Publications
by Eduard Prugovecki
|
It is with sorrow that we
report that Dr. Eduard Prugovecki passed away at his home in Lake
Chapala Mexico on October 13th
2003 |
NOTE: Some of the publications listed below are available at the SLAC-HEP
web site
Papers in Refereed
Journals
1. Multiplicative symmetries in axiomatic quantum field theory,
J. Math. Phys.
5, 442--455 (1964).
2. An axiomatic approach to the formalism of quantum mechanics,
Part I,
J. Math. Phys. 7,
1054--1069 (1966).
3. An axiomatic approach to the formalism of quantum mechanics,
Part II,
J. Math. Phys. 7,
1070--1096 (1966).
4. A formalism for generalized quantum mechanics,
J. Math. Phys. 7,
1680--1696 (1966).
5. A gauge-invariant model of quantum electrodynamics without
spinor fields,
Nuovo Cimento 45,
327--380 (1966).
6. A non-Hilbert-space formulation of quantum field theory,
J. Math. Phys. 7,
2l07--2120 (1966).
7. A theory of measurement of incompatible
observables in quantum mechanics,
Can. J. Phys. 45,
2173--2219 (1967).
8. Measure-theoretical description
of Klein-Gordon multiparticle states,
J. Math. Phys. 10,
933--945 (1969).
9. Topologies on generalized inner product spaces,
Can. J. Math.
21, 158--169 (1969).
10. Complete sets of observables,
Can. J. Phys. 47,
1083--1092 (1969).
11. Rigorous derivation of generalized Lippman-Schwinger equations
from time-dependent scattering theory,
Nuovo Cimento 63,
569--593 (1969).
12. (with E.B. Manoukian) On the existence of wave operators in
time-dependent potential scattering for long-range potentials,
Can. J. Phys. 49,
102--107 (1971).
13. On time-dependent scattering theory for long-range interactions,
Nuovo Cimento 4B,
106--123 (1971).
14. Integral representations of the wave and transition operators
in non-relativistic scattering theory,
Nuovo Cimento 4B,
124--134 (1971).
15. Riemann-Stieltjes integration of operator-valued functions
with respect to vector-valued function in Banach spaces,
SIAM J. Math. Anal.
3, 183--205 (1972).
16. (with E.B. Manoukian) Asymptotic behaviour of spin-momentum
distribution observables for Fermion fields with cut-off self-coupling,
Commun. Math. Phys.
24, 133--150 (1972).
17. (with E.B. Manoukian) Spin-momentum distribution observables
and asymptotic fields for fermion fields with cut-off self-interaction,
Nuovo Cimento 10B,
421--446 (1972).
18. Scattering theory in Fock space,
J. Math. Phys. 13,
969--976 (1972).
19. A postulational framework for theories of simultaneous measurement
of several observables,
Found. Phys. 3,
3--18 (1973).
20. Multichannel Stationary scattering theory in two-Hilbert space
formulation,
J. Math. Phys. 14,
957--962 (1973).
21. (with J. Zorbas) Modified Lippmann-Schwinger equations for
two-body scattering theory with long-range interactions,
J. Math. Phys. 14,
1397--1409 (1973).
22. The Bra and Ket formalism in extended Hilbert space,
J. Math. Phys.
14, 1410--1422 (1973).
23. (with J.Zorbas) Many-body modified Lippman-Schwinger equations
for Coulomb-like potentials,
Nucl. Phys. A213,
541--569 (1973).
24. (with A. Tip) On ergodic limits of normal states in quantum
statistical mechanics,
J. Math. Phys. 15,
275--282 (1974).
25. Fuzzy sets in the theory of measurement of incompatible observables,
Found. Phys. 4,
9--18 (1974).
26. On the T-matrix formula for multichannel Coulomb
scattering,
Phys. Lett. 49B,
305--307 (1974).
27. (with A. Tip) Scattering theory in a time-dependent external
field I: general theory,
J. Phys. A7,
572--585 (1974).
28 ( with A. Tip) Scattering theory in a time-dependent external
field II: applications,
J. Phys. A7,
585--596 (1974).
29. Eigenfunction expansions for stationary scattering theory in
spaces with negative norm,
Rep. Math. Phys. 7,
127--151(1975).
