The Origin of chiral anomaly and the noncommutative geometry

Dec, 1999
29 pages
Published in:
  • J.Math.Phys. 41 (2000) 2789-2804
e-Print:

Citations per year

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Abstract:
We describe the scalar and spinor fields on noncommutative sphere starting from canonical realizations of the enveloping algebra A=Uu(2)){\cal A}={\cal U}{u(2))}. The gauge extension of a free spinor model, the Schwinger model on a noncommutative sphere, is defined and the model is quantized. The noncommutative version of the model contains only a finite number of dynamical modes and is non-perturbatively UV-regular. An exact expresion for the chiral anomaly is found. In the commutative limit the standard formula is recovered.
Note:
  • 30 pages
  • field theory: scalar
  • fermion
  • gauge field theory: U(1)
  • Schwinger model
  • dimension: 2
  • anomaly: chiral
  • space-time: S(2)
  • differential geometry: noncommutative
  • path integral