Missed opportunities
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 35 (1980) no. 1 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{RM_1980_35_1_a20,
     author = {F. J. Dyson},
     title = {Missed opportunities},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     year = {1980},
     volume = {35},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/RM_1980_35_1_a20/}
}
TY  - JOUR
AU  - F. J. Dyson
TI  - Missed opportunities
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 1980
VL  - 35
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/RM_1980_35_1_a20/
LA  - ru
ID  - RM_1980_35_1_a20
ER  - 
%0 Journal Article
%A F. J. Dyson
%T Missed opportunities
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 1980
%V 35
%N 1
%U http://geodesic.mathdoc.fr/item/RM_1980_35_1_a20/
%G ru
%F RM_1980_35_1_a20
F. J. Dyson. Missed opportunities. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 35 (1980) no. 1. http://geodesic.mathdoc.fr/item/RM_1980_35_1_a20/

[1] D. Hilbert, “Mathematische Probleme”, Lecture to the second Intern. Congress of Math. (Paris, 1900), Arch. Math. und Phys. (3), 1 (1901), 44–63 ; 213–237 ; English transl.: Bull. Amer. Math. Soc., 8 (1902), 437–479 ; Problemy Gilberta, Nauka, M., 1969 | Zbl | DOI | MR | Zbl | MR

[2] The principle of Relativity, Aberdeen Univ. Press, Aberdeen, 1923

[3] I. G. MacDonald, “Affine root systems and Dedekind's $\eta$-function”, Invent. Math., 15 (1972), 91–143 | DOI | MR | Zbl

[4] G. H. Hardy, Ramanujan, Cambridge Univ. Press, Cambridge; Macmillan, New York, 1940, p. 161 | Zbl

[5] S. Ramanujan, “On certain arithmetical functions”, Transl. Cambridge Philos. Soc., 22 (1916), 159–184

[6] L. J. Mordell, “On Mr. Ramanujan's empirical expansions of modular functions”, Proc. Cambridge Philos. Soc., 19 (1917), 117–124 | Zbl

[7] E. Hecke, “Über Modulfunktionen und die Dirichletschen Reihen mit Eulescher Productenewicklung”, Math. Ann., 114 (1937), 1–28 ; 316–351 | DOI | MR | Zbl | MR | Zbl

[8] M. Newman, “An identify for the coefficients of certain modular formas”, J. London math. Soc., 30 (1955), 488–493 | DOI | MR | Zbl

[9] R. C. Gunning, Lectures on modular forms, Ann. of Math. Studies, 48, Princeton Univ. Press, Princeton, N.J., 1962 | MR | Zbl

[10] L. Winquist, “An elementary proof of $P(11m + 6)\equiv 0 \pmod{11}$”, J. Combinatorial Theory, 6 (1969), 56–59 | DOI | MR | Zbl

[11] C. G. J. Jacobi, Fundamenta nova theoriae functionum ellipticarum, v. 66, Königsberg, 1826, Eq. (5) | Zbl

[12] F. Klein, R. F̀ricke, Vorlesungen über die Theorie der elliptischen Modulfunktionen, Bd. 12, Teubner, Leipzig, 1892 | Zbl

[13] J. C. Maxwell, “A dynamical theory of the electronmagnetic field”, Philos. Trans. Roy. Soc. (London), 155 (1865), 459–512 | DOI

[14] J. C. Maxwell, Nature, Presidential-Address to section A (Mathematical and Physical Sciences) of the British Association (Liverpool, 1870), 2, 1870, 419–422

[15] I. Newton, Mathematical principles of natural philosophy, Translated into english by Andrew Motte in 1729, ed. F. Cajori, Univ. of California Press, Berkley, Calif., 1946, p. 397; I. Nyuton, Matematicheskie nachala naturalnoi filosofii, Perev. akad. A. N. Krylova, Sobr. tr. A. N. Krylova, t. 7, M., 1936 | MR

[16] H. J. S. Smith, Nature, Presidential Address to section A (Mathematical and Physical Sciences) of the British Association (Bradford, 1873), 8, 1873, 448–452

[17] J. C. Maxwell, A treatise on electricity and Magnetism, Oxford Univ. Press, Oxford, 1873 | Zbl

