-
1
-
-
33745040449
-
On the principles of elementary quantum mechanics
-
H. J. Groenewold, "On the principles of elementary quantum mechanics," Physica (Amsterdam) 12, 405-460 (1946).
-
(1946)
Physica (Amsterdam)
, vol.12
, pp. 405-460
-
-
Groenewold, H.J.1
-
2
-
-
0002061573
-
Sur certaines représentations unitaires d'un groupe infini de transformations
-
L. van Hove, "Sur certaines représentations unitaires d'un groupe infini de transformations," Proc. R. Acad. Sci. Belgium 26, 1-102 (1951).
-
(1951)
Proc. R. Acad. Sci. Belgium
, vol.26
, pp. 1-102
-
-
Van Hove, L.1
-
3
-
-
0000665694
-
Obstruction results in quantization theory
-
M. J. Gotay, H. Grundling, and G. M. Tuynman, "Obstruction results in quantization theory," J. Nonlinear Sci. 6, 469-498 (1996).
-
(1996)
J. Nonlinear Sci.
, vol.6
, pp. 469-498
-
-
Gotay, M.J.1
Grundling, H.2
Tuynman, G.M.3
-
4
-
-
0004282301
-
-
Benjamin-Cummings, Reading, MA, 2nd ed.
-
R. Abraham and J. E. Marsden, Foundations of Mechanics (Benjamin-Cummings, Reading, MA, 1978), 2nd ed.
-
(1978)
Foundations of Mechanics
-
-
Abraham, R.1
Marsden, J.E.2
-
5
-
-
0002608022
-
Obstructions to quantization
-
edited by J. E. Marsden and S. Wiggins Springer, New York, in press
-
M. J. Gotay, "Obstructions to quantization," in The Juan Simo Memorial Volume, edited by J. E. Marsden and S. Wiggins (Springer, New York, 1999) (in press).
-
(1999)
The Juan Simo Memorial Volume
-
-
Gotay, M.J.1
-
6
-
-
0000124459
-
Separate and joint analyticity in Lie groups representations
-
M. Flato and J. Simon, "Separate and joint analyticity in Lie groups representations," J. Funct. Anal. 13, 268-276 (1973).
-
(1973)
J. Funct. Anal.
, vol.13
, pp. 268-276
-
-
Flato, M.1
Simon, J.2
-
7
-
-
0004057551
-
-
Academic, New York, Sec. VIII.5
-
M. Reed and B. Simon, Functional Analysis I, II (Academic, New York, 1972, 1975), Sec. VIII.5.
-
(1972)
Functional Analysis I, II
-
-
Reed, M.1
Simon, B.2
-
8
-
-
85033970634
-
-
note
-
See Ref. 6, Cor. 1.
-
-
-
-
9
-
-
0001015478
-
Mathematical obstructions to quantization
-
P. R. Chernoff, "Mathematical obstructions to quantization," Hadronic J. 4, 879-898 (1981).
-
(1981)
Hadronic J.
, vol.4
, pp. 879-898
-
-
Chernoff, P.R.1
-
10
-
-
0003332429
-
Harmonic Analysis in Phase Space
-
Princeton University Press, Princeton, NJ
-
G. B. Folland, Harmonic Analysis in Phase Space, Ann. Math. Ser. Vol. 122 (Princeton University Press, Princeton, NJ, 1989).
-
(1989)
Ann. Math. Ser.
, vol.122
-
-
Folland, G.B.1
-
11
-
-
0002892921
-
Functorial geometric quantization and Van Hove's theorem
-
M. J. Gotay, "Functorial geometric quantization and Van Hove's theorem," Int. J. Theor. Phys. 19, 139-161 (1980).
-
(1980)
Int. J. Theor. Phys.
, vol.19
, pp. 139-161
-
-
Gotay, M.J.1
-
14
-
-
85033968437
-
-
note
-
See Ref. 10, Prop. 4.49.
-
-
-
-
15
-
-
85033953670
-
-
note
-
This representation actually drops to the double cover of HSp(2n,R), but we do not need this fact here.
-
-
-
-
16
-
-
85033943947
-
-
note
-
See Ref. 10, Prop. 4.58.
