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

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• Scalar and gauge translation-invariant noncommutative models
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• Quantum gauge theories on noncommutative 3-d space
• Noncommutative geometry, gauge theory and renormalization
• Parametric representation of a translation-invariant renormalizable noncommutative model
• $\kappa$-Poincaré invariant quantum field theories with KMS weight
• The Jacobian Conjecture, a Reduction of the Degree to the Quadratic Case
• Gauge theories on quantum spaces
• Combinatorial Hopf Algebras in (Noncommutative) Quantum Field Theory
• Loop Calculations for the Non-Commutative U(1) Gauge Field Model with Oscillator Term
• Noncommutative gauge theories on ${\mathbb{R}}_{\theta }^2$ as matrix models
• $\kappa$-Poincaré invariant orientable field theories at 1-loop
• Gauge theories on $\kappa$-Minkowski spaces: Twist and modular operators
• Curing the UV/IR mixing for field theories with translation-invariant $\star$ products
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• Noncommutative gauge theories on ${\mathbb{R}}_{\lambda }^3$: Perturbatively finite models
• Slavnov-Taylor identities, non-commutative gauge theories and infrared divergences
• Closed star product on noncommutative ${\mathbb{R}}^3$ and scalar field dynamics
• Symmetries of noncommutative scalar field theory
• One-loop $\beta$ functions of a translation-invariant renormalizable noncommutative scalar model
• Involutive representations of coordinate algebras and quantum spaces
• On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
• Derivations of the Moyal Algebra and Noncommutative Gauge Theories
• Twisted Grosse-Wulkenhaar ${\varphi }^{\star 4}$ model: dynamical noncommutativity and Noether currents
• Translation-Invariant Noncommutative Renormalization
• Harmonic oscillator in twisted Moyal plane: eigenvalue problem and relevant properties
• Spectral theorem in noncommutative field theories: Jacobi dynamics
• Color Grosse-Wulkenhaar models: One-loop $\beta$-functions
• Renormalization of the commutative scalar theory with harmonic term to all orders
• Quantum spaces, central extensions of Lie groups and related quantum field theories
• Noncommutative Supergeometry and Quantum Supergroups
• Spectrum of the harmonic oscillator in a general noncommutative phase space