[18] M. Pupin, From immigrant to inventor, Charles Scribner's Sons, 1924

[19] H. Bacry, J. M. Lévy-Leblond, “Possible kinematics”, J. Math. Phys., 9 (1968), 1605–1614 | DOI | MR | Zbl

[20] J. M. Lévy-Leblond, “Une nouvelle limite non-relativiste du groupe de Poincare”, Ann. Inst. H. Poincare Sect., A3 (1965), 1–12 | MR

[21] L. Carroll, Through the looking-glass and what Alice found there, Macmillan, London, 1871

[22] J. W. Gibbs, “On multiple algebra”, Proc. Amer. Assoc. Adv. Sci., Vice-presidential address to the section of mathematics and astronomy of the American association for the advancement of science, 35, 1886, 37–66

[23] W. R. Hamilton, “On quaternions; or on a new system of imaginaries in algebra”, Philos. Mag., 25 (1844), 10–13

[24] H. Grassmann, Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik, Otto Wigand, Leipzig, 1844

[25] R. Brauer, H. Weyl, “Spinors in $n$-dimensions”, Amer. J. Math., 57 (1935), 425–449 | DOI | MR

[26] A. Einstein, “Die grundlage der allegemeinen Relativitätstheorie”, Ann. Phys., 49 (1916), 769–822 ; A. Einshtein, Sobranie nauchnykh trudov, t. I, Nauka, M., 1965 | DOI | Zbl

[27] R. Haag, D. Kastler, “An elgebraic approach to quantum field theory”, J. Math. Phys., 5 (1964), 848–861 | DOI | MR | Zbl

[28] J. Dixmier, Les $C^*$-algebres et leurs representations, Gahiers Scientifiques, 29, Gauthier-Villars, Paris, 1964 ; Zh. Diksme, $C^*$-algebry i ikh predstavleniya, Nauka, M., 1974 | MR | MR

[29] R. P. Feynman, “Mathematical formulation of the quantum theory of electromagnetic interaction”, Phys. Rev. (2), 80 (1950), 440–457 | DOI | MR | Zbl

[30] R. E. Peierls, “The commutation laws of relativistic field theory”, Proc. Roy. London, Ser. A, 214 (1952), 143–157 | DOI | MR | Zbl

[31] I. M. Gelfand, A. M. Yaglom, “Integrirovanie v funktsionalnykh prostranstvakh i ego primenenie v kvantovoi fizike”, UMN, 11:1 (1956), 77–114 | MR

[32] E. Nelson, “Feynman integrals and the Schrödinger equation”, J. Math. Phys., 5 (1964), 332–343 | DOI | MR | Zbl

[33] C. M. Dewitt, “Feynman's path integral, definition without limiting procedure”, Commun. Math. Phys., 28 (1972), 47–55 | DOI | MR

[34] Rev. Economic Studies, 13 (1945), 1–9 | DOI

[35] E. W. Brown, “Resonance in the solar system”, Bull. Amer. Soc., 34 (1928), 265–289 | DOI

[36] C. J. Cohen, E. C. Hubbard, “Libration of the close approaches of Pluto to Neptune”, Astronom. J., 70 (1965), 10–13 | DOI | MR

[37] J. Hadamard, The psychology oi invention in the mathematical field, Princeton Univ. Press., Princeton, N.Y., 1945 ; Zh. Adamar, Issledovanie psikhologii protsessa izobreteniya v oblasti matematiki, Sovetskoe radio, M., 1970 | MR | Zbl

[38] B. J. Birch, “How the number of points of an elliptic curve over a fixed prime field varies”, J. London, Math. Soc., 43 (1968), 57–60 | DOI | MR | Zbl

[39] P. Deligne, “Formes modulaires et representations $l$-adiques”, Seminaire Bourbaki 1968, no. 355, 1969; P. Delin, “Modulyarnye formy i $l$-adicheskie predstavleniya”, Prilozhenie k knige: Zh. P. Serr, Abelevy $l$-adicheskie predstavleniya i ellipticheskie krivye, Mir, M., 1973

[40] L. D. Faddeev, “Symplectic structure and quantization of the Einstein gravitation theory”, Proc. Internat. Math. Congress, E2 (157), Nice, 1970, 78–82 | MR

[41] Yu. I. Manin, “Periody parabolicheskikh form i $P$-adicheskie ryady Gekke”, Matem. sb., 92:3 (1973), 378–401 | MR | Zbl

