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  • 2000-2004  (4)
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  • 1
    Electronic Resource
    Electronic Resource
    The origin of chiral anomaly and the noncommutative geometry (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 2789-2804 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We describe scalar and spinor fields on a noncommutative sphere starting from canonical realizations of the enveloping algebra A=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 nonperturbatively UV regular. An exact expression for the chiral anomaly is found. In the commutative limit the standard formula is recovered. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533271
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  • 2
    Electronic Resource
    Electronic Resource
    Quantum field theory on the noncommutative plane with Eq(2) symmetry (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 1647-1671 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study properties of a scalar quantum field theory on the two-dimensional noncommutative plane with Eq(2) quantum symmetry. We start from the consideration of a firstly quantized quantum particle on the noncommutative plane. Then we define quantum fields depending on noncommutative coordinates and construct a field theoretical action using the Eq(2)-invariant measure on the noncommutative plane. With the help of the partial wave decomposition we show that this quantum field theory can be considered as a second quantization of the particle theory on the noncommutative plane and that this field theory has (contrary to the common belief) even more severe ultraviolet divergences than its counterpart on the usual commutative plane. Finally we introduce the symmetry transformations of physical states on noncommutative spaces and discuss them in detail for the case of the Eq(2) quantum group. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533201
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  • 3
    Electronic Resource
    Electronic Resource
    Space-time noncommutativity, discreteness of time and unitarity (2001)
    Springer
    The European physical journal 20 (2001), S. 767-772 
    Details
    ISSN: 1434-6052
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract. Violation of unitarity for noncommutative field theory on compact space-times is considered. Although such theories are free of ultraviolet divergences they still violate unitarity, while in a usual field theory such a violation occurs when the theory is nonrenormalizable. The compactness of space-like coordinates implies discreteness of the time variable which leads to the appearance of unphysical modes and violation of unitarity even in the absence of a star-product in the interaction terms. Thus, this conclusion holds also for other quantum field theories with discrete time. Violation of causality, among others, occurs also in the case of the nonvanishing of the commutation relations between observables at space-like distances with a typical scale of noncommutativity. While this feature allows for a possible violation of the spin-statistics theorem, such a violation does not rescue the situation but makes causality violation scale as the inverse of the mass appearing in the considered model, i.e., it becomes even more severe. We also stress the role of smearing over the noncommutative coordinates entering the field operator symbols.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s100520100664
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  • 4
    Electronic Resource
    Electronic Resource
    Non-commutative standard model: model building (2003)
    Springer
    The European physical journal 29 (2003), S. 413-432 
    Details
    ISSN: 1434-6052
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract. A non-commutative version of the usual electro-weak theory is constructed. We discuss how to overcome the two major problems: (1) although we can have non-commutative U(n) (which we denote by U* (n)) gauge theory we cannot have non-commutative SU(n) and (2) the charges in non-commutative QED are quantized to just $0, \pm 1$ . We show how the latter problem with charge quantization, as well as with the gauge group, can be resolved by taking the $U_{*}(3)\times U_{*}(2)\times U_{*}(1)$ gauge group and reducing the extra U(1) factors in an appropriate way. Then we proceed with building the non-commutative version of the standard model by specifying the proper representations for the entire particle content of the theory, the gauge bosons, the fermions and Higgs. We also present the full action for the non-commutative standard model (NCSM). In addition, among several peculiar features of our model, we address the inherent CP violation and new neutrino interactions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1140/epjc/s2003-01204-7
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