Strong coupling asymptotics of the β-function in theory and QED

Suslov, I.

doi:10.1016/j.apnum.2010.05.006

Cited by 2 publications

(1 citation statement)

References 32 publications

(72 reference statements)

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“…This is in agreement with recent analysis [16,17]. From this we learn that this theory has only trivial fixed points: the coupling goes to zero in the infrared and goes to infinity in the ultraviolet.…”

Section: Running Coupling and Trivialitysupporting

confidence: 92%

Exact solution of Dyson-Schwinger equations for a scalar field theory

Frasca¹

2009

Preprint

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We exactly solve Dyson-Schwinger equations for a massless quartic scalar field theory. n-point functions are computed till n=4 and the exact propagator computed from the two-point function. The spectrum is so obtained, being the same of a harmonic oscillator. Callan-Symanzik equation for the two-point function gives the beta function. This gives the result that this theory has only trivial fixed points. In the low-energy limit the coupling goes to zero making the theory trivial and, at high energies, it reaches infinity. No Landau pole appears, rather this should be seen as a precursor, in a weak perturbation expansion, of the coupling reaching the trivial fixed point at infinity. Using a mapping theorem, recently proved, between massless quartic scalar field theory and gauge theories, we derive some properties of the latter.

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Section: Running Coupling and Trivialitysupporting

confidence: 92%

Exact solution of Dyson-Schwinger equations for a scalar field theory

Frasca¹

2009

Preprint

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Triviality problem and high-temperature expansions of higher susceptibilities for the Ising and scalar-field models in four-, five-, and six-dimensional lattices

Butera

Pernici

2012

Phys. Rev. E

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High-temperature expansions are presently the only viable approach to the numerical calculation of the higher susceptibilities for the spin and the scalar-field models on high-dimensional lattices. The critical amplitudes of these quantities enter into a sequence of universal amplitude ratios that determine the critical equation of state. We have obtained a substantial extension, through order 24, of the high-temperature expansions of the free energy (in presence of a magnetic field) for the Ising models with spin s≥1/2 and for the lattice scalar-field theory with quartic self-interaction on the simple-cubic and the body-centered-cubic lattices in four, five, and six spatial dimensions. A numerical analysis of the higher susceptibilities obtained from these expansions yields results consistent with the widely accepted ideas, based on the renormalization group and the constructive approach to Euclidean quantum field theory, concerning the no-interaction ("triviality") property of the continuum (scaling) limit of spin-s Ising and lattice scalar-field models at and above the upper critical dimensionality.

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Strong coupling asymptotics of the β-function in theory and QED

Cited by 2 publications

References 32 publications

Exact solution of Dyson-Schwinger equations for a scalar field theory

Exact solution of Dyson-Schwinger equations for a scalar field theory

Triviality problem and high-temperature expansions of higher susceptibilities for the Ising and scalar-field models in four-, five-, and six-dimensional lattices

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