Domain wall between the Dirac sea and the anti-Dirac sea

It was shown in work [1] that in the theory of gravity coupled with the Dirac field, each state |λ〉 has its own twin |λ; PT 〉, which is obtained by a discrete PT transformation. If in the state |λ〉 the Dirac sea is filled, then in the state |λ; PT 〉 there is an anti-Dirac filling. It is important that the energies of these states are the same. Therefore, there may be domains with different filling of the Dirac sea. Here we study an domain wall connecting two such neighboring domains.

The lack of vacuum polarization in quantum electrodynamics with spinors in fermion equations

In this paper, the versions of quantum electrodynamics (QED) with spinors in fermion equations are briefly examined. In the new variants of the theory, the concept of vacuum polarization is unnecessary. The new content of fermion vacuum (without the Dirac sea) in the examined versions of QED leads to new physical consequences, part of which can be tested experimentally in the future.

Octagon with finite bridge: free fermions and determinant identities

We continue the study of the octagon form factor which helps to evaluate a class of four-point correlation functions in $$ \mathcal{N} $$ N = 4 SYM theory. The octagon is characterised, besides the kinematical parameters, by a “bridge” of ℓ propagators connecting two nonadjacent operators. In this paper we construct an operator representation of the octagon with finite bridge as an expectation value in the Fock space of free complex fermions. The bridge ℓ appears as the level of filling of the Dirac sea. We obtain determinant identities relating octagons with different bridges, which we derive from the expression of the octagon in terms of discrete fermionic oscillators. The derivation is based on the existence of a previously conjectured similarity transformation, which we find here explicitly.

The Dirac Sea, T and C Symmetry Breaking, and the Spinor Vacuum of the Universe

We have developed a quantum field theory of spinors based on the algebra of canonical anticommutation relations (CAR algebra) of Grassmann densities in the momentum space. We have proven the existence of two spinor vacua. Operators C and T transform the normal vacuum into an alternative one, which leads to the breaking of the C and T symmetries. The CPT is the real structure operator; it preserves the normal vacuum. We have proven that, in the theory of the Dirac Sea, the formula for the charge conjugation operator must contain an additional generalized Dirac conjugation operator.

Light dark matter from inflaton decay

We propose a simple mechanism of light dark matter (DM) production from the decay of the oscillating inflaton condensation. If the reheating temperature after inflation is higher than the inflaton mass, which is of the same order of the momentum of the DM at the time of the production, the DM momentum can be suppressed compared to the temperature of the thermal plasma if the interaction of the DM is weak enough. Consequently, the DM can be cold enough to avoid the observational constraints on the warm DM, like the Lyman-α bound even if the DM mass is small. We study the bosonic and fermionic DM production from the inflaton decay, taking into account the effect of the stimulated emission and Pauli blocking, respectively. In both cases, the DM can be cold and abundant enough to be a viable candidate of the DM. We also apply our mechanism to the production of isocurvature-problem-free axion DM and Dirac sea DM of right-handed neutrino consistent the seesaw relation for the active neutrino masses.

Chiral Soliton Models and Nucleon Structure Functions

We outline and review the computations of polarized and unpolarized nucleon structure functions within the bosonized Nambu-Jona-Lasinio chiral soliton model. We focus on a consistent regularization prescription for the Dirac sea contribution and present numerical results from that formulation. We also reflect on previous calculations on quark distributions in chiral quark soliton models and attempt to put them into perspective.