30. (with A. Tip) Semi-groups of rank-preserving transformers on
minimal norm ideals in B(H),
Comp. Math. 30,
113--136 (1975).
31. Measurement in quantum mechanics as a stochastic process on
spaces of fuzzy events,
Found. Phys. 5,
557--571 (1975).
32. (with A. Tip) On two-atom scattering in a quantized radiation
field,
J. Phys. A. Math. Gen.
9, 225--228 (1976).
33. (with D. Masson) An effective-potential approach to stationary
scattering theory for long-range potentials,
J. Math. Phys. 17,
297--302 (1976).
34. Probability measures on fuzzy events in phase space,
J. Math. Phys. 17,
517--522 (1976).
35. Quantum two-particle scattering in fuzzy phase space,
J. Math. Phys. 17,
1673--1681 (1976).
36. Localizability of relativistic particles in fuzzy phase space,
J. Phys. A. Math. Gen.
9, 1851--1859 (1976).
37. (with S.T. Ali) Systems of imprimitivity and representations
of quantum mechanics on fuzzy phase spaces,
J. Math. Phys. 18,
219--228 (1977).
38. On fuzzy spin spaces,
J. Phys. A. Math. Gen.
10, 543--549 (1977).
39. Information-theoretical aspects of quantum measurement,
Int. J. Theor. Phys.
16, 321--331 (1977).
40. (with S.T. Ali) Classical and quantum statistical mechanics
in a common Liouville space,
Physica 89A,
501--521 (1977).
41. (with S.T. Ali) Quantum statistical mechanics on stochastic
phase space,
Int. J. Theor. Phys.
16, 689--706 (1977).
42. Liouville dynamics for optimal phase-space representations of
quantum mechanics,
Ann. Phys. (N.Y.) 110,
102--121 (1978).
43. A unified treatment of dynamics and scattering in classical
and quantum statistical mechanics,
Physica 90A,
202--228 (1978).
44. A quantum-mechanical Boltzmann equation for one-particle Gamma-distribution
functions,
Physica 90A,
229--248 (1978).
45. Relativistic quantum kinematics on stochastic phase spaces for
massive particles,
J. Math. Phys. 19,
2260--2270 (1978).
46. Stochastic phase space kinematics of the photon,
J. Math. Phys. 19,
227l--2277 (1978).
47. Consistent formulation of relativistic dynamics for massive
spin-zero particles in external fields,
Phys. Rev. D18,
3655--3675 (1978).
48. Stochastic phase spaces and master Liouville spaces in statistical
mechanics,
Found. Phys. 9,
575--587 (1979).
49. Dirac dynamics on stochastic phase spaces for spin 1/2 particles,
Rep. Math. Phys. 17,
401--417 (1980).
50. Quantum action principle and functional integration over paths
in stochastic phase space,
Nuovo Cimento 61A,
85--118 (1981).
51. A self-consistent approach to quantum field theory for extended
particles,
Found. Phys. 11,
355--382 (1981).
52. General aspects of stochastic quantum field theory,
Found. Phys. 11,
501--527 (1981).
53. (with S.T. Ali and R. Gagnon) Conserved quantum probability
currents on stochastic phase space,
Can. J. Phys. 59,
807--811 (1981).
54. Stochastic quantization of geometrodynamic curved space-time,
Nuovo Cimento 62B,
17--30 (1981).
55. Quantum space-time operationally based on propagators for extended
test particles,
Hadronic J. 4,
1018--1104 (198l).
56. (with S.T. Ali) Self-consistent relativistic modelfor extended
spin 1/2 particles in external fields,
Nuovo Cimento 63A,
171--203 (1981).
57. Born's reciprocity principle in stochastic phase space,
Lett. Nuovo Cimento
32, 277--280 (1981).
58. Quantum spacetime excitons as eigenfunctions of relativistic
harmonic oscillators,
Lett. Nuovo Cimento
32, 481--484 (1981).
59. (with J.A. Brooke) Gauge and reciprocally invariant formulation
of relativistic canonical commutation relations on quantum spacetime,
Lett. Nuovo Cimento
33, 171--175 (1982).
60. Time-energy uncertainty and relativistic canonical commutation
relations in quantum spacetime,
Found. Phys. 12,
555--564 (1982).
