{'fraction_non_alphanumeric': 0.021778584392014518, 'fraction_numerical': 0.0018148820326678765, 'mean_word_length': 5.2727272727272725, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Bundles of Quantum States

A brief introduction to Frölicher's notion of smoothness (F-smoothness) leads to a natural definition of a distributional bundle, that is a bundle whose fibers are distributional spaces constituted of generalised sections of 2-fibered classical bundles. Indeed the essential notions of finite-dimensional differential geometry can be seamlessly extended to such bundles. The case when the underlying classical bundle is a vector bundle over a mass-shell bundle yields the bundle of quantum states of a multi-particle system.