References
P. A. M. Dirac:Can. J. Math.,2 129 (1950);Lectures on Quantum Mechanics, inBelfer Graduate School of Science, Monographs Series (Yeshiva University, New York, N.Y., 1964).
J. L. Anderson andP. G. Bergmann:Phys. Rev.,83 1018 (1951);P. G. Bergmann andJ. Goldberg:Phys. Rev.,98, 531 (1955).
R. Cawley:Phys. Rev. Lett.,42, 413 (1979);Phys. Rev. D,21, 2988 (1980).
A. Frenkel:Phys. Rev. D,21 2986 (1980).
G. R. Allcock:Philos. Trans. R. Soc. London, Ser. A,279, 487 (1975);Kinam Rev. Fis.,2, 335 (1980).
R. Sugano andT. Kimura:Prog. Theor. Phys.,69 1241 (1983).
R. Di Stefano:Phys. Rev. D,27 1752 (1983).
M. J. Gotay andJ. M. Nester:J. Phys. A,17 3063 (1984).
M. J. Gotay:J. Phys. A,16 L-141 (1983).
A. J. Hanson, T. Regge andC. Teitelboim:Constrained Hamiltonian systems, inContributi del Centro Linceo Interdisciplinare di Scienze Matematiche, Fisiche e loro Applicazioni, n. 22 (Accademia Nazionale dei Lincei, Roma, 1975).
E. C. G. Sudarshan andN. Mukunda:Classical Mechanics: a Modern Perspective (Wiley, New York, N.Y., 1974).
K. Sundermeyer:Constraint Dynamics with Applications to Yang-Mills Theory, General Relativity, Classical Spin, Dual String Model, Lecture Notes in Physics, Vol.169 (Springer, Berlin, 1982).
G. Longhi andL. Lusanna (Editors):Constraint’s Theory and Relativistic Dynamics, Firenze Workshop 1986 (World Scientific, Singapore, 1987).
A. Ashtekar:New Perspectives in Canonical Gravity (Bibliopolis, Napoli, 1986).
I. T. Todorov:Sissa Report, Trieste, 1980 (unpublished); inQuantum Theory, Groups, Fields and Particles, edited byA. O. Barut (Reidel, Dordrecht, 1983).
J. A. Llosa, (Editor):Relativistic Action-at-a-distance: Classical and Quantum Aspects, inLecture Notes in Physics, Vol.162 (Springer, Berlin, 1982).
L. Lusanna: inProceedings of the VII Seminar on Problems of High Energy Physics and Quantum Field Theory, Protvino, USSR 1984, Vol.1, p. 123;Nuovo Cimento B,65, 135 (1981).
A. Lichnerowicz:C. R. Acad. Sci. Paris, Ser. A,280 523 (1975).
J. Sniatycki: inProceedings of Journées Relativistes, Caen, 1970; inProceedings of the Biennal Seminar of Mathematical Congress,2, 125 (1972);Ann. Inst. Henri Poincaré,20, 365 (1984).
W. Tulczyiew:Symposia Math.,14 247 (1974).
M. J. Gotay:Presymplectic Manifolds, Geometric Constraint Theory and the Dirac-Bergmann Theory of Constraints, Dissertation, University of Maryland, Phys. Dept. preprint 80-063 (1979) (unpublished);M. J. Gotay, J. M. Nester andG. Hinds:J. Math. Phys.,19, 2388 (1978).
J. Sniatycki: inLecture Notes in Mathematics, Vol.1037,Proceedings of the Clausthal Workshop, 1981, edited byA. Dold andB. Eckmann (Springer, Berlin, 1983);J. Geom. Phys.,2, 1 (1985).
M. J. Gotay andJ. Sniatycki:Commun. Math. Phys.,82 377 (1981).
G. Marmo, N. Mukunda andJ. Samuel:Riv. Nuovo Cimento,6 1 (1983).
R. P. Feynman:Acta Phys. Pol.,24 697 (1963);L. D. Faddeev andV. N. Popov:Phys. Lett. B,25, 30 (1967);B. S. de Witt:Phys. Rev.,162, 1195 and 1239 (1967);A. A. Slavnov:Theor. Math. Phys.,10, 153 (1972).
C. Becchi, A. Rouet andR. Stora:Phys. Lett. B,52 344 (1974);CNRS Centre de Physique Théorique, Marseille, Colloquium on Recent Progress in Lagrangian Field Theory, June 1974; Commun. Math. Phys.,42, 127 (1975);Ann. Phys. (N.Y.),98, 287 (1976).
E. S. Fradkin andG. A. Vilkovisky:Phys. Lett. B,55, 224 (1975); preprint CERN/TH.2332 (1977) (unpublished);I. A. Batalin andG. A. Vilkovisky:Phys. Lett. B,69, 309 (1977).
