Noncommutative Field Theory on Yang's Space-Time Algebra, Covariant Moyal Star Product and Matrix Model

2004/06/20 by Sho Tanaka, Tanaka, Sho
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/0406166

15 pages

arxiv created 2004/06/20 · arxiv updated 2009/12/01

Abstract

Noncommutative field theory on Yang's quantized space-time algebra (YSTA) is studied. It gives a theoretical framework to reformulate the matrix model as quantum mechanics of D₀ branes in a Lorentz-covariant form. The so-called kinetic term (∼ P_i²) and potential term (∼ [X_i,X_j]²) of D₀ branes in the matrix model are described now in terms of Casimir operator of SO(D,1), a subalgebra of the primary algebra SO(D+1,1) which underlies YSTA with two contraction- parameters, λ and R. D-dimensional noncommutative space-time and momentum operators X_μ and P_μ in YSTA show a distinctive spectral structure, that is, space-components X_i and P_i have discrete eigenvalues, and time-components X₀ and P₀ continuous eigenvalues, consistently with Lorentz-covariance. According to the method of Lorentz-covariant Moyal star product proper to YSTA, the field equation of D₀ brane on YSTA is derived in a nontrivial form beyond simple Klein-Gordon equation, which reflects the noncommutative space-time structure of YSTA.

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