Negative energy sea

A detailed study of the Dirac equation and its solutions will not be required it will simply be assumed, as already indicated, that the S3rstem of N electrons above the negative-energy sea may be described using a wavefunction constructed from antisymraetrized products of (positive energy) spin-orbitals of type (29). It is, however, necessary to know the basic properties of the operators Q/i, which appear in the Dirac equation... 

Since the NJL model is not renormalizable, we need some regularization procedure to get a meaningful finite value for the vacuum contribution. Consider the sum of the negative energy over the Dirac sea,... 

The definition of the no-sea approximation for is not completely unambiguous. As discussed in Appendix B we define it through neglect of all vacuum fermion loops in the derivation of an approximate [/]. Alternatively, one could project out all negative energy states, thus generating a direct equivalent of the standard no-pair approximation. As one would expect the differences between these two schemes to be small, we do not differentiate between these approximations here. 

The relativistic mean meson field (R.MF) theory formulated by Teller and others [8, 9, 10] and by Walecka [11] is quite successful in both infinite nuclear matter and finite nuclei[12, 13, 14]. In the RMF model, only positive-energy baryonic states are considered to study the properties of ordinary nuclei. This is the so-called no-sea-approximation . However, an interesting feature of the RMF theory is the existence of bound negative-energy baryonic states. This happens because the interaction with the vector field generated by the baryon-... 

In a non-relativistic theory we would now continue by adding a second quantized operator for two-body interactions. In the relativistic case we need to step back and first consider the interpretation of the eigenvalues of the Hamiltonian. Dirac stated that positrons could be considered as holes in an infinite sea of electrons . In this interpretation the reference state for a system with neither positrons nor electrons is the state in which all negative energy levels are filled with electrons. This vacuum state... 

It looks like the redefinition or renormalization, as the procedure is usually called solves most of the problems associated with the Dirac sea of electrons formalism. One problem still remains, however. For any reasonable choice of one may unambiguously assign a spinor to either the positive or the negative energy subspace. Such an assignment is, however, not universally valid as can... 

As common in relativistic electronic structure theory, one invokes the so-called no-sea approximation where one neglects all vacuum contributions of the filled negative energy continuum [41]. The only remaining effect of the sea is the restriction for electrons to occupy only states of positive energy. Then the density is constructed from DKS one-electron orbitals of a single-determinant A-electron wave function ... 

When he was 26 years old, Dirac made the absurd assumption that what people call a vacuum is in reality a sea of electrons occupying the negative energy continuum (known as the Dirac electronic sea). The sea was supposed to consist of an infinite number of electrons, which had to imply catastrophic consequences concerning, for example, the infinite mass of the Universe, but Dirac did not feel any doubt about his notion. " We see only those electrons that have positive energy " said Dirac. Why he was so determined Well, Dirac s concept of the sea was proposed to convince us that due to the Pauli exclusion principle, the doubly occupied sea electronic states... 

None of the many fathers of the Fock-Klein-Gordon equation dared to take into account another possibility, the one with the negative square root in Eq. (3.40), a step made by Paul Dirac. In this case the Dirac s argument about the electron sea and the Pauli exclusion principle would not work, since we have to do with the bosons We would have an abyss of negative energies, a disaster for the theory. 

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