Cornwall-Jackiw-Tomboulis effective potential for canonical noncommutative field theories

Abstract

We apply the Cornwall-Jackiw-Tomboulis (CJT) formalism to the scalar $\lambda {\varphi }^4$ theory in canonical-noncommutative spacetime. We construct the CJT effective potential and the gap equation for general values of the noncommutative parameter ${\theta }_{\mu \nu }$. We observe that under the hypothesis of translational invariance, which is assumed in the effective potential construction, differently from the commutative case (${\theta }_{\mu \nu }=0$), the renormalizability of the gap equation is incompatible with the renormalizability of the effective potential. We argue that our result, is consistent with previous studies suggesting that a uniform ordered phase would be inconsistent with the infrared structure of canonical noncommutative theories.

15 pages, LaTex

References in corpus (29)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• The quantum structure of spacetime at the Planck scale and quantum fields
• Noncommutative Perturbative Dynamics
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• The IR/UV Connection in the Non-Commutative Gauge Theories
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Deformed Boost Transformations That Saturate at the Planck Scale
• Comments on Noncommutative Perturbative Dynamics
• Self-consistent Improvement of the Finite Temperature Effective Potential
• Two-Loop Diagrams in Noncommutative ${\varphi }_4^4$ theory
• Phase structure of non-commutative scalar field theories
• Stripes from (noncommutative) stars
• Wilsonian Renormalization Group and the Non-Commutative IR/UV Connection
• Noncommutative Field Theory and Spontaneous Symmetry Breaking
• Phenomenology of Particle Production and Propagation in String-Motivated Canonical Noncommutative Spacetime
• Nonuniform symmetry breaking in noncommutative $\lambda {\Phi }^4$ theory
• On the CJT Formalism in Multi-Field Theories
• Simulating non-commutative field theory
• UV/IR mixing and the Goldstone theorem in noncommutative field theory
• On the UV renormalizability of noncommutative field theories
• Non--Commutative Field Theories beyond Perturbation Theory
• Self-consistently Improved Finite Temperature Effective Potential for Gauge Theories
• Spontaneous Symmetry Breaking in Noncommutative Field Theory
• Non-commutative Gross-Neveu model at large N
• Field Theoretical Background for Thermal Physics
• Wave Propagation and IR/UV Mixing in Noncommutative Spacetimes
• Effective Potential and Spontaneous Symmetry Breaking in the Noncommutative phi^6 Model

Cited by in corpus (6)

• Effects of Renormalizing the chiral SU(2) Quark-Meson-Model
• Spontaneous breaking of translational invariance in non-commutative lambda phi^4 theory in two dimensions
• Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED
• Non-Commutative (Softly Broken) Supersymmetric Yang-Mills-Chern-Simons
• Wave Propagation and IR/UV Mixing in Noncommutative Spacetimes
• Effective Potential and Spontaneous Symmetry Breaking in the Noncommutative phi^6 Model