Group representations in indefinite metric spaces

P.M. van den Broek

doi:10.1007/BFb0016127

Group representations in indefinite metric spaces

P.M. van den Broek

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

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Abstract

A group G of symmetry transformations of the rays of an indefinite metric space V with metric operator eta leads to a projective representation U of G in V in terms of eta-unitary, eta-antiunitary, eta-pseudounitary, and eta-pseudoantiunitary operators. We investigate the restrictions which are put on the irreducible components of U by the metric, and examine to what extent it is possible to decompose V into a direct sum of indefinite metric spaces, each carrying a projective representation of G. Attention is restricted to the cases where the subgroup of G which is represented by eta-unitary operators is of index 1 or 2.

Original language	English
Title of host publication	Group Theoretical Methods in Physics
Subtitle of host publication	Proceedings of the XIIth International Colloquium Held at the International Centre for Theoretical Physics, Trieste, Italy, September 5–11, 1983
Editors	G. Denardo, G. Ghirardi, T. Weber
Place of Publication	Berlin, Heidelberg
Publisher	Springer
Pages	99-100
Number of pages	2
ISBN (Electronic)	978-3-540-38859-3
ISBN (Print)	978-3-540-13335-3
DOIs	https://doi.org/10.1007/BFb0016127
Publication status	Published - 1984
Event	12th International Colloquium on Group Theoretical Methods in Physics 1983 - Trieste, Italy Duration: 5 Sept 1984 → 11 Sept 1984 Conference number: 12

Publication series

Name	Lecture Notes in Physics
Publisher	Springer
Volume	201
ISSN (Print)	0075-8450
ISSN (Electronic)	1616-6361

Conference

Conference	12th International Colloquium on Group Theoretical Methods in Physics 1983
Country/Territory	Italy
City	Trieste
Period	5/09/84 → 11/09/84

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10.1007/BFb0016127

Broek1984groupFinal published version, 79.5 KB

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van den Broek, P. M. (1984). Group representations in indefinite metric spaces. In G. Denardo, G. Ghirardi, & T. Weber (Eds.), Group Theoretical Methods in Physics: Proceedings of the XIIth International Colloquium Held at the International Centre for Theoretical Physics, Trieste, Italy, September 5–11, 1983 (pp. 99-100). (Lecture Notes in Physics; Vol. 201). Springer. https://doi.org/10.1007/BFb0016127

van den Broek, P.M. / Group representations in indefinite metric spaces. Group Theoretical Methods in Physics: Proceedings of the XIIth International Colloquium Held at the International Centre for Theoretical Physics, Trieste, Italy, September 5–11, 1983. editor / G. Denardo ; G. Ghirardi ; T. Weber. Berlin, Heidelberg : Springer, 1984. pp. 99-100 (Lecture Notes in Physics).

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abstract = "A group G of symmetry transformations of the rays of an indefinite metric space V with metric operator eta leads to a projective representation U of G in V in terms of eta-unitary, eta-antiunitary, eta-pseudounitary, and eta-pseudoantiunitary operators. We investigate the restrictions which are put on the irreducible components of U by the metric, and examine to what extent it is possible to decompose V into a direct sum of indefinite metric spaces, each carrying a projective representation of G. Attention is restricted to the cases where the subgroup of G which is represented by eta-unitary operators is of index 1 or 2.",

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van den Broek, PM 1984, Group representations in indefinite metric spaces. in G Denardo, G Ghirardi & T Weber (eds), Group Theoretical Methods in Physics: Proceedings of the XIIth International Colloquium Held at the International Centre for Theoretical Physics, Trieste, Italy, September 5–11, 1983. Lecture Notes in Physics, vol. 201, Springer, Berlin, Heidelberg, pp. 99-100, 12th International Colloquium on Group Theoretical Methods in Physics 1983, Trieste, Italy, 5/09/84. https://doi.org/10.1007/BFb0016127

Group representations in indefinite metric spaces. / van den Broek, P.M.
Group Theoretical Methods in Physics: Proceedings of the XIIth International Colloquium Held at the International Centre for Theoretical Physics, Trieste, Italy, September 5–11, 1983. ed. / G. Denardo; G. Ghirardi; T. Weber. Berlin, Heidelberg: Springer, 1984. p. 99-100 (Lecture Notes in Physics; Vol. 201).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

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N2 - A group G of symmetry transformations of the rays of an indefinite metric space V with metric operator eta leads to a projective representation U of G in V in terms of eta-unitary, eta-antiunitary, eta-pseudounitary, and eta-pseudoantiunitary operators. We investigate the restrictions which are put on the irreducible components of U by the metric, and examine to what extent it is possible to decompose V into a direct sum of indefinite metric spaces, each carrying a projective representation of G. Attention is restricted to the cases where the subgroup of G which is represented by eta-unitary operators is of index 1 or 2.

AB - A group G of symmetry transformations of the rays of an indefinite metric space V with metric operator eta leads to a projective representation U of G in V in terms of eta-unitary, eta-antiunitary, eta-pseudounitary, and eta-pseudoantiunitary operators. We investigate the restrictions which are put on the irreducible components of U by the metric, and examine to what extent it is possible to decompose V into a direct sum of indefinite metric spaces, each carrying a projective representation of G. Attention is restricted to the cases where the subgroup of G which is represented by eta-unitary operators is of index 1 or 2.

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A2 - Denardo, G.

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van den Broek PM. Group representations in indefinite metric spaces. In Denardo G, Ghirardi G, Weber T, editors, Group Theoretical Methods in Physics: Proceedings of the XIIth International Colloquium Held at the International Centre for Theoretical Physics, Trieste, Italy, September 5–11, 1983. Berlin, Heidelberg: Springer. 1984. p. 99-100. (Lecture Notes in Physics). doi: 10.1007/BFb0016127

Group representations in indefinite metric spaces

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