A New Gauge-Invariant Regularization Scheme Based on Lorentz-Invariant Noncommutative Quantum Field Theory(Particles and Fields)
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概要
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IR/UV mixing in non-commutative (NC) field theory is investigated in the Carlson-Carone-Zobin (CCZ) formalism of Lorentz-invariant NC field theory with the assumption that the fields are 'independent' of the 'internal' coordinates θ^<μν>. A new regularization scheme called 'NC regularization' is then proposed. This scheme removes the Lorentz-invariant IR singularity by subtraction from the theory. It requires the usual UV limit Λ → ∞ to be accompanied by the commutative limit a → 0 with Λ^2a^2 fixed, where a is the length parameter in the theory. The new UV limit gives the usual renormalized amplitude of the one-loop self-energy diagram of the φ^3 model. It is shown that the new regularization is gauge-invariant ; the 'non-transverse' part of the vacuum polarization in QED is automatically transverse in Lorentz-invariant NCQED, but the two transverse pieces, one of which is already transverse in QED, possess a Lorentz-invariant IR singularity which should be 'subtracted off' at zero external momentum squared. This subtraction leads to the same result as the renormalized one obtained by Pauli-Villars-Gupta or dimensional regularizations. Other diagrams with three-point vertices that contribute to the photon self-energy in Lorentz-non-invariant NCQED all vanish due to Lorentz invariance under the assumption adopted, while the tadpole diagram gives a finite contribution to the charge renormalization, which vanishes if Λ^2a^2 → 0. Lorentz-invariant NC φ^4 and scalar Yukawa models are also studied in the one-loop approximation. A comment is made that Lorentz invariance might lead to a decoupling of U(1) from SU(N) in NC U(N) gauge theory.
- 理論物理学刊行会の論文
- 2004-06-25
著者
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Morita Katsusada
Department Of Physics Dalhousie University Halifax : Nagoya University
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MORITA Kenji
Department of Physics, Waseda University
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MORITA Kazuhiko
Department of Physics, Hokkaido University
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MORITA Katsusada
Department of Physics, Faculty of Science, Nagoya University
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Morita Katsusada
Yukawa Institute for Theoretical Physics, Kyoto University
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