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Quantum Mechanics with Basic Field Theory by Bipin R. Desai

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37 Multiparticle systems and second quantization

The quantum mechanics of single particles is extended to multiparticle systems and singleparticle operators are defined in terms of this multiparticle space. Creation and destruction operators are incorporated with commutation relations that correspond to whether the particles are fermions or bosons. These operators are much like the raising and lowering operators for the harmonic oscillator which allow one to add or subtract the number of particles in a multiparticle state. We use this path to introduce second quantization. We then write Klein- Gordon, Dirac, and Maxwell fields in second quantization and define the negative-energy solutions as corresponding to positive-energy antiparticles. The ...

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