Open AccessDescribing Curved Spaces by Matrices
Author(s) -
Masanori Hanada,
H. Kawai,
Yusuke Kimura
Publication year - 2005
Publication title -
progress of theoretical physics
Language(s) - English
Resource type - Journals
eISSN - 1347-4081
pISSN - 0033-068X
DOI - 10.1143/ptp.114.1295
Subject(s) - physics , manifold (fluid mechanics) , mathematical physics , diffeomorphism , covariant transformation , interpretation (philosophy) , covariant derivative , lorentz group , matrix (chemical analysis) , action (physics) , space (punctuation) , pure mathematics , symmetry (geometry) , lorentz transformation , equations of motion , spin (aerodynamics) , unitary state , operator (biology) , quantum mechanics , mathematics , geometry , biochemistry , political science , transcription factor , thermodynamics , gene , philosophy , materials science , linguistics , computer science , engineering , composite material , programming language , mechanical engineering , repressor , law , chemistry
It is shown that a covariant derivative on any d-dimensional manifold M canbe mapped to a set of d operators acting on the space of functions on theprincipal Spin(d)-bundle over M. In other words, any d-dimensional manifold canbe described in terms of d operators acting on an infinite dimensional space.Therefore it is natural to introduce a new interpretation of matrix models inwhich matrices represent such operators. In this interpretation thediffeomorphism, local Lorentz symmetry and their higher-spin analogues areincluded in the unitary symmetry of the matrix model. Furthermore the Einsteinequation is obtained from the equation of motion, if we take the standard formof the action S=-tr([A_{a},A_{b}][A^{a},A^{b}]).Comment: 22 pages, 1 figure. V3: eqs (80) and (81) correcte
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