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Moyal quantization with compact symmetry groups and noncommutative harmonic analysis
(1990)
The phase-space approach to quantization of systems whose symmetry group is compact and semisimple is developed from two basic principles: covariance and traciality. This generalizes results and methods already implemented ...
Sums over paths adapted to quantum theory in phase space
(1986)
The concept of phase space plays a decisive role in the study of the transition from classical to quantum physics. This is particularly the case in areas such as nonlinear dynamics and chaos, geometric quantization and the ...
Stora's fine notion of divergent amplitudes
(2016-11)
Stora and coworkers refined the notion of divergent quantum amplitude, somewhat upsetting the standard power-counting recipe. This unexpectedly clears the way to new prototypes for free and interacting field theories of ...
The metaplectic representation and boson fields
(1991-12)
We construct explicitly the infinite-dimensional metaplectic representation and show how its use simplifies and rigorizes several questions in bosonic Quantum Field Theory. The representation permutes Gaussian elements in ...
Density functional theory on phase space
(2012)
Forty-five years after the point de départ [Hohenberg and Kohn, Phys. Rev. 1964, B864, 136] of density functional theory, its applications in chemistry and the study of electronic structures keep steadily growing. However, ...
From geometric quantization to Moyal quantization
(1995-06)
We show how the Moyal product of phase-space functions, and the Weyl correspondence between symbols and operator kernels, may be obtained directly using the procedures of geometric quantization, applied to the symplectic ...
The Wigner transformation is of finite order
(1987-05)
The Wigner integral transformation, which intertwines the twisted product and the composition of kernels, is of order 24. Indeed, it commutes with, and its sixth power equals, the Fourier cotransformation.
The Kirillov picture for the Wigner particle
(2018-06)
We discuss the Kirillov method for massless Wigner particles, usually (mis)named "continuous spin" or "infinite spin" particles. These appear in Wigner's classification of the unitary representations of the Poincaré group, ...
Algebras of distributions suitable for phase-space quantum mechanics. III. The dual space of the algebra L_b(S)
(1989-09)
The strong dual space of the topological algebra L_b(S), where S is
the Schwartz space of smooth declining functions on R, may be obtained
as an inductive limit of projective limits of Hilbert spaces. To that
end, we ...
The Moyal representation of quantum mechanics and special function theory
(1990-03)
It is shown that the phase-space formulation of quantum mechanics is a rich source of special function identities. The Moyal formalism is reviewed for two phase spaces: the real plane and the sphere; and this is used to ...