-
7
-
-
0003425132
-
-
Teubner, Leipzig, 1935, 1956; English transl. by Chelsea, New York
-
C. Caratheodory, Variationsrechnung und Partielle Differentialgleichungen erster Ordnung, Teubner, Leipzig, 1935, 1956; English transl. by Chelsea, New York, 1982.
-
(1982)
Variationsrechnung und Partielle Differentialgleichungen erster Ordnung
-
-
Caratheodory, C.1
-
8
-
-
0000233462
-
On the generalization of symplectic geometry to multiple integrals in the calculus of variations
-
Springer, Berlin and New York
-
P. Dedecker, On the generalization of symplectic geometry to multiple integrals in the calculus of variations, Lecture Notes in Math., Vol. 570, Springer, Berlin and New York, 1977.
-
(1977)
Lecture Notes in Math
, vol.570
-
-
Dedecker, P.1
-
9
-
-
0010137663
-
The invariance group for Hamiltonian systems of partial differential equations
-
D. G. B. Edelen, The invariance group for Hamiltonian systems of partial differential equations, Arch. Rational Mech. Anal. 5 (1961) 95-176.
-
(1961)
Arch. Rational Mech. Anal
, vol.5
, pp. 95-176
-
-
Edelen, D.G.B.1
-
11
-
-
84972538776
-
On the geometry of manifolds of maps
-
H. I. Eliasson, On the geometry of manifolds of maps, J. Differential Geometry 1 (1967) 169-197.
-
(1967)
J. Differential Geometry
, vol.1
, pp. 169-197
-
-
Eliasson, H.I.1
-
12
-
-
84911249749
-
Variational integrals in fibre bundles
-
Amer. Math. Soc., Providence RI
-
H. I. Eliasson, Variational integrals in fibre bundles, Proc. Sympos. Pure Math., Vol. 16, Amer. Math. Soc., Providence, RI, 1970, 67-89.
-
(1970)
Proc. Sympos. Pure Math
, vol.16
, pp. 67-89
-
-
Eliasson, H.I.1
-
13
-
-
0000094449
-
The Poincare-Cartan invariant in the calculus of variations
-
P. L. Garcia, The Poincare-Cartan invariant in the calculus of variations, Sympos. Math. 14 (1974) 219-246.
-
(1974)
Sympos. Math
, vol.14
, pp. 219-246
-
-
Garcia, P.L.1
-
14
-
-
84972496539
-
Gauge algebras, curvature and symplectic structure
-
P. L. Garcia, Gauge algebras, curvature and symplectic structure, J. Differential Geometry 12 (1977) 209-227.
-
(1977)
J. Differential Geometry
, vol.12
, pp. 209-227
-
-
Garcia, P.L.1
-
15
-
-
49349121570
-
Critical principal connections and gauge invariance
-
P. L. Garcia, Critical principal connections and gauge invariance, Rep. Math. Phys. 13 (1978) 337-344.
-
(1978)
Rep. Math. Phys
, vol.13
, pp. 337-344
-
-
Garcia, P.L.1
-
16
-
-
84911257612
-
Tangent structure of Yang-Mills equations and Hodge Theory
-
Springer, Berlin and New York
-
P. L. Garcia, Tangent structure of Yang-Mills equations and Hodge Theory, Lecture Notes in Math., vol. 775, Springer, Berlin and New York, 1980.
-
(1980)
Lecture Notes in Math
, vol.775
-
-
Garcia, P.L.1
-
17
-
-
26544443735
-
Symplectic approach to the theory of quantized fields
-
P. L. Garcia & A. Perez-Rendon, Symplectic approach to the theory of quantized fields. I, Comm. Math. Phys. 13 (1969) 24-44.
-
(1969)
I, Comm. Math. Phys
, vol.13
, pp. 24-44
-
-
Garcia, P.L.1
Perez-Rendon, A.2
-
18
-
-
0001009551
-
Symplectic approach to the theory of quantized fields
-
P. L. Garcia, Symplectic approach to the theory of quantized fields. II, Arch. Rational Mech. Anal. 43 (1971) 101-124.
-
(1971)
II, Arch. Rational Mech. Anal
, vol.43
, pp. 101-124
-
-
Garcia, P.L.1
-
19
-
-
24844474738
-
Reducibility of the symplectic structure of minimal interactions
-
Springer Berlin and New York
-
P. L. Garcia, Reducibility of the symplectic structure of minimal interactions, Lecture Notes in Math., Vol. 676, Springer, Berlin and New York, 1978, 409-433.
-
(1978)
Lecture Notes in Math
, vol.676
, pp. 409-433
-
-
Garcia, P.L.1
-
20
-
-
0000026189
-
Geometrization of the canonical formalism in the classical field theory
-
K. Gawedzski, Geometrization of the canonical formalism in the classical field theory, Rep. Math. Phys. 3 (1972) 307-326.
-
(1972)
Rep. Math. Phys
, vol.3
, pp. 307-326
-
-
Gawedzski, K.1
-
21
-
-
0010074486
-
Canonical formalism for the local-type functionals in the classical field theory
-
K. Gawedzski, Canonical formalism for the local-type functionals in the classical field theory, Rep. Math. Phys. 6 (1974) 465-476.
