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- W4384520143 abstract "In theoretical and mathematical physics, we are often interested in the transition from the classical to the quantum picture of mechanics. In the classical setting, we usually consider space-time, formed by some Euclidean space $$mathbb {R}^n$$ of dimension n, and consider a state of a mass particle moving in space-time as an element of the phase space, i.e., an element of Euclidean space $$mathbb {R}^{2n}$$ of dimension 2n, hence twice the dimension we started with. The first n entries are the position coordinates $$x_1,ldots ,x_n$$ in space and the other n entries represent the momentum coordinates $$p_1,ldots ,p_n$$ associated with each position coordinate $$x_i$$ for all $$i=1,ldots , n$$ . Observables are given by smooth functions f on the phase space, i.e., $$fin C^infty (mathbb {R}^{2n})$$ . By time-evolution, each position and momentum coordinate of the considered mass particle changes and thus everything depends on the time t. So, in fact, we have $$(x_1(t),ldots ,x_n(t),p_1(t),ldots ,p_n(t))$$ ." @default.
- W4384520143 created "2023-07-18" @default.
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- W4384520143 date "2023-01-01" @default.
- W4384520143 modified "2023-09-27" @default.
- W4384520143 title "Introduction" @default.
- W4384520143 doi "https://doi.org/10.1007/978-981-99-3530-7_1" @default.
- W4384520143 hasPublicationYear "2023" @default.
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