A new perturbative approach to nonlinear partial differential equations (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 3031-3038 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper shows how to solve some nonlinear wave equations as perturbation expansions in powers of a parameter that expresses the degree of nonlinearity. For the case of the Burgers equation ut+uux=uxx, the general nonlinear equation ut+uδux=uxx is considered and expanded in powers of δ. The coefficients of the δ series to sixth order in powers of δ is determined and Padé summation is used to evaluate the perturbation series for large values of δ. The numerical results are accurate and the method is very general; it applies to other well-studied partial differential equations such as the Korteweg–de Vries equation, ut+uux =uxxx.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529047
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  • 2
    Electronic Resource
    Electronic Resource
    The delta expansion in zero dimensions (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 2143-2150 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The recently introduced δ-expansion (or logarithmic-expansion) technique for obtaining nonperturbative information about quantum field theories is reviewed in the zero-dimensional context. There, it is easy to study questions of analytic continuation that arise in the construction of the Feynman rules that generate the δ series. It is found that for six- and higher-point Green's functions, a cancellation occurs among the most divergent terms, and that divergences that arise from summing over an infinite number of internal lines are illusory. The numerical accuracy is studied in some detail: The δ series converges inside a circle of radius one for positive bare mass squared, and diverges if the bare mass squared is negative, but in all cases, low-order Padé approximants are extremely accurate. These general features are expected to hold in higher dimensions, such as four.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528216
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  • 3
    Electronic Resource
    Electronic Resource
    A new perturbative approach to nonlinear problems (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1447-1455 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A recently proposed perturbative technique for quantum field theory consists of replacing nonlinear terms in the Lagrangian such as φ4 by (φ2)1+δ and then treating δ as a small parameter. It is shown here that the same approach gives excellent results when applied to difficult nonlinear differential equations such as the Lane–Emden, Thomas–Fermi, Blasius, and Duffing equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528326
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  • 4
    Electronic Resource
    Electronic Resource
    δ expansion for a quantum field theory in the nonperturbative regime (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2722-2725 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The δ expansion, a recently proposed nonperturbative technique in quantum field theory, is used to calculate the dimensionless renormalized coupling constant of a λ(cursive-phi2)1+δ quantum field theory in d-dimensional space-time at the critical point defined by λ→∞ with the renormalized mass held fixed. The calculation is performed to leading order in δ and compared with previous lattice strong-coupling calculations. The numerical results are good and provide new evidence that the theory in four dimensions is free for all δ.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528975
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  • 5
    Electronic Resource
    Electronic Resource
    Continued fraction as a discrete nonlinear transform (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 364-367 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The connection between a Taylor series and a continued fraction involves a nonlinear relation between the Taylor coefficients {an} and the continued fraction coefficients {bn}. In many instances it turns out that this nonlinear relation transforms a complicated sequence {an} into a very simple one {bn}. This simplification is illustrated in the context of graph combinatorics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530777
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  • 6
    Electronic Resource
    Electronic Resource
    Absence of species doubling in finite-element quantum electrodynamics (1995)
    Springer
    Letters in mathematical physics 34 (1995), S. 285-295 
    Details
    ISSN: 1573-0530
    Keywords: 81T25 ; 81T50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In this Letter, it will be demonstrated explicitly that the finite-element formulation of quantum electrodynamics is free from fermion doubling. We do this by (1) examining the lattice fermion propagator and using it to compute the one-loop vacuum polarization on the lattice, and (2) by an explict computation of vector and axial-vector current anomalies for an arbitrary rectangular lattice in the Schwinger model. There it is shown that requiring that the vector current be conserved necessitates the use of a square lattice, in which case the axial-vector current is anomalous.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01872782
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  • 7
    Electronic Resource
    Electronic Resource
    Finite-element lattice Hamiltonian matrix elements: Anharmonic oscillators (1996)
    Springer
    Letters in mathematical physics 36 (1996), S. 177-187 
    Details
    ISSN: 1573-0530
    Keywords: Primary: 81Q99 ; Secondary: 39A10 ; lattice field theory ; Hamiltonians ; finite-element method ; Gaussian knots ; quantum systems ; matrix elements
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The finite-element approach to lattice field theory is both highly accurate (relative errors ∼1/N 2, whereN is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly preserved at the lattice sites). In this Letter, we construct matrix elements for the time evolution operator for the anharmonic oscillator, for which the continuum Hamiltonian isH=p 2/2+λq 2k /2k. Construction of such matrix elements does not require solving the implicit equations of motion. Low-order approximations turn out to be quite accurate. For example, the matrix element of the time evolution operator in the harmonic oscillator groundstate gives a result for thek=2 anharmonic oscillator groundstate energy accurate to better than 1% while a two-state approximation reduces the error to less than 0.1%. Accurate wavefunctions are also extracted. Analogous results may be obtained in the continuum, but there the computation is more difficult, and not generalizable to field theories in more dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00714380
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  • 8
    Electronic Resource
    Electronic Resource
    The Young Julian Schwinger. V. Winding Up at the Radiation Lab, Going to Harvard, and Marriage (1999)
    Springer
    Foundations of physics 29 (1999), S. 1119-1162 
    Details
    ISSN: 1572-9516
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this series of articles the early life and work of the young Julian Schwinger are explored. In the present article, we discuss Schwinger's winding up his work at the MIT Radiation Laboratory, being offered a tenured professorship at Harvard University, getting married, and settling down into a highly productive teaching and research career.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018841800257
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  • 9
    Electronic Resource
    Electronic Resource
    Constructive approach to supergravity (1980)
    Springer
    General relativity and gravitation 12 (1980), S. 67-81 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Starting from a first-order formulation of the Lagrangian of noninteracting massless helicity-2 and helicity-3/2 particles, we deduce global supersymmetry transformations. Then, allowing the supersymmetry transformations to become local requires, if supersymmetry is to be maintained, the introduction of a unique primitive interaction through the “gravitino” stress tensor and torsion. Finally, the imposition of exact supersymmetry invariance leads by a short, constructive process to full supergravity and the complete form of the supersymmetry transformations. In particular, no explicit use is made of general coordinate invariance, and the self-consistency of the gravitational coupling emerges from the local supersymmetry requirement alone.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00756169
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  • 10
    Electronic Resource
    Electronic Resource
    The Young Julian Schwinger. I. A New York City Childhood (1999)
    Springer
    Foundations of physics 29 (1999), S. 767-786 
    Details
    ISSN: 1572-9516
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this series of articles the early life and work of the young Julian Schwinger are explored. In this first article, Schwinger's childhood, growing-up, and early education are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018878624422
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