-
-
-
-
17
-
-
85033957046
-
-
note
-
See Ref. 13, Sec. 16.
-
-
-
-
18
-
-
85033956001
-
-
note
-
Recall that two e.s.a. operators strongly commute iff their spectral resolutions commute, cf. Sec. VIII.5 of Ref. 7. Two operators A, B weakly commute on a domain D if they commute in the ordinary sense, i.e., [A,B] is defined on D and vanishes.
-
-
-
-
19
-
-
0003272801
-
Introduction to the representation theory of compact and locally compact groups
-
Cambridge University Press, Cambridge
-
A. Robert, Introduction to the Representation Theory of Compact and Locally Compact Groups, London Math. Soc. Lect. Note Ser. Vol. 80 (Cambridge University Press, Cambridge, 1983).
-
(1983)
London Math. Soc. Lect. Note Ser.
, vol.80
-
-
Robert, A.1
-
20
-
-
85033957524
-
-
private communication
-
M. Dubois-Violette (private communication, 1998).
-
(1998)
-
-
Dubois-Violette, M.1
-
21
-
-
0000786864
-
Algebraic difficulties of preserving dynamical relations when forming quantum-mechanical operators
-
R. Arens and D. Babbit, "Algebraic difficulties of preserving dynamical relations when forming quantum-mechanical operators," J. Math. Phys. 6, 1071-1075 (1965).
-
(1965)
J. Math. Phys.
, vol.6
, pp. 1071-1075
-
-
Arens, R.1
Babbit, D.2
-
22
-
-
0001393178
-
Derivations of Lie brackets and canonical quantization
-
A. Joseph, "Derivations of Lie brackets and canonical quantization," Commun. Math. Phys. 17, 210-232 (1970).
-
(1970)
Commun. Math. Phys.
, vol.17
, pp. 210-232
-
-
Joseph, A.1
-
23
-
-
0002620976
-
Quantum kinematics on smooth manifolds
-
edited by S. I. Andersson and H.-D. Doebner, Lect. Notes Math.
-
B. Angermann, H.-D. Doebner, and J. Tolar, "Quantum kinematics on smooth manifolds," in Nonlinear Partial Differential Operators and Quantization Procedures, edited by S. I. Andersson and H.-D. Doebner, Lect. Notes Math. 1087, 171-208 (1983).
-
(1983)
Nonlinear Partial Differential Operators and Quantization Procedures
, vol.1087
, pp. 171-208
-
-
Angermann, B.1
Doebner, H.-D.2
Tolar, J.3
-
24
-
-
85033971770
-
Nonlinear Schrödinger equations and Hamiltonian dynamics
-
edited by H.-D. Doebner, V. K. Dobrev, and P. Nattermann World Scientific, Singapore
-
B. Hennig, "Nonlinear Schrödinger equations and Hamiltonian dynamics," in Nonlinear, Deformed, and Irreversible Quantum Systems, edited by H.-D. Doebner, V. K. Dobrev, and P. Nattermann (World Scientific, Singapore, 1995), pp. 155-165.
-
(1995)
Nonlinear, Deformed, and Irreversible Quantum Systems
, pp. 155-165
-
-
Hennig, B.1
-
27
-
-
0002456709
-
On a full quantization of the torus
-
edited by J.-P. Antoine et al. Plenum, New York
-
M. J. Gotay, "On a full quantization of the torus," in Quantization, Coherent States and Complex Structures, edited by J.-P. Antoine et al. (Plenum, New York, 1995), pp. 55-62.
-
(1995)
Quantization, Coherent States and Complex Structures
, pp. 55-62
-
-
Gotay, M.J.1
-
30
-
-
85033957245
-
Nonexistence of finite-dimensional quantizations of a noncompact symplectic manifold
-
edited by J. Slovák and O. Kowalski Masaryk University, Brno, Czech Republic, in press
-
M. J. Gotay and H. Grundling, "Nonexistence of finite-dimensional quantizations of a noncompact symplectic manifold," in Differential Geometry and Its Applications 1998, edited by J. Slovák and O. Kowalski (Masaryk University, Brno, Czech Republic, 1999) (in press).
-
(1999)
Differential Geometry and Its Applications 1998
-
-
Gotay, M.J.1
Grundling, H.2
|