61. Reciprocally invariant electrodynamics on quantum spacetime,
Nuovo Cimento 68B,
261--276 (1982).
62. (with J.A.Brooke and W.Guz) The reciprocity principle in stochastic
quantum mechanics,
Hadronic J. 5,
1717--1733 (1982).
63. Geometrization of quantum mechanics and the new interpretation
of the scalar product in Hilbert space,
Phys. Rev. Lett.
49, 1065--1068 (1982).
64. Finite charge and field renormalization in reciprocally invariant
quantum electrodynamics,
Lett. Nuovo Cimento
37, 501--504 (1983).
65. (with D. Greenwood) Stochastic microcausality in relativistic
quantum mechanics,
Found. Phys. 14,
883--906 (1984).
66. (with J. A. Brooke) Hadronic exciton states and propagaators
derived from reciprocy theory on quantum spacetime,
Nuovo Cimento 79A,
237--247 (1984).
67. The stochastic quantum mechanics approach to the unification
of relativity and quantum theory,
Found. Phys. 14,
1147--1162 (1984).
68. A fibre bundle formulation of quantum geometry,
Nuovo Cimento 89A,
105--125 (1985).
69. Foundational aspects of stochastic quantum mechanics and related
quantum geometrics,
Hadronic J. Suppl.
1, 518--549 (1985).
70. (with J. A. Brooke) Relativistic canonical commutation relation
and the geometrization of quantum mechanics,
Nuovo Cimento
89A, 126--148 (1985).
71. (with S. T. Ali) Mathematical problems of stochastic quantum
mechanics: harmonic analysis on phase space and quantum geometry,
Acta Appl. Math. 6,
1--18 (1986).
72. (with S. T. Ali) Extended harmonic
analysis of phase space representations for the Galilei group,
Acta Appl. Math. 6,
19--46 (1986).
73. (with S. T. Ali) Harmonic analysis and systems of covariance
for phase space representations of the Poincaré group,
Acta Appl. Math.
6, 47--62 (1986).
74. A Poincaré gauge-invariant formulation of general-relativistic
quantum geometry,
Nuovo Cimento A
97, 597--628 (1987).
75. Geometro-stochastic quantization of massive fields in curved
space-time,
Nuovo Cimento A
97, 837--878 (1987).
76. On Newton-Cartan quantum geometries,
Class. Quantum Grav.
4, 1659--1678 (1987).
77. On string-like excitons in the geometro-stochastic quantization
of gravity,
Nuovo Cimento A
100, 289--297 (1988).
78. Geometro-stochastic quantization of gauge fields in curved spacetime,
Nuovo Cimento A 100,
827--868 (1988).
79. Geometro-stochastic quantization of gravity, I,
Found. Phys. Lett.
2, 81--104 (1989).
80. Geometro-stochastic quantitation of gravity, II,
Found. Phys. Lett.
2, 163--190 (1989).
81. Generally covariant geometro-stochastic quantum gravity,
Nuovo Cimento A 102,
881--923 (1989).
82. (with S. Warlow) Foundational aspects of geometro-stochastic
quantization of Dirac fields in curved spacetime,
Found. Phys. Lett.
2, 409--423 (1989).
83. (with S. Warlow) Geometro-stochastic quantization and
parallel transport of fermion fields in curved spacetime,
Rep. Math Phys.
29, 105--130 (1989).
84. On geometro-stochastic theory of measurement and quantum geometry,
Found. Phys. Lett.
3, 409--423 (1990).
85. Geometro-stochastic locality in quantum spacetime and quantum
diffusions,
Found. Phys. 21,
93--124 (1991).
86. (with W. Drechsler) Geometro-stochastic quantization of a theory
of extended elementary objects,
Found. Phys. 21,
513--546 (1991).
87. Geometro-stochastic quantization,
Suppl Rend. Cir. Mat. Palermo
25, 133--139 (1991).
88. Geometrical phases and the informational completeness of quantum
frames,
Found. Phys. Lett.
4, 129--148 (1991).
89. Realism, positivism, instrumentalism, and quantum geometry,
Found. Phys. 22,
143--186 (1992).
90. Foundational problems in quantum gravity and quantum cosmology,
Found. Phys. 22,
755--806 (1992).
