On the integrabillty of certain symmetric representations of the Lie algebra of SO0(4,1)

Research output: Contribution to journalArticle

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Abstract

A proof of the existence of an essentially self-adjoint extension of a symmetric SO0(4,1) Nelson operator, which is constructed out of the generators of a positive mass, arbitrary spin unitary irreducible representation of the Poincaré group, is presented. Our analysis of SO0(4,1) and its Lie algebra provides us with an example of an observation of Harish-Chandra: There exist subspaces of the space of differentiable vectors of a representation of a noncompact group which are invariant under the Lie algebra, but the closures of the subspaces are not invariant under the group. The chief results of this paper should hold true for SO0(n,1). In particular, we should have a realization of an arbitrary principal series irreducible unitary representation of SO0(n,1) on the direct sum of two identical unitary irreducible representation spaces of the motion group in an n-dimensional Minkowski space, which has one timelike dimension.

Original languageEnglish (US)
Pages (from-to)365-374
Number of pages10
JournalJournal of Mathematical Physics
Volume26
Issue number3
DOIs
StatePublished - Jan 1 1985

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Lie Algebra
algebra
Irreducible Representation
Subspace
Self-adjoint Extension
Invariant
Minkowski space
Unitary Representation
Minkowski Space
Arbitrary
Direct Sum
One Dimension
closures
Differentiable
n-dimensional
Closure
generators
Generator
operators
Series

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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On the integrabillty of certain symmetric representations of the Lie algebra of SO0(4,1). / Bohm, A.; Moylan, Patrick J.

In: Journal of Mathematical Physics, Vol. 26, No. 3, 01.01.1985, p. 365-374.

Research output: Contribution to journalArticle

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