[42] Modular functions of one variable. 1, 2, 3, 4, 5, 6, Lecture Notes in Math., 320, 1973; 349, 1973; 350, 1973; 476, 1975; 601, 1977; 627, 1977

[43] O. M. Fomenko, “Prilozheniya teorii modulyarnykh form k teorii chisel”, Algebra, Geometriya, Topologiya, 15, VINITI, M., 1976, 5–91

[44] V. G. Kac, Infinite-dimensional Algebras, Dedikind's $\eta$-function, classical Möbius function and the very strange formula, Preprint MIT, 1977; Adv. in Math., 30 (1978), 85–136 | DOI | MR | Zbl

[45] Yu. A. Golfand, E. P. Likhtman, “Rasshirenie algebry generatorov gruppy Puankare i narushenie $P$-invariantnosti”, Pisma v ZhETF, 13 (1971), 452–455

[46] J. Wess, B. Zumino, “A lagrangian model invariant under supergauge transformations”, Phys. Lett., 49 (1974), 52–54 | DOI

[47] L. Corwin, Y. Ne'eman, S. Sternberg, “Graded Lie algebras in mathematics and physics”, Rev. Mod. Phys., 47 (1975), 573–603 | DOI | MR | Zbl

[48] V. I. Ogievetskii, A. Meznichesku, “Simmetrii mezhdu bozonami i fermionami”, UFN, 117 (1975), 637–684 | MR

[49] F. A. Berezin, G. I. Kats, “Gruppy Li s kommutiruyuschimi i antikommutiruyuschimi peremennymi”, Matem. sb., 82:3 (1970), 343–358 | MR

[50] V. G. Kac, “Lie Superalgebras”, Adv. in Math., 26 (1977), 8–96 | DOI | MR | Zbl

[51] B. Zumino, Supersymmetry and supergravity, CERN Preprint TH 2356, 1977 | MR

[52] E. S. Abers, B. W. Lee, “Gauge theories”, Phys. Rev., 9C (1973); Kvantovaya teoriya kalibrovochnykh polei, Mir, M., 1977

[53] A. A. Belavin, A. M. Polyakov, A. S. Schwartz, Y. S. Tyupkin, “Pseudoparticle solutions of the Yang-Mills equations”, Phys. Lett., 59 B (1975), 85–88 | DOI | MR

[54] R. Jackiw, C. Nohl, C. Rebbi, Classical and semi-classical solutions of the Yang-Mills theory, Preprint MIT No 675, 1977

[55] A. M. Polyakov, “Quark Confinement and Topology of Gauge groups”, Nucl. Phys., B 120 (1977), 429–458 | DOI | MR

[56] G. 't Hooft, “Computation of the quantum effects due to a four-dimensional pseudoparticle”, Phys. Rev., D 14 (1976), 3432–3435

[57] M. F. Atiyah, R. S. Ward, “Instantons and algebraic geometry”, Commun. Math. Phys., 55 (1977), 117–124 | DOI | MR | Zbl

[58] V. G. Drinfeld, Yu. I. Manin, “Avtodualnye polya Yanga-Millsa nad sferoi”, Funkts. analiz, 12:2 (1978), 78–79 | MR

[59] M. F. Atiyah, N. J. Hitchin, V. G. Drinfeld, Yu. I. Manin, “Construction of instantons”, Phys. Lett., 65 A (1978), 185–187 | DOI | MR

[60] V. G. Drinfeld, Y. I. Manin, A description of instantons, Preprint ITEP No 72, 1978 | MR

[61] I. N. Bernshtein, S. I. Gelfand, I. M. Gelfand, “Algebraicheskie rassloeniya nad $P^N$ i zadachi lineinoi algebry”, Funkts. analiz, 12:3 (1978), 66–67 | MR

[62] A. A. Beilinson, “Kogerentnye puchki iz $P^N$ i problemy lineinoi algebry”, Funkts. analiz, 12:3 (1978), 68–69 | MR | Zbl

[63] E. Witten, “An Interpretation of classical Yang-Mills theory”, Phys. Lett., 77B (1978), 394–398

[64] S. A. Albeverio, R. J. Hoegh-Krohn, Mathematical theory of Feynman Path Integrals, Lecture Notes in Math., 523, 1976 | MR | Zbl

