no. 1
The extended future tube conjecture for SO(1, 𝑛)
Heinzner, Peter1 ; Schützdeller, Patrick2
1 Fakultät und Institut für Mathematik Ruhr-Universität Bochum Gebäude NA 4/74 D-44780 Bochum, Germany
2 Fakultät und Institut für Mathematik Ruhr-Universität Bochum Gebäude NA 4/69 D-44780 Bochum, Germany
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 1, pp. 39-52.

Let C be the open upper light cone in ℝ 1+n with respect to the Lorentz product. The connected linear Lorentz group SO ℝ (1,n) 0 acts on C and therefore diagonally on the N-fold product T N where T=ℝ 1+n +iC⊂ℂ 1+n . We prove that the extended future tube SO ℂ (1,n)·T N is a domain of holomorphy.

Classification : 32A07, 32D05, 32M05
Heinzner, Peter 1 ; Schützdeller, Patrick 2

1 Fakultät und Institut für Mathematik Ruhr-Universität Bochum Gebäude NA 4/74 D-44780 Bochum, Germany
2 Fakultät und Institut für Mathematik Ruhr-Universität Bochum Gebäude NA 4/69 D-44780 Bochum, Germany 
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     title = {The extended future tube conjecture for {SO(1,} ${\it {n}}$)},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {39--52},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 3},
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Heinzner, Peter; Schützdeller, Patrick. The extended future tube conjecture for SO(1, ${\it {n}}$). Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 1, pp. 39-52. http://archive.numdam.org/item/ASNSP_2004_5_3_1_39_0/

[B] R. Bremigan, Invariant analytic domains in complex semisimple groups, Transform. Groups 1 (1996), 279-305. | MR | Zbl

[FK] J. Faraut - A. Koranyi, “Analysis on Symmetric Cones”, Oxford Press, Oxford, 1994. | MR | Zbl

[HW] D. Hall - A. D. Wightman, A theorem on invariant analytic functions with applications to relativistic quantum field theory, Kgl. Danske Videnskap. Selkap, Mat.-Fys. Medd. 31 (1965) 1-14. | Zbl

[He1] P. Heinzner, Geometric invariant theory on Stein spaces, Math. Ann. 289 (1991), 631-662. | MR | Zbl

[He2] P. Heinzner, The minimum principle from a Hamiltonian point of view, Doc. Math. J. 3 (1998), 1-14. | MR | Zbl

[HeHuL] P. Heinzner - A. T. Huckleberry - F. Loose, Kählerian extensions of the symplectic reduction, J. reine angew. Math. 455 (1994), 123-140. | MR | Zbl

[HeMP] P. Heinzner - L. Migliorini - M. Polito, Semistable quotients, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 26 (1998), 233-248. | Numdam | MR | Zbl

[J] R. Jost, The general theory of quantized fields, In: “Lectures in applied mathematics”, vol. IV, 1965. | MR | Zbl

[Kr] H. Kraft, Geometrische Methoden in der Invariantentheorie, In: “Aspects of Mathematics”, Vieweg Verlag, 1984. | MR | Zbl

[N] R. Narasimhan, The Levi Problem for Complex Spaces II, Math. Ann. 146 (1962), 195-216. | MR | Zbl

[SV] A. G. Sergeev - V. S. Vladimirov, Complex analysis in the future tube, In: “Encyclopaedia of mathematical sciences” (Several complex variables II) vol. 8 (1994), 179-253. | Zbl

[StW] R. F. Streater - A. S. Wightman, “PCT spin statistics, and all that”, W. A. Benjamin, INC., 1964. | MR | Zbl

[W] A. S. Wightman, Quantum field theory and analytic functions of several complex variables, J. Indian Math. Soc. 24 (1960), 625-677. | MR | Zbl

[Z] X. Y. Zhou, A proof of the extended future tube conjecture, Izv. Math. 62 (1998), 201-213. | MR | Zbl