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Zeeman Spectroscopy of the Star Algebra

We solve the problem of finding all eigenvalues and eigenvectors of the Neumann matrix of the matter sector of open bosonic string field theory, including the zero modes, and switching on a background B-field. We give the discrete eigenvalues as roots of t

6.2TheRegion

ξ1

(0,1)17

1.Introduction

AfterRastelli,SenandZwiebachcalculated,in[1],thespectrumandalltheeigenvectorsofthezero-momentumNeumannmatrixinthemattersectorM,ithasbecomeclearthattheknowledgeofthespectrumisveryusefultoperformexactcalculationsinstring eldtheory[2,3,4].Also,ithasrecentlybeenshownbyDouglas,Liu,MooreandZwiebachin[5]thatthisallowsustowritethestar-productoftwozero-momentumstring eldsasacontinuoustensorproductofMoyalproducts,eachofwhichcorrespondingtooneeigenvalueinthespectrumofM.ThenoncommutativityparameterθofeachoftheseMoyalproductsisgivenasafunctionoftheeigenvalueλ.Forλ= 1

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