Finite-element quantum electrodynamics: Canonical formulation, unitarity, and the magnetic moment of the electron

Miller, Dean F.; Milton, Kimball A.; Siegemund-Broka, Stephan

doi:10.1103/physrevd.46.806

Cited by 6 publications

(12 citation statements)

References 10 publications

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“…V and VI also hold in the continuum, by virtue of (3.5), but the calculations are much more tedious without the use of the finite-element formula (5.1). It is in two or more space-time dimensions that the essential nature of the lattice in such calculations comes into play [4,5,14]. The high accuracy contrasted with the simplicity of the approach leads us to expect that we can extract spectral information, anomalies, and symmetry breaking from an examination of the time-evolution operator in gauge theories.…”

Section: Discussionmentioning

confidence: 99%

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Finite-element lattice Hamiltonian matrix elements: Anharmonic oscillators

Milton

Das

1996

Lett Math Phys

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The finite-element approach to lattice field theory is both highly accurate (relative errors ∼ 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 ma- * E-mail: kmilton@uoknor.edu or k.milton@ic.ac.uk (until 1 July 1995) † Permanent address ‡ E-mail: rdas@bashful.ossm.edu 1 trix 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.

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Section: Discussionmentioning

confidence: 99%

“…We have applied this technique to examples in quantum mechanics and to quantum field theories in two and four space-time dimensions. In particular, recent work has concentrated on Abelian and non-Abelian gauge theories [2][3][4][5][6], especially on issues of chiral symmetry breaking.…”

Section: Introductionmentioning

confidence: 99%

Finite-element lattice Hamiltonian matrix elements: Anharmonic oscillators

Milton

Das

1996

Lett Math Phys

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“…We now take matrix elements of the current in Fock-space states defined in terms of the momentum-space expansion of the free Dirac field [8,7] ψ m,1 = s,p µ ω b ps u ps e i(p+1/2)m2π/M + d † ps v ps e −i(p+1/2)m2π/M . (5.17)…”

Section: Current Anomalies In (3+1) Dimensionsmentioning

confidence: 99%

“…4. However, it is not clear how to extend such calculations to four dimensions because, unlike the original formulation [7], in general interactions here break unitarity. In a particular gauge in which the transfer matrix is unitary, the current anomalies are computed in the smallest nontrivial four-dimensional lattice in Sec.…”

Section: Introductionmentioning

confidence: 99%

Quasilocal formulation of non-Abelian finite-element gauge theory

Milton

1996

Phys. Rev. D

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Recently it was shown how to formulate the finite-element equations of motion of a non-Abelian gauge theory, by gauging the free lattice difference equations, and simultaneously determining the form of the gauge transformations. In particular, the gauge-covariant field strength was explicitly constructed, locally, in terms of a path-ordered product of exponentials ͑link operators͒. On the other hand, the Dirac and Yang-Mills equations were nonlocal, involving sums over the entire prior lattice. Earlier, Matsuyama had proposed a local Dirac equation constructed from just the above-mentioned link operators. Here, we show how his scheme, which is closely related to our earlier one, can be implemented for a non-Abelian gauge theory. Although both Dirac and Yang-Mills equations are now local, the field strength is not. The technique is illustrated with a direct calculation of the current anomalies in two and four space-time dimensions. Unfortunately, unlike the original finite-element proposal, this scheme is in general nonunitary.

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“…The form for the equations of motion was immediately generalizable, but only the first two terms in the field strength were given in 1990 [9]. Attention shifted to lattice QED [10].…”

Section: Introductionmentioning

confidence: 99%

Non-Abelian finite-element gauge theory

Milton¹

1995

Nuclear Physics B

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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. *

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Finite-element quantum electrodynamics: Canonical formulation, unitarity, and the magnetic moment of the electron

Cited by 6 publications

References 10 publications

Finite-element lattice Hamiltonian matrix elements: Anharmonic oscillators

Finite-element lattice Hamiltonian matrix elements: Anharmonic oscillators

Quasilocal formulation of non-Abelian finite-element gauge theory

Non-Abelian finite-element gauge theory

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