Abstract
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.
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References
Baym, G. (1969). Lectures on Quantum Mechanics, New York: Benjamin.
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© 1981 Springer-Verlag New York Inc.
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Glimm, J., Jaffe, A. (1981). Quantum Theory. In: Quantum Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0121-9_1
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DOI: https://doi.org/10.1007/978-1-4684-0121-9_1
Publisher Name: Springer, New York, NY
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