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Anomalies in Translation-Invariant Noncommutative Gauge Theories

Varshovi, Amir Abbass | 2011

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 43569 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Ardalan, Farhad; Sadoghi, Neda
  7. Abstract:
  8. Using the achievements of differential geometry an extended form of descent equations is worked out which leads to a set of modified consistent anomalies. A gauge invariant partition function is also defined for gauge theories with the standard quantization results. It is shown that the (extended) descent equations and consequently the (modified) consistent anomalies and Schwinger terms can be extracted from this modified partition function naturally. Moreover Translation-invariant products are discussed in the setting of α-cohomology and it is shown that loop calculations of Translation-invariant quantum field theories are entirely determined by α-cohomology class of star product in all orders. Then a matrix model formulation for translation-invariant noncommutative gauge theories is given in the setting of quantum geometry by means of differential graded algebras and quantum groups. Using this matrix model a Noncommutative version of geometric quantization, (anti-)BRST symmetry and (anti-)ghost field is worked out which leads to a noncommutative description of anomalous behaviors. This results in the ability of extracting the explicit form of (modified) consistent anomalies and Schwinger terms for translation-invariant noncommutative gauge theories
  9. Keywords:
  10. Anomaly ; Gauge Theory ; Non Commutative Geometry ; Matrix Model ; Partition Function ; Consistent Anomaly ; BRST Symmetry ; Translation-Invariant Products

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