摘要We study exactly the solvable noncommutative scalar quantum field models of (2n) or (2n+1) dimensions. By writing out an equivalent action of the noncommutative field, it is shown that the special condition B.θ=±I in field theoretic context means the full restoration of the maximal U (∞) gauge symmetries broken due to kinetic term. It is further shown that the model can be obtained by dimensional reduction of a 2n-dimensional exactly solvable noncommutative Ф4 quantum field model closely related to the 1+1-dimensional Moyal/matrix-valued nonlinear Schrodinger (MNLS) equation. The corresponding quantum fundamental commutation relation of the MNLS model is also given explicitly.
Abstract：We study exactly the solvable noncommutative scalar quantum field models of (2n) or (2n+1) dimensions. By writing out an equivalent action of the noncommutative field, it is shown that the special condition B.θ=±I in field theoretic context means the full restoration of the maximal U (∞) gauge symmetries broken due to kinetic term. It is further shown that the model can be obtained by dimensional reduction of a 2n-dimensional exactly solvable noncommutative Ф4 quantum field model closely related to the 1+1-dimensional Moyal/matrix-valued nonlinear Schrodinger (MNLS) equation. The corresponding quantum fundamental commutation relation of the MNLS model is also given explicitly.
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2007, Vol. 24 
