Lorentz-invariant non-commutative space-time based on DFR algebra

Hiromi Kase, Katsusada Morita, Yoshitaka Okumura, Eizo Umezawa

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

It is argued that the familiar algebra of non-commutative space-time with c-number θμν is inconsistent from a theoretical point of view. Consistent algebras are obtained by promoting θμν to an anti-symmetric tensor operator θ̂μν. The simplest among them is the Doplicher-Fredenhagen-Roberts (DFR) algebra, in which the triple commutator among the coordinate operators is assumed to vanish. This allows us to define the Lorentz-covariant operator fields on the DFR algebra as operators diagonal in the 6-dimensional θ-space of the hermitian operators, θ̂μν . It is shown that we then recover the Carlson-Carone-Zobin (CCZ) formulation of the Lorentz-invariant non-commutative gauge theory with no need for the compactification of the extra 6 dimensions. It is also pointed out that a general argument concerning the normalizability of the weight function in the Lorentz metric leads to the division of the θ-space into two disjoint spaces not connected by any Lorentz transformation, so that the CCZ covariant moment formula holds in each space separately. A non-commutative generalization of Connes' two-sheeted Minkowski space-time is also proposed. Two simple models of quantum field theory are reformulated on M4 × Z2 obtained in the commutative limit.

Original languageEnglish
Pages (from-to)663-685
Number of pages23
JournalProgress of Theoretical Physics
Volume109
Issue number4
DOIs
Publication statusPublished - 01-04-2003

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algebra
operators
Lorentz transformations
Minkowski space
commutators
division
gauge theory
tensors
moments
formulations

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

Cite this

Kase, Hiromi ; Morita, Katsusada ; Okumura, Yoshitaka ; Umezawa, Eizo. / Lorentz-invariant non-commutative space-time based on DFR algebra. In: Progress of Theoretical Physics. 2003 ; Vol. 109, No. 4. pp. 663-685.
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Lorentz-invariant non-commutative space-time based on DFR algebra. / Kase, Hiromi; Morita, Katsusada; Okumura, Yoshitaka; Umezawa, Eizo.

In: Progress of Theoretical Physics, Vol. 109, No. 4, 01.04.2003, p. 663-685.

Research output: Contribution to journalArticle

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