91. On foundational and geometric critical aspects of quantum electrodynamics,
Found. Phys. 24,
335--362 (1994).
92. On the general covariance and strong equivalence principles
in quantum general relativity,
Found. Phys. 24,
989--1076 (1994).
93. Quantum geometric field propagation in curved spacetime,
Class. Quantum Grav.
11, 1981--1994 (1994).
94. On quantum-geometric connections and propagators in curved spacetime,
Class. Quantum Grav.
13, 1007--1021 (1996).
95. On locality in quantum general
relativity and quantum gravity,
Found.
Phys. 26, 1645--1668 (1996)
Articles Published
in Conference Proceedings
1. Extended Hilbert Space formulation of Dirac's Bra and Ket formalism
and its application to abstract stationary scattering theory,
pp. 322--333 in Foundations
of Quantum Mechanics and Ordered Linear Spaces,
A. Hartkamper and H. Neumann,
eds. (Springer, Berlin and New York, 1974).
2. (with J. Zorbas) Stationary techniques for scattering in the
presence of long-range forces,
pp. 63--82 in Atomic Scattering
Theory --- Mathematical and Computational Aspects,
J. Nuttal, ed. (University
of Western Ontario Press, London, Ontario, 1978).
3. (with S.T. Ali) Phase space representations of the Poincaré
group and their applications to relativistic particle dynamics
in Proc. of the Integrative
Conference on GroupTheory and Math. Physics,
Austin, Texas 1978 (Springer,
Berlin, 1979).
4. (with S.T. Ali) Consistent models of spin 0 and 1/2 extended
particles scattering in external fields,
pp. 197--203 in Mathematical
Methods and Applications of Scattering Theory,
J.A. DeSanto, A.W. Saenz and
W.W. Zachary, eds. (Springer, Berlin, 1980).
5. Quantum geometry and the EPR Gedanken experiment,
pp. 525--539 in Symposium
on the Foundations of Modern Physics,
P. Lahti and P. Mittelstaedt
eds. (World Scientific, Singapore, 1985).
6. Geometro-stochastic quantization and quantum geometry,
pp. 365--372 in Lectures
in Physics, vol 382,
V.V. Dodonov and V.I. Manko,
eds. (Springer, Berlin, 1991).
7. Foundational aspects of geometro-stochastic quantum general relativity,
pp. 317--325 in The
Interpretation of Quantum Theory: Where Do We Stand?
L. Accardi, ed. (Encyclopedia
Italiana, Rome, 1994).
8. Geometro-stochastic quantization and quantum geometry,
pp. 87-102 in Quantization,
Coherent States, and Complex Structures,
J.-P. Antoine, S.T. Ali, W.
Lisiecki, I.M. Mladenov and A Odzijewicz, eds.
(Plenum, London, 1995).
9. Quantum geometry and gravity,
pp. 278- 302 in Quantum
Gravity: International School of Cosmology and
Gravitation XIV Course, Erice Italy 11 - 19 May, 1995,
P.G. Bergmann, V. de Sabbata
and H.-J. Treder, eds. (World Scientific, Singapore,
and London, 1996).
Scientific
Monographs
1. Quantum Mechanics in
Hilbert Space
in the Pure and Applied Mathematics
Series,
Eds. S. Eilenberg and H. Bass,
Academic Press, New York and London,
1st edition 1971; 2nd edition
1981, 685 pp.
2. Stochastic Quantum Mechanics and Quantum Spacetime:
A consistent unification
of relativity and quantum theory based on stochastic spaces
in the Fundamental Theory
of Physics Series, ed. A. van der Merwe, Reidel, Dordrecht
1st printing
1984, revised printing, 1986, 302 pp.
3. Quantum Geometry: A Framework for Quantum General Relativity
in the Fundamental Theories
of Physics Series, ed. A. van der Merwe,
Kluwer, Dordrecht, 1992, 526 pp.
4. Principles of Quantum General Relativity
World Scientific, Singapore
and London, 1995, 373 pp.
Futuristic
Novels
1. Memoirs
of the Future: A Futuristic Novel
Cross Cultural Publications,
Notre Dame, 2001, 483 pp.
2. Dawn
of the New Man: A Futuristic Novel
of Social Change
Xlibris,
Philadelphia, 2002, 506 pp.