Free Fields, Harmonic Oscillators, and Identical Bosons
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چکیده
A free quantum field and its canonical conjugate are equivalent to a family of harmonic oscillators (one oscillator for each plane wave), which is in turn equivalent to a quantum theory of free identical bosons. In this note, I will show how all of this works for the relativistic scalar field φ̂(x) and its conjugate π̂(x). And then I will turn around and show that a quantum theory of any kind of identical bosons is equivalent to a family of oscillators. (Harmonic for the free particles, non-harmonic if the particles interact with each other.) Moreover, for the non-relativistic particles, the oscillator family is in turn equivalent to a non-relativistic quantum field theory.
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Free Fields, Harmonic Oscillators, and Identical Bosons
A free quantum field and its canonical conjugate are equivalent to a family of harmonic oscillators (one oscillator for each plane wave), which is in turn equivalent to a quantum theory of free identical bosons. In this note, I will show how all of this works for the relativistic scalar field φ̂(x) and its conjugate π̂(x). And then I will turn around and show that a quantum theory of any kind of ...
متن کاملFree Fields, Harmonic Oscillators, and Identical Bosons
A free quantum field and its canonical conjugate are equivalent to a family of harmonic oscillators (one oscillator for each plane wave), which is in turn equivalent to a quantum theory of free identical bosons. In this note, I will show how all of this works for the relativistic scalar field φ̂(x) and its conjugate π̂(x). And then I will turn around and show that a quantum theory of any kind of ...
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