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Adds the notion of fields to the
QuantumMechanicsframework. (Quantum mechanics and field theories are quite intertwined as per the current structure of the project. There shall be an effort put onto differentiating one from the other in the future; some kind of enum for selecting which theory to apply on the simulation, maybe?)This is crucial for emergence, which is the envisioned foundation of Deus.
An atlas$\mathcal{A} = \set{(U _\alpha, \varphi _\alpha) \mid \alpha \in I}$ is a set of pairs of charts $U _\alpha$ and their homeomorphism $\varphi _\alpha \colon U _\alpha \rightarrow V _\alpha$ , where $U _\alpha \subseteq M$ and $V _\alpha \subseteq \mathbb{R}^n$ . An $n$ -dimensional manifold $M$ is, then, a topological space whose distinct points have disjoint neighborhoods (that is: is a Hausdorff space); given a basis $B = \set{A_i} _{i \in \mathbb{N}}$ , where $U _\alpha = \bigcup\set{ A_i \in B \mid A_i \subseteq U _\alpha}$ , such space is also second-countable — $B$ contains open subsets of $M$ .