Is the 2nd quantization physically essential in the description of relativistic fermions obeying Dirac equation?(adsbygoogle = window.adsbygoogle || []).push({});

In the case of the non-relativistic Schrodinger equation, the 2nd quantization is only a matter of convenience and doesn't actually change any physics, for both bosons and fermions. (Interestingly, canonical quantization of the Schrodinger field gives the same result as choosing the occupation number basis and defining creation and annihilation operators appropriately.)

For the relativistic theories, the 2nd quantization has an essential physical meaning at least for bosons. Due to negative energy(or frequency) states, the vacuum isn't well-defined in the first place unless we quantize the field.

However, for relativistic fermions, it seems to me that the 2nd quantization is just a matter of convenience as it is for the non-relativistic particles. Dirac's hole theory looks just fine to me.

Is my opinion right? If not, what is the problem? Is it that the electromagnetic field can't be included properly in Dirac's hole theory, or that the hole theory gives wrong predictions? If so, can anyone explain the details?

Thanks in advance.

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# The necessity of the 2nd quantization?

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