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Paper   IPM / M / 16514
School of Mathematics
  Title:   ∗-cohomology, third type Chern character and anomalies in general translation-invariant noncommutative Yang-Mills
  Author(s):  Amir Abbas Varshovi
  Status:   To Appear
  Journal: IJGMMP
  Supported by:  IPM
  Abstract:
A representation of general translation-invariant star products ? in the algebra of M(C) = limN�??�?? MN (C) is introduced which results in the Moyal-Weyl-Wigner quantization. It provides a matrix model for general translation-invariant noncommutative quantum field theories in terms of the noncommutative calculus on differential graded algebras. Upon this machinery a cohomology theory, the so called ?-cohomology, with groups Hk ? (C), k �?� 0, is worked out which provides a cohomological framework to formulate general translation-invariant noncommutative quantum field theories based on the achievements for the commutative fields, and is comparable to the Seiberg-Witten map for the Moyal case. Employing the Chern-Weil theory via the integral classes of Hk ? (Z) a noncommutative version of the Chern character is defined as an equivariant form which contains topological information about the corresponding translation-invariant noncommutative Yang-Mills theory. Thereby we study the mentioned Yang-Mills theories with three types of actions of the gauge fields on the spinors, the ordinary, the inverse, and the adjoint action, and then some exact solutions for their anomalous behaviors are worked out via employing the homotopic correlation on the integral classes of ?-cohomology. Finally, the corresponding consistent anomalies are also derived from this topological Chern character in the ?-cohomology.

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