Some Peculiarities of Newton-Hooke Space-Times

TL;DR

This paper explores unique features of Newton-Hooke space-times, focusing on quantum mechanics and anomalous cases, using Lagrangian formalism and path integral methods to clarify physical probabilities.

Contribution

It provides a detailed analysis of Newton-Hooke quantum mechanics and anomalous space-times, highlighting their peculiar properties and formalism-based insights.

Findings

Identification of extraordinary Newton-Hooke quantum mechanics

Discussion of anomalous Newton-Hooke space-times

Clarification of probability density in the path integral framework

Abstract

Newton-Hooke space-times are the non-relativistic limit of (anti-)de Sitter space-times. We investigate some peculiar facts about the Newton-Hooke space-times, among which the "extraordinary Newton-Hooke quantum mechanics" and the "anomalous Newton-Hooke space-times" are discussed in detail. Analysis on the Lagrangian/action formalism is performed in the discussion of the Newton-Hooke quantum mechanics, where the path integral point of view plays an important role, and the physically measurable density of probability is clarified.