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Perturbative aspects of ultraviolet and infrared dynamics of noncommutative quantum field theory is examined in detail. It is observed that high loop momentum contribution to the nonplanar diagram develops a new infrared singularity with respect to the external momentum. This singular behavior is closely related to that of ultraviolet divergence of planar diagram. It is also shown that such a relation is precise in noncommutative Yang-Mills theory, but the same feature does not persist in noncommutative generalization of QED.
The concept of a noncommutative field is formulated based on the interplay between twisted Poincare symmetry and residual symmetry of the Lorentz group. Various general dynamical results supporting this construction, such as the light-wedge causality
We discuss the obstruction to the construction of a multiparticle field theory on a $kappa$-Minkowski noncommutative spacetime: the existence of multilocal functions which respect the deformed symmetries of the problem. This construction is only poss
We consider the deformed Poincare group describing the space-time symmetry of noncommutative field theory. It is shown how the deformed symmetry is related to the explicit symmetry breaking.
The study of the heat-trace expansion in noncommutative field theory has shown the existence of Moyal nonlocal Seeley-DeWitt coefficients which are related to the UV/IR mixing and manifest, in some cases, the non-renormalizability of the theory. We s
We consider a noncommutative field theory with space-time $star$-commutators based on an angular noncommutativity, namely a solvable Lie algebra: the Euclidean in two dimension. The $star$-product can be derived from a twist operator and it is shown