I. A. Batalin andE. S. Fradkin:Phys. Lett. B,128 303 (1983);Riv. Nuovo Cimento,9, 1 (1986);Nucl. Phys. B,279, 514 (1987);L. D. Faddeev andS. L. Shatashvili:Phys. Lett. B,167, 225 (1986).
M. Henneaux:Phys. Rep.,126 1 (1985);Classical Foundations of BRS Symmetry (Bibliopolis, Napoli, 1988).
B. Konstant andS. Sternberg:Ann. Phys. (N.Y.),176 49 (1987);M. Henneaux andC. Teitelboim:Commun. Math. Phys.,115, 213 (1988);L. Bonora andP. Cotta-Ramusino:Commun. Math. Phys.,87, 589 (1983).
L. Lusanna:Phys. Rep.,185 1 (1990).
E. Noether:Nachr. Ges. Wiss. Göttingen, Math. Phys. Klasse, H.2, 235 (1918); English Translation inTransp. Theory and Stat. Phys.,1, 183 (1971).
J. D. Logan:Invariant Variational Principles (Academic Press, New York, N.Y., 1977);B. F. Plybon:J. Math. Phys.,12, 57 (1971);N. P. Konopleva andV. N. Popov:Gauge Fields (Harwood, New York, N.Y., 1981).
B. M. Barbashov andV. V. Nesterenko:Fortschr. Phys.,31 535 (1983).
L. Lusanna:Nuovo Cimento B,52 141 (1979).
P. G. Bergmann andR. Schiller:Phys. Rev.,89 4 (1953);P. G. Bergmann, I. Goldberg, A. Janis andE. Newman:Phys. Rev.,103, 807 (1956);P. G. Bergmann andA. J. Janis:Phys. Rev.,111, 1191 (1958);J. G. Fletcher:Rev. Mod. Phys.,32, 65 (1960);V. I. Ogiyevetsky andI. V. Polubarinov:Nucl. Phys.,76, 677 (1966);W. R. Davis andJ. W. York jr.:Nuovo Cimento B,65, 1 (1970);R. Sugano:Prog. Theory. Phys.,70, 36 (1983);A. M. Chervyakov andV. V. Nesterenko:Theor. Math. Phys.,64, 82 (1985);L. Castellani:Ann. Phys. (N.Y.),143, 357 (1982);A. Barducci, R. Giachetti, J. Gomis andE. Sorace:J. Phys. A,17, 3277 (1984);J. Gomis, K. Kamimura andJ. M. Pons:Prog. Theor. Phys.,71, 1051 (1984);Europhys. Lett.,2, 187 (1986);I. Gràcia andJ. M. Pons: Barcelona University, preprint UB-ECM-PF 1/88.
S. Shanmugadhasan:J. Math. Phys.,14 677 (1973);R. L. Schafir:J. Phys. A,15, L-331 (1982);C. Battle, J. Gomis, J. M. Pons andN. Roman:J. Math. Phys.,27, 2963 (1986).
R. Courant andD. Hilbert:Methods of Mathematical Physics (Interscience, New York, N.Y., 1953), Vol. 1;L. S. Schulman:Techniques and Applications of Path Integration (Wiley, New York, N.Y., 1981);B. S. de Witt: inRelativity, Groups and Topology, Proc. XIII Les Houches, 1963, edited byC. de Witt andB. S. de Witt (Gordon and Breach, London, 1964);G. Caviglia:J. Math. Phys.,24, 2065 (1983);Int. J. Theor. Phys.,23, 461 (1984);Gen. Rel. Grav.,16, 283 (1984).
I. A. Batalin andG. A. Vilkovisky:J. Math. Phys.,26 172 (1985);D. Z. Freedman andP. van Nieuwenhuizen:Phys. Rev. D,14, 912 (1976).
M. J. Gotay andJ. M. Nester:Ann. Inst. Henri Poincaré A,30 129 (1979);A,32, 1 (1980).
R. Sugano andH. Kamo:Prog. Theor. Phys.,67 1966 (1982);R. Sugano:Prog. Theor. Phys.,68, 1377 (1982);70, 36 (1983);R. Sugano andT. Kimura:Prog. Theor. Phys.,69, 252 and 1256 (1983);Nuovo Cimento A,87, 57 (1985);R. Sugano, T. Sohkawa andT. Kimura:Prog. Theor. Phys.,73, 1025 (1985);R. Sugano, Y. Saito andT. Kimura:Prog. Theor. Phys.,76, 283 (1986).
R. Skinner andR. Rusk:J. Math. Phys.,24, 2589 and 2595 (1983);K. Kamimura:Nuovo Cimento B,69, 33 (1982).
R. Skinner:J. Math. Phys.,24 2581 (1983);G. Morandi, C. Ferrario, G. Lo Vecchio, G. Marmo andC. Rubano:Phys. Rep.,188, 147 (1990).
