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Derivation of an Operator-Based Spatial Noncommutativity Parameter



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Derivation of an Operator Based Spatial Noncommutativity Parameter A thesis submitted in partial fulfillment of the requirement for the degree of Bachelor of Science with Honors in Physics from the College of William and Mary in Virginia by Kevin Carr Sapp Accepted for Honors Advisor Dr Carl E Carlson Dr Jeffrey Nelson Dr Nahum Zobin Williamsburg Virginia April 23 2008 Abstract The idea that the operators defining spacetime could be noncommuting has gained popularity in recent years The formulation in which the commutators themselves are a set of commuting numbers has been applied to a number of quantum phenomena to determine what effects it might have Most of the work overall has focused on this set of commuting numbers but some earlier theories of noncommutative coordinates established the coordinate commutator as having an operator based matrix value involving the angular momentum operator and Do plicher et al obtained a very similar algebra without mention of the angular momentum Beginning from the relativistic geometry used to derive this result we hope to explore an alternative foundation for a noncommutative geometry of space and determine its effects on some well studied quantities in atomic physics i Acknowledgements I would like to thank my advisor Dr Carl Carlson for his help and support in undertaking this project I am also very grateful to Dr Jeffrey Nelson Dr Nahum Zobin and Dr William J Kossler for sitting on my honors committee I extend thanks also to the College of William and Mary for providing me with this opportunity for learning both inside and outside a class setting to those who helped me on short notice and outside their field Ashwin Rastogi Brian DeSalvo and to all my friends and family who have supported me through this process ii 1 Introduction The commutativity of space time has been challenged in at least two different contexts in the history of modern physics and each of these instances resulted in a different interpretation of this



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