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

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dc.creatorTanaka, Sho
dc.date2004-06-20
dc.date.accessioned2026-07-07T04:17:05Z
dc.date.available2026-07-07T04:17:05Z
dc.descriptionNoncommutative 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 $D_0$ branes in a Lorentz-covariant form. The so-called kinetic term ($\sim {\hat{P_i}}^2)$ and potential term ($\sim {[\hat{X_i},\hat{X_j}]}^2)$ of $D_0$ 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 $\hat{X_μ}$ and $\hat{P_μ}$ in YSTA show a distinctive spectral structure, that is, space-components $\hat{X_i}$ and $\hat{P_i}$ have discrete eigenvalues, and time-components $\hat{X_0}$ and $\hat{P_0}$ continuous eigenvalues, consistently with Lorentz-covariance. According to the method of Lorentz-covariant Moyal star product proper to YSTA, the field equation of $D_0$ brane on YSTA is derived in a nontrivial form beyond simple Klein-Gordon equation, which reflects the noncommutative space-time structure of YSTA.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/hep-th/0406166
dc.identifierhttp://arxiv.org/abs/hep-th/0406166
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/52611
dc.subjectHigh Energy Physics - Theory
dc.titleNoncommutative Field Theory on Yang's Space-Time Algebra, Covariant Moyal Star Product and Matrix Model
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