M. Abraham andJ. M. Marsden:Foundations of Mechanics (Benjamin, Mass., 1979) 2nd edition;J. Sniatycki andW. M. Tulczyew:Ann. Inst. Henri Poincaré A,16, 23 (1972);W. M. Tulczyew:Ann. Inst. Henri Poincaré A,27, 101 (1977).
M. J. Gotay andJ. M. Nester: inGroup Theoretical Methods in Physics, Austin, 1978, Lecture Notes in Physics, Vol.94 (Springer, Berlin, 1979).
D. M. Appleby:J. Phys. A,15 1191 (1982);A. Cabo:J. Phys. A,19, 629 (1986).
J. A. Schouten andM. van der Kulk:Pfaff’s Problem and its Generalizations (Clarendon, Oxford, 1949);L. P. Eisenhart:Continuous Groups of Transformations (Princeton University Press, Princeton, N.J., 1933).
P. G. Bergmann, R. Penfield, R. Schiller andH. Zatzkis:Phys. Rev.,80, 81 (1950).
A. Wintner:The Analytical Foundations of Celestial Mechanics (Princeton University Press, Princeton, N.J., 1941);T. Levi-Civita andU. Amaldi:Lezioni di Meccanica Razionale, Vol. II, Part 2 (Zanichelli, Bologna, 1927).
W. Sarlet andF. Cantrijn:SIAM Rev.,23 467 (1981).
J. Rosen:Int. J. Theor. Phys.,4 287 (1971);Ann. Phys. (N.Y.),69, 342 (1972);82, 54 and 70 (1970);Am. J. Phys.,46, 1030 (1978);J. Phys. A,13, 803 (1980).
E. Candotti, C. Palmieri andB. Vitale:Nuovo Cimento A,70 233 (1970);A,7, 271 (1972);C. Palmieri andB. Vitale:Nuovo Cimento A,66, 299 (1970).
A. Trautman: inGravitation, edited byL. Witten (Wiley, New York, N.Y., 1962); inLectures on General Relativity, Brandeis Summer Institute in Theoretical Physics (Prentice Hall, Inc., Englewood Cliffs, 1964).
N. Mukunda:Ann. Phys. (N.Y.),99 408 (1976);Phys. Scr.,21, 783 (1980).
J. M. Arms, J. E. Marsden andV. Moncrief:Commun. Math. Phys.,78 455 (1981)J. Sniatycki: inNonlinear Partial Differential Operators and Quantizations Procedure, Clausthal 1981, Lecture Notes in Mathematics, Vol.1037 (Springer, Berlin, 1983).
R. Casalbuoni andG. Longhi:Nuovo Cimento A,25 482 (1975); see alsoX. Gràcia andJ. M. Pons: Universitat de Barcelona preprint UB-ECM-PF 13/90 (1990), where there is not reparametrization invariance.
N. H. Christ andT. D. Lee:Phys. Rev. D,22 939 (1980).
R. Schmidt:Infinite Dimensional Hamiltonian Systems (Bibliopolis, Napoli, 1987).
E. J. Saletan andA. H. Cromer:Theoretical Mechanics (Wiley, New York, N.Y., 1971).
C. A. P. Galvão andL. J. Negri:J. Phys. A,16 4183 (1983).
E. T. Whittaker:A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Dover, New York, N.Y., 1936), 4th edition.
P. G. Bergmann andA. Komar:Int. J. Theor. Phys.,5 15 (1972).
I. A. Batalin andG. A. Vilkovisky:J. Math. Phys.,26 172 (1985).
L. Lusanna:J. Math. Phys.,31 428 (1990).
L. Lusanna:J. Math. Phys.,31 2126 (1990).
L. Lusanna: in preparation.
G. Marmo andL. Lusanna: in preparation.
C. Batlle, J. Gomis, J. M. Pons andN. Roman-Roy:J. Math. Phys.,27, 2953 (1986);Lett. Math. Phys.,13, 17 (1987);J. Phys. A,20, 5113 (1987);J. M. Pons:J. Phys. A,21, 2705 (1988);X. Gràcia andJ. M. Pons:Lett. Math. Phys.,17, 175 (1989);Ann. Phys. (N.Y.),187, 355 (1988);C. Batlle, J. Gomis, X. Gràcia andJ. M. Pons:J. Math. Phys.,30, 1345 (1989);J. Gomis, M. Henneaux andJ. M. Pons:Class. Q. Grav.,7 (1990);J. F. Carinena, C. Lopez andN. Roman-Roy:J. Geom. Phys.,4, 315 (1987);J. F. Carinena andC. Lopez:Lett. Math. Phys.,14, 203 (1987).
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Lusanna, L. The second noether theorem as the basis of the theory of singular Lagrangians and Hamiltonians constraints. Riv. Nuovo Cim. 14, 1–75 (1991). https://doi.org/10.1007/BF02810161
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DOI: https://doi.org/10.1007/BF02810161