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This monograph contains a functional analytic introduction to Dirac's formalism. The first part presents some new mathematical notions in the setting of triples of Hilbert spaces, mentioning the concept of Dirac basis. The second part introduces a conceptually new theory of generalized functions, integrating the notions of the first part.The last part of the book is devoted to a mathematical interpretation of the main features of Dirac's formalism. It involves a pairing between distributional bras and kets, continuum expansions and continuum matrices.

Quantum theory. --- Dirac, P. A. M. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Dirac, Paul Adrien Maurice, --- Dirac, Paul A. M. --- Dirak, Polʹ, --- Quantum theory

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J.E. Moyal has been pronounced 'one of Australia's most remarkable thinkers'. Yet, he was, essentially, a scientific maverick. Educated in a modest high school in Tel Aviv, he took himself to France to train as an engineer, statistician and mathematician and escaped to England as France fell. It was from outside academia that he entered into communication with the 'high priest' of British theoretical physics, P.A.M. Dirac, challenging him with the idea of a statistical basis of quantum mechanics. Their correspondence forms the core of this book and opens up an important and hitherto unknown chapter for physicists, mathematicians and historians of science. Moyal's classic paper, 'A statistical basis for quantum mechanics', also reproduced here in full, has come to underlie an explosion of research and to underpin an array of major technological developments. Joe Moyal emerges in this small biography as a witty and intrepid character, a scuba diver and wine connoisseur, a generous teacher and researcher, and a man whose academic life-spanning France, Ireland, Britain, the USA and Australia-intersected with some of the leading scientists of the 20th century.

Mathematicians --- Aerospace engineers --- Quantum theory --- Mathematics. --- Moyal, J. E. --- Dirac, P. A. M. --- Engineers --- Scientists --- Dirac, Paul Adrien Maurice, --- Dirac, Paul A. M. --- Dirak, Polʹ, --- Moyal, José Enrique, --- Moyal, Jo, --- Moyal, Joe,

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This monograph contains a functional analytic introduction to Dirac's formalism. The first part presents some new mathematical notions in the setting of triples of Hilbert spaces, mentioning the concept of Dirac basis. The second part introduces a conceptually new theory of generalized functions, integrating the notions of the first part. The last part of the book is devoted to a mathematical interpretation of the main features of Dirac's formalism. It involves a pairing between distributional bras and kets, continuum expansions and continuum matrices.

Quantum theory. --- Théorie quantique --- Dirac, P. A. M. --- Quantum theory --- Dirac, P A M --- 517.98 --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Functional analysis and operator theory --- 517.98 Functional analysis and operator theory --- Dirac, Paul Adrien Maurice, --- Dirac, Paul A. M. --- Dirak, Polʹ, --- Dirac, P A M - (Paul Adrien Maurice), - 1902-1984

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Quantum theory --- Théorie quantique --- History --- Histoire --- -Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Matrix mechanics. --- Physicists --- History. --- Planck, Max, --- Einstein, Albert, --- Bohr, Niels Henrik David, --- Sommerfeld, Arnold, --- Schrödinger, Erwin, --- -History --- Matrix mechanics --- -Quantum theory --- -Biography --- Dirac, Paul Adrien Maurice --- Quantum statistics --- Wave mechanics --- Physical scientists --- Biography --- Dirac, P. A. M. --- Dirac, Paul Adrien Maurice, --- Dirac, Paul A. M. --- Dirak, Polʹ, --- Quantum theory - - Collected works - History --- Quanta, theorie des --- -Physicists

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Physicists --- Quantum electrodynamics --- Quantum theory --- Space and time --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Space of more than three dimensions --- Space-time --- Space-time continuum --- Space-times --- Spacetime --- Time and space --- Fourth dimension --- Infinite --- Metaphysics --- Philosophy --- Space sciences --- Time --- Beginning --- Hyperspace --- Relativity (Physics) --- Electrodynamics, Quantum --- QED (Physics) --- Quantum field theory --- Schwinger action principle --- Broglie, Louis de, --- Dirac, P. A. M. --- Wigner, Eugene Paul, --- Dirac, Paul Adrien Maurice, --- Dirac, Paul A. M. --- Dirak, Polʹ, --- Broglie, Louis, --- De Broglie, Louis, --- Broĭlʹ, Lui de --- De Broĭlʹ, Lui --- Theory of relativity. Unified field theory --- Broglie, Louis de --- de Broglie --- de Broglie, Louis Victor --- de Broglie, Louis Victor Pierre Raymond --- de Broglie, Louis --- Quantum electrodynamics. --- Quantum theory. --- Space and time.