Since the aim of the first part of this book is to discuss classical mechanics from the symplectic point of view, some readers might be a little surprised by the title of the present chapter because it has a certain quantum-mechanical connotation. In fact “uncertainty principles” are mostly studied within the realm of quantum mechanics, even if the study of uncertainties is also a part of classical statistical mechanics. However, as we have shown in our paper , the formalism of the uncertainty principle is actually not as “quantum” as it may seem, but appears in classical mechanics if one uses the notion of symplectic capacity.
KeywordsCovariance Matrix Uncertainty Principle Hermitian Matrix Classical Statistical Mechanic Fourier Inversion Formula
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