Inequivalence of Quantum Field Theories on Noncommutative Spacetimes: Moyal versus Wick-Voros Planes Articles uri icon

publication date

  • April 2010


  • 8


  • 81

International Standard Serial Number (ISSN)

  • 1550-7998

Electronic International Standard Serial Number (EISSN)

  • 1550-2368


  • In this paper, we further develop the analysis started in an earlier paper on the inequivalence of certain quantum field theories on noncommutative spacetimes constructed using twisted fields. The issue is
    of physical importance. Thus it is well known that the commutation
    relations among spacetime coordinates, which define a noncommutative
    spacetime, do not constrain the deformation induced on the algebra of
    functions uniquely. Such deformations are all mathematically equivalent
    in a very precise sense. Here we show how this freedom at the level of
    deformations of the algebra of functions can fail on the quantum field
    theory side. In particular, quantum field theory on the Wick-Voros and
    Moyal planes are shown to be inequivalent in a few different ways. Thus
    quantum field theory calculations on these planes will lead to different
    physics even though the classical theories are equivalent. This result
    is reminiscent of chiral anomaly in gauge theories and has obvious
    physical consequences. The construction of quantum field theories on the
    Wick-Voros plane has new features not encountered for quantum field
    theories on the Moyal plane. In fact it seems impossible to construct a
    quantum field theory on the Wick-Voros plane which satisfies all the
    properties needed of field theories on noncommutative spaces. The Moyal
    twist seems to have unique features which make it a preferred choice for
    the construction of a quantum field theory on a noncommutative