Classical mechanics is the limit ħ → 0 of quantum mechanics. Nonrelativistic (Newtonian) mechanics is the limit c → ∞ of special relativity. Here ħ is Planck’s constant and c is the speed of light. Quantum field theory is the combination of quantum mechanics with special relativity. It contains both parameters c and ħ, and it has two distinct degenerate limits: c → ∞ and ħ → 0. The classical limit of a quantum field (ħ → 0) actually gives rise to two distinct limits: a classical field limit and a classical particle limit, with choice between these two limits depending on the sequence of states in which the limit is taken. Only the second (particle) limit has the further nonrelativistic limit of classical particle mechanics.
KeywordsQuantum Mechanic Quantum Theory Dirac Equation Coulomb Potential Selfadjoint Operator
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- [Baym, 1969], [Kato, 1966], [Jauch and Rohrlich, 1976].Google Scholar