[65] V. N. Gribov, “Kvantovanie kalibrovochnykh polei”, Fizika vysokikh energii, Trudy LIYaF, 1977, 64–91

[66] V. N. Popov, Kontinualnye integraly v kvantovoi teorii polya i statisticheskoi mekhanike, Atomizdat, M., 1976 | MR

[67] I. D. Faddeev, “Introduction to functional method”, Method in field theory, Nor. Holland, 1976, 1–40 | MR

[68] A. A. Belavin, V. E. Zakharov, “Yang-Mills equations as inverse scaterring problem”, Phys. Lett., 73 B (1978), 53–57 | DOI | MR

[69] V. E. Zakharov, A. V. Mikhailov, “Relyativistski-invariantnye dvumernye modeli teorii polya, integriruemye metodom obratnoi zadachi”, ZhETF, 74:6 (1978) | MR

[70] C. Gardner, J. Green, M. Kruskal, R. Miura, “A method for solving the Korteweg de Vries equation”, Phys. Rev. Lett., 19 (1967), 1045–1098 | DOI

[71] B. A. Dubrovin, V. B. Matveev, S. P. Novikov, “Nelineinye uravneniya tipa Kortevega-de Friza, konechnozonnye lineinye operatory i abelevy mnogoobraziya”, UMN, 31:1 (1976), 55–136 | MR | Zbl

[72] I. M. Krichever, “Metody algebraicheskoi geometrii v teorii nelineinykh uravnenii”, UMN, 33:6 (1977), 183–208

[73] L. D. Faddeev, Obratnaya zadacha kvantovoi teorii rasseyaniya. II, Itogi nauki i tekhniki. Sovremennye problemy matematiki, 3, VINITI, M., 1974

[74] I. M. Gelfand, L. A. Dikii, “Asimptotika rezolventy Shturm–Liuvillevskikh uravnenii i algebra uravnenii Kortevega–de Friza”, UMN, 30:5 (1975), 68–100 | MR

[75] Yu. I. Manin, “Algebraicheskie aspekty nelineinykh differentsialnykh uravnenii”, Itogi nauki i tekhniki. Sovremennye problemy matematiki, 11, VINITI, M., 1978, 5–152

[76] V. E. Zakharov, “Metod obratnoi zadachi rasseyaniya”, I. A. Kunin, Teoriya uprugikh sred s mikrostrukturoi, Gl. V, Nauka, M., 1975

[77] Zh. Dedonne, “Sovremennoe razvitie matematiki”, Matematika, 10:3 (1966), 3–11

[78] G. E. Volovik, V. P. Mineev, “Issledovanie osobennostei v ${}^3\mathrm{He}$ i zhidkikh kristallakh”, ZhETF, 72 (1977), 2256–2274 | MR

[79] M. Kleman, L. Michel, “On the classification of deffects in the smectic Phases”, J. de Phys. Lettres, 39 (1978), 129–132

[80] V. L. Golo, M. I. Monastyrsky, “Gauge groups and topological invariants of vaquum manifolds”, Ann. Inst. Henri Poincare (SEC A), 28 (1978), 75–89 | MR | Zbl

[81] P. Goddard, D. Olive, “The developments in the theory of magnetic monopoles”, Rep. on Prog. Phys., 41 (1978), 1357–1438 | DOI

[82] D. Finkelstein, C. W. Misner, “Some new concervation laws”, Ann. Phys., 6 (1959), 230–243 | DOI | MR | Zbl

[83] O. I. Bogoyavlenskii, S. P. Novikov, “Odnorodnye modeli v obschei teorii otnositelnosti”, UMN, 31:5 (1976), 33–48 | MR | Zbl

[84] R. V. Moody, “Euclidean Lie algebras”, Canad. J. Math., 21 (1969), 1432–1455 | MR

[85] A. O. L. Atkin, “Ramanujan congruences for $p_{-k}(n)$”, Canad. J. Math., 20 (1968), 67–68 ; corrigendum, ibid., 21 (1969), 256 | MR | Zbl

[86] A. Ogg, Modular forms and Direchlet series, Benjamin, New York, 1969 | MR | Zbl

[87] R. P. Feynman, “Space-time approach to non-relativistic quantum mecanics”, Rev. Modern Phys., 20 (1948), 367–387 ; Noveishee razvitie elektrodinamiki, IL, M., 1954 | DOI | MR