2008

Twisted Poincare Invariance, Noncommutative Gauge Theories and UV-IR Mixing

Balachandran, A. P., Pinzul, A., Queiroz, A. R.

Understand

In the absence of gauge fields, quantum field theories on the Groenewold-Moyal (GM) plane are invariant under a twisted action of the Poincare group if they are formulated following [1, 2, 3, 4, 5, 6].

In that formulation, such theories also have no UV-IR mixing [7].
Here we investigate UV-IR mixing in gauge theories with matter following the approach of [3, 4].
We prove that there is UV-IR mixing in the one-loop diagram of the S-matrix involving a coupling between gauge and matter fields on the GM plane, the gauge field being nonabelian.

Built on

P. Aschieri, M. Dimitrijevic, F. Meyer, and J. Wess, Noncommutative Geometry and Gravity
1912
Earlier work this paper cites.
S. Minwalla, M. Van Raamsdonk, and N. Seiberg, Noncommutative Perturbative Dynamics
2000
Earlier work this paper cites.
D. Bahns, S. Doplicher, K. Fredenhagen, and G. Piacitelli, On the unitarity problem in space/time noncommutative theories
2002
Earlier work this paper cites.

Similar

M. Chaichian, P. P. Kulish, K. Nishijima, and A. Tureanu, On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and its Implications on Noncommutative QFT
2004
Cited alongside, same era.
P. Aschieri, C. Blohmann, M. Dimitrijevic, F. Meyer, P. Schupp, and J. Wess, A Gravity Theory on Noncommutative Spaces
2005
Cited alongside, same era.
A. P. Balachandran, A. Pinzul, B. A. Qureshi, and S. Vaidya, Poincaré Invariant Gauge and Gravity Theories on the Groenewold-Moyal Plane
Cited in the paper.
A. P. Balachandran, A. Pinzul, B. A. Qureshi, and S. Vaidya, Twisted Gauge and Gravity Theories on the Groenewold-Moyal Plane
Original
Cited in the paper.
A. P. Balachandran, A. Pinzul, B. A. Qureshi, and S. Vaidya, S-Matrix on the Moyal Plane: Locality versus Lorentz Invariance
Original
Cited in the paper.
A. P. Balachandran, A. Pinzul, and B. A. Qureshi, Twisted Poincaré Invariant Quantum Field Theories
Original
Cited in the paper.
E. Akofor, A. P. Balachandran, S. G. Jo, and A. Joseph, Quantum Fields on the Groenwold-Moyal Plane: C, P, T and CPT
Original
Cited in the paper.

Then

D. Bahns, S. Doplicher, K. Fredenhagen, and G. Piacitelli, Field theory on noncommutative spacetimes: Quasiplanar Wick products
2005
Later among the works it cites.
A. P. Balachandran, A. Pinzul, and B. A. Qureshi, UV-IR Mixing in Non-commutative Plane
2006
Later among the works it cites.

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