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No. 18 - Department of Mathematics
No. 18 - Department of Mathematics

... Despite the progress obtained, several fundamental questions are still left unanswered. First of all, a systematic way of taking into account the above-mentioned wrapping corrections has not yet been provided, due to their highly complicated nature [22]. Furthermore, no rigorous proof of integrabil ...
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... For example, if the basis states represent different levels of evidence for a hypothesis, then the Markov process produces a path consisting of a sequence of evidence states. Perhaps it is best to describe this assumption by way of a simple physical example known as the paradox of the recombined bea ...
fulltext - DiVA portal
fulltext - DiVA portal

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... enfolds in its real power only when we set free the action principle from these constraints, and allow the selection of the endpoint and of the maximal action as well. Liberating the action principle from its straitjacket one can expect to obtain a deeper insight and a broader picture of the most fu ...
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... Second, the fact that entropy always increases with time is counterbalanced by the fact that the volume of three-dimensional space is also always increasing. Thus the entropy may always be increasing, whereas the density of entropy (i.e. entropy per volume) can be the same in every cycle, and the cy ...
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How brains make decisions

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Canonical quantization

In physics, canonical quantization is a procedure for quantizing a classical theory, while attempting to preserve the formal structure, such as symmetries, of the classical theory, to the greatest extent possible.Historically, this was not quite Werner Heisenberg's route to obtaining quantum mechanics, but Paul Dirac introduced it in his 1926 doctoral thesis, the ""method of classical analogy"" for quantization, and detailed it in his classic text. The word canonical arises from the Hamiltonian approach to classical mechanics, in which a system's dynamics is generated via canonical Poisson brackets, a structure which is only partially preserved in canonical quantization.This method was further used in the context of quantum field theory by Paul Dirac, in his construction of quantum electrodynamics. In the field theory context, it is also called second quantization, in contrast to the semi-classical first quantization for single particles.
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