Extended Future Tube Conjecture

A. G. Sergeev ; Xian-Yu Zhou

Informatics and Automation, Problems of the modern mathematical physics, Tome 228 (2000), pp. 32-51.

Résumé

We present an idea of the proof of the extended future tube conjecture from the axiomatic quantum field theory and discuss its relation to some other results from this theory and complex geometric invariant theory.

Bibliographie

[1] Bogolyubov N. N., Vladimirov V. S., “Odna teorema ob analiticheskom prodolzhenii obobschennykh funktsii”, Nauch. dokl. vyssh. shk. Fiz.-mat. nauki, 1958, no. 3, 26–35

[2] Bogolyubov N. N., Vladimirov V. S., “Predstavlenie $n$-tochechnykh funktsii”, Tr. MIAN, 112, 1971, 5–21 | Zbl

[3] Bros J., Epstein H., Glaser V., “On the connection between analyticity and Lorentz covariance of Wightman functions”, Commun. Math. Phys., 6 (1967), 77–100 | DOI | MR | Zbl

[4] Wightman A. S., “Quantum field theory and analytic functions of several complex variables”, J. Indian Math. Soc., 24 (1960–1961), 625–677 | MR

[5] Vladimirov V. S., “Analytic functions of several complex variables and axiomatic quantum field theory”, Actes Congres International Mathematiques Nice, v. 3, Gauthier-Villars, Paris, 1971, 21–26

[6] Vladimirov V. S., “Analiticheskie funktsii neskolkikh kompleksnykh peremennykh i kvantovaya teoriya polya”, Tr. MIAN, 135, 1975, 68–80 | Zbl

[7] Vladimirov V. S., “Several complex variables in mathematical physics”, Séminair Lelong–Skoda, Lect. Notes Math., 919, Springer-Verl., Berlin, 1982, 358–386

[8] Vladimirov V. S., Zharinov V. V., “Analiticheskie metody v matematicheskoi fizike”, Tr. MIAN, 175, 1986, 113–133 | MR | Zbl

[9] Vladimirov V. S., Sergeev A. G., “Kompleksnyi analiz v trube buduschego”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 8, VINITI, M., 1985, 191–266

[10] Zavyalov B. I., Trushin V. B., “O rasshirennoi $n$-tochechnoi trube”, TMF, 27 (1976), 3–15

[11] Iost R., Obschaya teoriya kvantovannykh polei, Mir, M., 1967 | MR

[12] Kiselman C. O., “The partial Legendre transformation for plurisubharmonic functions”, Invent. math., 49 (1978), 137–148 | DOI | MR | Zbl

[13] Loeb J. J., “Pseudo-convexité des ouverts invariants et convexité geodesique dans certains espaces symetriques”, Lect. Notes Math., 1198, 1983–1984, 172–190 | MR

[14] Loeb J. J., “Action d'une forme réelle d'un groupe de Lie complexe sur les fonctions plurisousharmoniques”, Ann. Inst. Fourier, 35 (1985), 59–97 | MR | Zbl

[15] Luna D., “Slices étales”, Bull. Soc. math. France, 33 (1973), 81–105 | MR | Zbl

[16] Sergeev A. G., Khaintsner P., “Rasshirennyi matrichnyi disk yavlyaetsya oblastyu golomorfnosti”, Izv. AN SSSR. Ser. mat., 55 (1991), 647–657 | MR

[17] Sergeev A. G., Chzhou Schan-Yui., “Ob invariantnykh oblastyakh golomorfnosti”, Tr. MIAN, 203, 1994, 159–172 | Zbl

[18] Snow D. M., “Reductive group actions on Stein spaces”, Math. Ann., 259 (1982), 79–97 | DOI | MR | Zbl

[19] Striter R. F., Vaitman A. S., RST, spin i statistika i vse takoe, Nauka, M., 1966

[20] Zhou Xiangyu, “On orbit connectedness, orbit convexity, and envelopes of holomorphy”, Izv. RAN. Ser. mat., 58 (1994), 196–205 | MR

[21] Chzhou Schan-Yui, “Dokazatelstvo gipotezy o rasshirennoi trube buduschego”, Izv. RAN. Ser. mat., 62 (1998), 211–224 | MR

[22] Chzhou Schan-Yui, “Invariantnaya versiya lemmy Kartana i kompleksifikatsii invariantnykh oblastei golomorfnosti”, Dokl. RAN, 366:5 (1999), 608–612 | MR