Non-Relativistic Non-Commutative Field Theory and UV/IR Mixing

Abstract

We study a non-commutative non-relativistic scalar field theory in 2+1 dimensions. The theory shows the UV/IR mixing typical of QFT on non-commutative spaces. The one-loop correction to the two-point function turns out to be given by a delta-function in momentum space. The one-loop correction to the four-point function is of logarithmic type. We also evaluate the thermodynamic potential at two-loop order. To avoid an IR-singularity we have to introduce a chemical potential. The suppression of the non-planar contribution with respect to the planar one turns out to depend crucially on the value of the chemical potential.

LaTex2e, 12 pages, 2 figures; v2: refs corrected and updated, minor changes

References in corpus (21)

• Noncommutative Perturbative Dynamics
• The IR/UV Connection in the Non-Commutative Gauge Theories
• Comments on Noncommutative Perturbative Dynamics
• Perturbative analysis on infrared and ultraviolet aspects of noncommutative QED on R^4
• Renormalization of Quantum Field Theories on Noncommutative R^d, I. Scalars
• Two-Loop Diagrams in Noncommutative ${\varphi }_4^4$ theory
• Chiral Gauge Anomalies on Noncommutative R^4
• Axial Anomaly in Noncommutative QED on R^4
• Evidence for Winding States in Noncommutative Quantum Field Theory
• Noncommutative Gauge Dynamics From The String Worldsheet
• Bi-local Fields in Noncommutative Field Theory
• Stretched Strings in Noncommutative Field Theory
• A Note on UV/IR for Noncommutative Complex Scalar Field
• Renormalization of noncommutative Yang-Mills theories: A simple example
• Diagrams of Noncommutative Phi-Three Theory from String Theory
• UV/IR Mixing for Noncommutative Complex Scalar Field Theory, II (Interaction with Gauge Fields)
• Thermal effects in perturbative noncommutative gauge theories
• The Interplay Between $\theta$ and T
• On the stringy nature of winding modes in noncommutative thermal field theories
• Noncommutative Gauge Theory, Divergences and Closed Strings
• Noncommutative Super Yang-Mills Theories with 8 Supercharges and Brane Configurations

Cited by in corpus (23)

• Quantum Field Theory on Noncommutative Spaces
• Gauge-fixing independence of IR divergences in non-commutative U(1), perturbative tachyonic instabilities and supersymmetry
• Star Operation in Quantum Mechanics
• Instability of Non-Commutative SYM Theories at Finite Temperature
• Excitations in Hot Non-Commutative Theories
• Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing
• D3-brane Holography
• UV/IR mixing and the Goldstone theorem in noncommutative field theory
• Galilean symmetry in noncommutative field theory
• The BRS invariance of noncommutative U(N) Yang-Mills theory at the one-loop level
• Effective Finite Temperature Partition Function for Fields on Non-Commutative Flat Manifolds
• Volume independence for Yang-Mills fields on the twisted torus
• Canonical Quantization of Noncommutative Field Theory
• Dynamics of O(N) Model in a Strong Magnetic Background Field as a Modified Noncommutative Field Theory
• Remarks on the Formulation of Quantum Mechanics on Noncommutative Phase Spaces
• A Note on Unitarity of Non-Relativistic Non-Commutative Theories
• High-Temperature Effective Potential of Noncommutative Scalar Field Theory: Reduction of Degree of Freedom by Noncommutativity
• Strong Field, Noncommutative QED
• Noncommutative Field Theories and Smooth Commutative Limits
• Investigation of Neutralino Pair Production in Photon-Photon Collider at ILC
• Correlation functions in the non-commutative Wess-Zumino-Witten model
• Renormalization Group Flow for Noncommutative Fermi Liquids
• D-branes, gauge/string duality and noncommutative theories