The extended future tube conjecture for SO(1, 𝑛 )

Peter Heinzner[1]; Patrick Schützdeller[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

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2004)

  • Volume: 3, Issue: 1, page 39-52
  • ISSN: 0391-173X

Abstract

top
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 + i C ⊂ ℂ 1 + n . We prove that the extended future tube SO ℂ ( 1 , n ) · T N is a domain of holomorphy.

How to cite

top

Heinzner, Peter, and Schützdeller, Patrick. "The extended future tube conjecture for SO(1, ${\it {n}}$)." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 3.1 (2004): 39-52. <http://eudml.org/doc/84527>.

@article{Heinzner2004,
abstract = {Let $C$ be the open upper light cone in $\mathbb \{R\}^\{1+n\}$ with respect to the Lorentz product. The connected linear Lorentz group $ \{\rm SO\}_\mathbb \{R\}(1,n)^0$ acts on $C$ and therefore diagonally on the $N$-fold product $T^N$ where $T = \mathbb \{R\}^\{1+n\} + iC \subset \mathbb \{C\}^\{1+n\}.$ We prove that the extended future tube $\{\rm SO\}_\mathbb \{C\}(1,n)\cdot T^N$ is a domain of holomorphy.},
affiliation = {Fakultät und Institut für Mathematik Ruhr-Universität Bochum Gebäude NA 4/74 D-44780 Bochum, Germany; Fakultät und Institut für Mathematik Ruhr-Universität Bochum Gebäude NA 4/69 D-44780 Bochum, Germany},
author = {Heinzner, Peter, Schützdeller, Patrick},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {1},
pages = {39-52},
publisher = {Scuola Normale Superiore, Pisa},
title = {The extended future tube conjecture for SO(1, $\{\it \{n\}\}$)},
url = {http://eudml.org/doc/84527},
volume = {3},
year = {2004},
}

TY - JOUR
AU - Heinzner, Peter
AU - Schützdeller, Patrick
TI - The extended future tube conjecture for SO(1, ${\it {n}}$)
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2004
PB - Scuola Normale Superiore, Pisa
VL - 3
IS - 1
SP - 39
EP - 52
AB - Let $C$ be the open upper light cone in $\mathbb {R}^{1+n}$ with respect to the Lorentz product. The connected linear Lorentz group $ {\rm SO}_\mathbb {R}(1,n)^0$ acts on $C$ and therefore diagonally on the $N$-fold product $T^N$ where $T = \mathbb {R}^{1+n} + iC \subset \mathbb {C}^{1+n}.$ We prove that the extended future tube ${\rm SO}_\mathbb {C}(1,n)\cdot T^N$ is a domain of holomorphy.
LA - eng
UR - http://eudml.org/doc/84527
ER -

References

top
  1. [B] R. Bremigan, Invariant analytic domains in complex semisimple groups, Transform. Groups 1 (1996), 279-305. Zbl0867.22004MR1424446
  2. [FK] J. Faraut – A. Koranyi, “Analysis on Symmetric Cones”, Oxford Press, Oxford, 1994. Zbl0841.43002MR1446489
  3. [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. Zbl0078.44302
  4. [He1] P. Heinzner, Geometric invariant theory on Stein spaces, Math. Ann. 289 (1991), 631-662. Zbl0728.32010MR1103041
  5. [He2] P. Heinzner, The minimum principle from a Hamiltonian point of view, Doc. Math. J. 3 (1998), 1-14. Zbl0939.32021MR1620612
  6. [HeHuL] P. Heinzner – A. T. Huckleberry – F. Loose, Kählerian extensions of the symplectic reduction, J. reine angew. Math. 455 (1994), 123-140. Zbl0803.53042MR1293876
  7. [HeMP] P. Heinzner – L. Migliorini – M. Polito, Semistable quotients, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 26 (1998), 233-248. Zbl0922.32017MR1631577
  8. [J] R. Jost, The general theory of quantized fields, In: “Lectures in applied mathematics”, vol. IV, 1965. Zbl0127.19105MR177667
  9. [Kr] H. Kraft, Geometrische Methoden in der Invariantentheorie, In: “Aspects of Mathematics”, Vieweg Verlag, 1984. Zbl0569.14003MR768181
  10. [N] R. Narasimhan, The Levi Problem for Complex Spaces II, Math. Ann. 146 (1962), 195-216. Zbl0131.30801MR182747
  11. [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. Zbl0787.32001
  12. [StW] R. F. Streater – A. S. Wightman, “PCT spin statistics, and all that”, W. A. Benjamin, INC., 1964. Zbl0135.44305MR161603
  13. [W] A. S. Wightman, Quantum field theory and analytic functions of several complex variables, J. Indian Math. Soc. 24 (1960), 625-677. Zbl0105.22101MR149854
  14. [Z] X. Y. Zhou, A proof of the extended future tube conjecture, Izv. Math. 62 (1998), 201-213. Zbl0922.32007MR1622270

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.