### 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 language | English |
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Number of pages | 1 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 63 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2001 Jan 1 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

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**High-temperature effective potential of noncommutative scalar field theory : Reduction of degrees of freedom by noncommutativity.** / Huang, Wung-Hong.

Research output: Contribution to journal › Article

TY - JOUR

T1 - High-temperature effective potential of noncommutative scalar field theory

T2 - Reduction of degrees of freedom by noncommutativity

AU - Huang, Wung-Hong

PY - 2001/1/1

Y1 - 2001/1/1

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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U2 - 10.1103/PhysRevD.63.125004

DO - 10.1103/PhysRevD.63.125004

M3 - Article

AN - SCOPUS:85038323748

VL - 63

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 12

ER -