The Decay of Unstable Noncommutative Solitons |
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Authors: | Thomas Chen Jürg Fröhlich Johannes Walcher |
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Institution: | Courant Institute of Mathematical Sciences, New York University, New York, NY 10012-1185, USA, US Institute for Theoretical Physics, ETH H?nggerberg, 8093 Zürich, Switzerland, CH Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA, US
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Abstract: | We study the classical decay of unstable scalar solitons in noncommutative field theory in 2+1 dimensions. This can, but
does not have to, be viewed as a toy model for the decay of D-branes in string theory. In the limit that the noncommutativity
parameter θ is infinite, the gradient term is absent, there are no propagating modes and the soliton does not decay at all.
If θ is large, but finite, the rotationally symmetric decay channel can be described as a highly excited nonlinear oscillator
weakly coupled to a continuum of linear modes. This system is closely akin to those studied in the context of discrete breathers.
We here diagonalize the linear problem and compute the decay rate to first order using a version of Fermi's Golden Rule, leaving
a more rigorous treatment for future work.
Received: 16 January 2003 / Accepted: 21 March 2003
Published online: 7 May 2003
Communicated by H. Araki, D. Buchholz, and K. Fredenhagen |
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Keywords: | |
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