Abstract
The replacement of Newton’s equation by quantum mechanical wave equations in the 1920s implied that by that time all known fundamental degrees of freedom in physics were described by fields like A(x, t) or Ψ(x, t), and their dynamics was encoded in wave equations.
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Notes
- 1.
Please review Appendix A if you are not familiar with Lagrangian mechanics, or if you need a reminder.
- 2.
The unconventional behavior for the Schrödinger field can be traced back to how it arises from the Klein-Gordon or Dirac fields in the non-relativistic limit, see Chapter 21.
- 3.
E. Noether, Nachr. König. Ges. Wiss. Göttingen, Math.-phys. Klasse, 235 (1918), see also arXiv:physics/0503066.
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Dick, R. (2012). Principles of Lagrangian Field Theory. In: Advanced Quantum Mechanics. Graduate Texts in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8077-9_16
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DOI: https://doi.org/10.1007/978-1-4419-8077-9_16
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