High-temperature effective potential of noncommutative scalar field theory: Reduction of degrees of freedom by noncommutativity

Wung-Hong Huang

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Abstract

The renormalization of effective potentials for the noncommutative scalar field theory at high temperatures is investigated to the two-loop approximation. The Feynman diagrams in evaluating the effective potential may be classified into two types: the planar diagrams and nonplanar diagrams. The nonplanar diagrams, which depend on the parameter of noncommutativity, do not appear in the one-loop potential. Despite their appearance at the two-loop level, they do not have an inclination to restore the symmetry breaking in the tree level, in contrast with the planar diagrams. This phenomenon is explained as a consequence of the drastic reduction of the degrees of freedom in the nonplanar diagrams when the thermal wavelength is smaller than the noncommutativity scale. Our results show that the nonplanar two-loop contribution to the effective potential can be neglected in comparsion with that from the planar diagrams.

Original languageEnglish
Number of pages1
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume63
Issue number12
DOIs
Publication statusPublished - 2001 Jan 1

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degrees of freedom
diagrams
scalars
Feynman diagrams
inclination
broken symmetry
approximation
wavelengths

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)

Cite this

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abstract = "The renormalization of effective potentials for the noncommutative scalar field theory at high temperatures is investigated to the two-loop approximation. The Feynman diagrams in evaluating the effective potential may be classified into two types: the planar diagrams and nonplanar diagrams. The nonplanar diagrams, which depend on the parameter of noncommutativity, do not appear in the one-loop potential. Despite their appearance at the two-loop level, they do not have an inclination to restore the symmetry breaking in the tree level, in contrast with the planar diagrams. This phenomenon is explained as a consequence of the drastic reduction of the degrees of freedom in the nonplanar diagrams when the thermal wavelength is smaller than the noncommutativity scale. Our results show that the nonplanar two-loop contribution to the effective potential can be neglected in comparsion with that from the planar diagrams.",
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N2 - The renormalization of effective potentials for the noncommutative scalar field theory at high temperatures is investigated to the two-loop approximation. The Feynman diagrams in evaluating the effective potential may be classified into two types: the planar diagrams and nonplanar diagrams. The nonplanar diagrams, which depend on the parameter of noncommutativity, do not appear in the one-loop potential. Despite their appearance at the two-loop level, they do not have an inclination to restore the symmetry breaking in the tree level, in contrast with the planar diagrams. This phenomenon is explained as a consequence of the drastic reduction of the degrees of freedom in the nonplanar diagrams when the thermal wavelength is smaller than the noncommutativity scale. Our results show that the nonplanar two-loop contribution to the effective potential can be neglected in comparsion with that from the planar diagrams.

AB - The renormalization of effective potentials for the noncommutative scalar field theory at high temperatures is investigated to the two-loop approximation. The Feynman diagrams in evaluating the effective potential may be classified into two types: the planar diagrams and nonplanar diagrams. The nonplanar diagrams, which depend on the parameter of noncommutativity, do not appear in the one-loop potential. Despite their appearance at the two-loop level, they do not have an inclination to restore the symmetry breaking in the tree level, in contrast with the planar diagrams. This phenomenon is explained as a consequence of the drastic reduction of the degrees of freedom in the nonplanar diagrams when the thermal wavelength is smaller than the noncommutativity scale. Our results show that the nonplanar two-loop contribution to the effective potential can be neglected in comparsion with that from the planar diagrams.

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