arXiv subjects

K. A. Milton

Publications and source records attributed to K. A. Milton.

60 records · Page 4Linked to original sources

arXiv1998

Analytic Perturbative Approach to QCD

A technique called analytic perturbation theory, which respects the required analytic properties, consistent with causality, is applied to the definition of the running coupling in the timelike region, to the description of inclusive $τ$-decay, to deep-inelastic scattering sum rules, and to the investigation of the renormalization scheme ambiguity. It is shown that in the region of a few GeV the results are rather different from those obtained in the ordinary perturbative description and are practically renormalization scheme independent.

hep-ph↗

arXiv1998

Analytic Perturbation Theory and Renormalization Scheme Dependence in Tau Decay

We apply analytic perturbation theory in next-to-next-to-leading order to inclusive semileptonic $τ$-decay and study the renormalization scheme dependence. We argue that the renormalization scheme ambiguity is considerably reduced in the analytic perturbation theory framework and we obtain a rather stable theoretical prediction.

hep-ph↗

arXiv1997

Analytic Perturbation Theory and Inclusive Tau Decay

We apply analytic perturbation theory to the inclusive decay of a $τ$ lepton into hadrons. It is shown that the resulting analyticity of the coupling constant strongly influences the value of the QCD $Λ$-parameter extracted from the experimental data on $τ$ decay.

hep-ph↗

arXiv1996

Analytic perturbation theory in QCD and Schwinger's connection between the beta-function and the spectral density

We argue that a technique called analytic perturbation theory leads to a well-defined method for analytically continuing the running coupling constant from the spacelike to the timelike region, which allows us to give a self-consistent definition of the running coupling constant for timelike momentum. The corresponding $β$-function is proportional to the spectral density, which confirms a hypothesis due to Schwinger.

hep-ph↗

arXiv1995

Non-Abelian Finite-Element Gauge Theory

We complete the formulation of the equations of motion of a non-Abelian gauge field coupled to fermions on a finite-element lattice in four space-time dimensions. This is accomplished by a straightforward iterative approach, in which successive interaction terms are added to the Dirac and Yang-Mills equations of motion, and to the field strength, in order to preserve lattice gauge invariance exactly, yielding a series in powers of $ghA$. Here $g$ is the coupling constant, $h$ is the lattice spacing, and $A$ is the gauge potential. Gauge transformations of the potentials are determined simultaneously. The interaction terms in the equations of motion are nonlocal, and can be expressed either by an iterative formula or by a difference equation. On the other hand, the field strength is locally constructed from the potentials in terms of a path-ordered product of exponentials.

hep-th↗

arXiv1995

Finite-Element Lattice Hamiltonian Matrix Eleents. Anharmonic Oscillators

The finite-element approach to lattice field theory is both highly accurate (relative errors $\sim 1/N^2$, where $N$ 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 paper we construct matrix elements for the time evolution operator for the anharmonic oscillator, for which the continuum Hamiltonian is $H=p^2/2+λq^{2k}/2k$. 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 ground state gives a result for the $k=2$ anharmonic oscillator ground state 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.

hep-th↗