-
(1974)
Rep. Math. Phys
, vol.6
, pp. 465-476
-
-
Gawedzski, K.1
-
23
-
-
84972514538
-
Integrability criteria for systems of nonlinear partial differential equations
-
H. Goldschmidt, Integrability criteria for systems of nonlinear partial differential equations, J. Differential Geometry 1 (1967) 269-307.
-
(1967)
J. Differential Geometry
, vol.1
, pp. 269-307
-
-
Goldschmidt, H.1
-
24
-
-
0000082862
-
The Hamilton-Cartan formalism in the calculus of variations
-
(Grenoble)
-
H. Goldschmidt & S. Sternberg, The Hamilton-Cartan formalism in the calculus of variations, Ann. Inst. Fourier (Grenoble) 23 (1973) 203-267.
-
(1973)
Ann. Inst. Fourier
, vol.23
, pp. 203-267
-
-
Goldschmidt, H.1
Sternberg, S.2
-
26
-
-
0001837631
-
A finite-dimensional canonical formalism in the classical field theory
-
J. Kijowski, A finite-dimensional canonical formalism in the classical field theory, Comm. Math. Phys. 30 (1973) 99-128.
-
(1973)
Comm. Math. Phys
, vol.30
, pp. 99-128
-
-
Kijowski, J.1
-
27
-
-
0346854496
-
Multiphase spaces and gauge in the calculus of variations
-
J. Kijowski, Multiphase spaces and gauge in the calculus of variations, Bull. Acad. Polon Sci. Ser. Sci. Math. 22 (1974) 1219-1225.
-
(1974)
Bull. Acad. Polon Sci. Ser. Sci. Math
, vol.22
, pp. 1219-1225
-
-
Kijowski, J.1
-
28
-
-
0000247184
-
A canonical structure for classical field theories
-
J. Kijowski & W. Szyrba, A canonical structure for classical field theories, Comm. Math. Phys. 46 (1976) 83-206.
-
(1976)
Comm. Math. Phys
, vol.46
, pp. 83-206
-
-
Kijowski, J.1
Szyrba, W.2
-
29
-
-
0003347176
-
A symplectic framework for field theories
-
Springer, Berlin and New York
-
J. Kijowski & W. M. Tulczyjew, A symplectic framework for field theories, Lecture Notes in Math., Vol. 107, Springer, Berlin and New York, 1979.
-
(1979)
Lecture Notes in Math
, vol.107
-
-
Kijowski, J.1
Tulczyjew, W.M.2
-
30
-
-
0002535842
-
Quantization and unitary representations
-
Springer Berlin and New York
-
B. Konstant, Quantization and unitary representations, Lecture Notes in Math., Vol. 170, Springer, Berlin and New York, 1970, 87-209.
-
(1970)
Lecture Notes in Math
, vol.170
, pp. 87-209
-
-
Konstant, B.1
-
31
-
-
0000650888
-
Lagrange theory in fibered manifolds
-
D. Krupka, Lagrange theory in fibered manifolds, Rep. Math. Phys. 2 (1970) 121-133.
-
(1970)
Rep. Math. Phys
, vol.2
, pp. 121-133
-
-
Krupka, D.1
-
32
-
-
0016424320
-
A geometric theory of ordinary first order variational problems in fibered manifolds I: Critical sections
-
D. Krupka, A geometric theory of ordinary first order variational problems in fibered manifolds I: Critical sections, J. Math. Anal. Appl. 49 (1975) 180-206.
-
(1975)
J. Math. Anal. Appl
, vol.49
, pp. 180-206
-
-
Krupka, D.1
-
33
-
-
0000384732
-
Geometry of jet bundles and the structure of Lagrangian and Hamiltonian formalisms
-
Springer Berlin and New York
-
B. A. Kuperschmidt, Geometry of jet bundles and the structure of Lagrangian and Hamiltonian formalisms, Lecture Notes in Math., Vol. 775, Springer, Berlin and New York, 1980, 162-218.
-
(1980)
Lecture Notes in Math
, vol.775
, pp. 162-218
-
-
Kuperschmidt, B.A.1
-
35
-
-
49549151837
-
Reduction of symplectic manifolds with symmetry
-
J. E. Marsden & A. Weinstein, Reduction of symplectic manifolds with symmetry, Rep. Math. Phys. 5 (1974) 121-130.
-
(1974)
Rep. Math. Phys
, vol.5
, pp. 121-130
-
-
Marsden, J.E.1
Weinstein, A.2
-
36
-
-
34250908849
-
Mehrdimensionaler Hamiltonscher Formalisms
-
H. Marx, Mehrdimensionaler Hamiltonscher Formalisms, Z. Phys. 164 (1961) 129-738.
-
(1961)
Z. Phys
, vol.164
, pp. 129-738
-
-
Marx, H.1
-
37
-
-
84972525941
-
Symmetry groups and group invariant solutions of partial differential equations
-
P. J. Olver, Symmetry groups and group invariant solutions of partial differential equations, J. Differential Geometry 14 (1979) 497-542.
