Topic
Canonical transformation
About: Canonical transformation is a research topic. Over the lifetime, 1854 publications have been published within this topic receiving 38019 citations.
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TL;DR: In this article, the authors construct flexible and powerful canonical transformations as generative models using symplectic neural networks, which transforms physical variables towards a latent representation with an independent harmonic oscillator Hamiltonian.
Abstract: Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. We construct flexible and powerful canonical transformations as generative models using symplectic neural networks. The model transforms physical variables towards a latent representation with an independent harmonic oscillator Hamiltonian. Correspondingly, the phase space density of the physical system flows towards a factorized Gaussian distribution in the latent space. Since the canonical transformation preserves the Hamiltonian evolution, the model captures nonlinear collective modes in the learned latent representation. We present an efficient implementation of symplectic neural coordinate transformations and two ways to train the model. The variational free energy calculation is based on the analytical form of physical Hamiltonian. While the phase space density estimation only requires samples in the coordinate space for separable Hamiltonians. We demonstrate appealing features of neural canonical transformation using toy problems including two-dimensional ring potential and harmonic chain. Finally, we apply the approach to real-world problems such as identifying slow collective modes in alanine dipeptide and conceptual compression of the MNIST dataset.
15 citations
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TL;DR: In this article, Souriau's space fiber quantifiant is shown under certain conditions to be realized in contact structure, and illustrative examples of contact structures are examined, and different geometric concepts in canonical quantization are discussed.
Abstract: Differential geometric concepts in canonical quantization are discussed. Souriau'sespace fibre quantifiant is shown under certain conditions to be realized in contact structure. Illustrative examples of contact structures are examined.
15 citations
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TL;DR: In this paper, a new approach to the canonical transformation theory for presymplectic systems and the relativistic free massive point is presented, based on the extended formalism for the time-dependent systems.
Abstract: Two applications of the canonical-transformation theory for presymplectic systems developed in a previous paper are presented: a new approach to the extended formalism for the time-dependent systems and the relativistic free massive point. For this last system some examples of canonical transformations are constructed explicitly.
15 citations
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TL;DR: In this article, a canonical tranformation approach to the effective interaction between two holes, based on the three-band Hubbard model but ready to include extra interactions as well, was proposed.
14 citations
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TL;DR: The complex canonical transformation introduced by Ashtekar (1987) in general relativity is extended to simple supergravity by as discussed by the authors, which is a variant of the canonical transformation used in classical general relativity.
Abstract: The complex canonical transformation introduced by Ashtekar (1987) in general relativity is extended to simple supergravity.
14 citations