Vacuum configurations for renormalizable non-commutative scalar models

Abstract

In this paper we find non-trivial vacuum states for the renormalizable non-commutative ${\varphi }^4$ model. An associated linear sigma model is then considered. We further investigate the corresponding spontaneous symmetry breaking.

17 pages

References in corpus (10)

• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Noncommutative Induced Gauge Theory
• Induced Gauge Theory on a Noncommutative Space
• Constructive ${\varphi }^4$ field theory without tears
• Two and Three Loops Beta Function of Non Commutative ${\Phi }_4^4$ Theory
• Parametric Representation of Noncommutative Field Theory
• Non-Commutative Complete Mellin Representation for Feynman Amplitudes
• Renormalization of the Orientable Non-commutative Gross-Neveu Model
• Overview of the parametric representation of renormalizable non-commutative field theory
• One-loop Beta Functions for the Orientable Non-commutative Gross-Neveu Model

Cited by in corpus (11)

• A translation-invariant renormalizable non-commutative scalar model
• Induced Gauge Theory on a Noncommutative Space
• On the vacuum states for noncommutative gauge theory
• Commutative limit of a renormalizable noncommutative model
• Parametric representation of a translation-invariant renormalizable noncommutative model
• Combinatorial Hopf Algebras in (Noncommutative) Quantum Field Theory
• One-loop $\beta$ functions of a translation-invariant renormalizable noncommutative scalar model
• Derivations of the Moyal Algebra and Noncommutative Gauge Theories
• Translation-Invariant Noncommutative Renormalization
• Color Grosse-Wulkenhaar models: One-loop $\beta$-functions
• Spectrum of the harmonic oscillator in a general noncommutative phase space