-
(1979)
J. Differential Geometry
, vol.14
, pp. 497-542
-
-
Olver, P.J.1
-
38
-
-
84971195219
-
On the Hamiltonian structure of evolution equations
-
P. J. Olver, On the Hamiltonian structure of evolution equations, Math. Proc. Cambridge Philos. Soc. 88 (1980) 71-88.
-
(1980)
Math. Proc. Cambridge Philos. Soc
, vol.88
, pp. 71-88
-
-
Olver, P.J.1
-
39
-
-
0011585389
-
Expression symplectique des problems variationnels
-
R. Ouzilou, Expression symplectique des problems variationnels, Sympos. Math. 14 (1972) 85-98.
-
(1972)
Sympos. Math
, vol.14
, pp. 85-98
-
-
Ouzilou, R.1
-
40
-
-
0003279657
-
A global formulation of the Lie theory of transformation groups
-
R. S. Palais, A global formulation of the Lie theory of transformation groups, Mem. Amer. Math. Soc. No. 2 (1957).
-
(1957)
Mem. Amer. Math. Soc
, Issue.2
-
-
Palais, R.S.1
-
43
-
-
84972522051
-
A minimal interaction principle for classical fields
-
A. Perez-Rendon, A minimal interaction principle for classical fields, Sympos. Math. 14 (1974) 293-321.
-
(1974)
Sympos. Math
, vol.14
, pp. 293-321
-
-
Perez-Rendon, A.1
-
44
-
-
84972498876
-
General relativity as a gauge theory
-
Berlin and New York Springer
-
A. Perez-Rendon, General relativity as a gauge theory, Lecture Notes in Math., Vol. 836, Springer, Berlin and New York, 1980, 440-454.
-
(1980)
Lecture Notes in Math
, vol.836
, pp. 440-454
-
-
Perez-Rendon, A.1
-
46
-
-
84972501863
-
Lagrangiennes dans les theories jauge par rapport au groupe de Poincare
-
(English summary) [Lagrangians in gauge theories in relation to the Poincare group].Torino
-
A. Perez-Rendon, Lagrangiennes dans les theories jauge par rapport au groupe de Poincare. (English summary) [Lagrangians in gauge theories in relation to the Poincare group] Rend. Sem. Mat. Univ. Politec. Torino 40 (1982), no. 3, (1984) 21-34.
-
(1984)
Rend. Sem. Mat. Univ. Politec
, vol.40
, Issue.3
, pp. 21-34
-
-
Perez-Rendon, A.1
-
49
-
-
34250952273
-
Über die Existenz Kanonischer Transformationen bei Mehrenen Unabhängigen Veränderlichen
-
H. Rüssman, Über die Existenz Kanonischer Transformationen bei Mehrenen Unabhängigen Veränderlichen, Arch. Rational Mech. Anal. 8 (1962) 353-357.
-
(1962)
Arch. Rational Mech. Anal
, vol.8
, pp. 353-357
-
-
Rüssman, H.1
-
50
-
-
84976001136
-
On the geometric structure of classical field theory in Lagrangian formulation
-
J. Śnìatycki, On the geometric structure of classical field theory in Lagrangian formulation, Proc. Cambridge Philos. Soc. 68 (1970) 466-484.
-
(1970)
Proc. Cambridge Philos. Soc
, vol.68
, pp. 466-484
-
-
Śnìatycki, J.1
-
52
-
-
0040610079
-
Some preliminary remark on the formal variational calculus of Gel'fand and Dikki
-
Springer Berlin and New York
-
S. Sternberg, Some preliminary remark on the formal variational calculus of Gel'fand and Dikki, Lecture Notes in Math., Vol. 676, Springer, Berlin and New York, 1978, 399-407.
-
(1978)
Lecture Notes in Math
, vol.676
, pp. 399-407
-
-
Sternberg, S.1
-
53
-
-
49449125898
-
A symplectic structure for the Einstein-Maxwell field
-
W. Szcyrba, A symplectic structure for the Einstein-Maxwell field, Rep. Math. Phys. 12 (1977) 169-191.
-
(1977)
Rep. Math. Phys
, vol.12
, pp. 169-191
-
-
Szcyrba, W.1
-
54
-
-
0001306167
-
Symmetries, conservation laws and variational principles
-
Springer, Berlin and New York
-
F. Takens, Symmetries, conservation laws and variational principles, Lecture Notes in Math., Vol. 597, Springer, Berlin and New York, 1977.
-
(1977)
Lecture Notes in Math
, vol.597
-
-
Takens, F.1
-
55
-
-
0004069538
-
Symplectic geometry and Fourier analysis
-
Brookline, MA
-
N. R. Wallach, Symplectic geometry and Fourier analysis, Math. Sci. Press, Brookline, MA, 1977.
-
(1977)
Math. Sci
-
-
Wallach, N.R.1
-
56
-
-
84972531238
-
The local structure of Poisson manifolds
-
A. Weinstein, The local structure of Poisson manifolds, J. Differential Geometry 18 (1983) 523-557.
-
(1983)
J. Differential Geometry
, vol.18
, pp. 523-557
-
-
Weinstein, A.1
|