Waves on noncommutative spacetimes

Balachandran, A. P. and Gupta, Kumar S. and Kürkçüoğlu, Seçkin (2005) Waves on noncommutative spacetimes. Physical Review D, 73 (2). ISSN 1550-7998

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Official URL: http://doi.org/10.1103/PhysRevD.73.025021

Abstract

Waves on “commutative” spacetimes like R^d are elements of the commutative algebra C^0(R^d) of functions on R^d . When C^0(R^d) is deformed to a noncommutative algebra A_θ(R^d) with deformation parameter θ (A_0(R^d) = C^0(R^d)), waves being its elements, are no longer complex-valued functions on R^d . Rules for their interpretation, such as measurement of their intensity, and energy, thus need to be stated. We address this task here. We then apply the rules to interference and diffraction for d ≤ 4 and with time-space noncommutativity. Novel phenomena are encountered. Thus when the time of observation T is so brief that T ≤ 2θw, where w is the frequency of incident waves, no interference can be observed. For larger times, the interference pattern is deformed and depends on θw/T . It approaches the commutative pattern only when θw/T → 0. As an application, we discuss interference of star light due to cosmic strings.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 05 Oct 2017 19:31
Last Modified: 16 Jul 2018 11:33
URI: http://dair.dias.ie/id/eprint/163

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