conduction electrons in an electrical conductor, called a Fermi sea, contains electrons with energies up to the chemical potential of the system. An unfilled state in the Fermi sea behaves like a positively charged electron, though it is referred to as a "hole" rather than a "positron". The negative charge of the Fermi sea is balanced by the positively charged ionic lattice of the material. In quantum field theory In quantum field theories such as quantum electrodynamics, the Dirac field is subject to a process of second quantization, which resolves some of the paradoxical features of the equation. Further discussion of Lorentz covariance of the Dirac equation The Dirac equation is Lorentz covariant. Articulating this helps illuminate not only the Dirac equation, but also the Majorana spinor and Elko spinor, which although closely related, have subtle and important differences. Understanding Lorentz covariance is simplified by keeping in mind the geometric character of the process. Let be a single, fixed point in the spacetime manifold. Its location can be expressed in multiple coordinate systems. In the physics literature, these are written as and , with the understanding that both and describe the same point , but in different local frames of reference (a frame of reference over a small extended patch of spacetime). One can imagine as having a fiber of different coordinate frames above it. In geometric terms, one says that spacetime can be characterized as a fiber bundle, and specifically, the frame bundle. The difference between two points and in the same fiber is a combination of rotations and Lorentz boosts. A choice of coordinate frame is a (local) section through that bundle. Coupled to the frame bundle is a second bundle, the spinor bundle. A section through the spinor bundle is just the particle field (the Dirac spinor, in the present case). Different points in the spinor fiber correspond to the same physical object (the fermion) but expressed in different Lorentz frames. Clearly, the frame bundle and the spinor bundle must be tied together in a consistent fashion to get consistent results; formally, one says that the spinor bundle is the associated bundle; it is associated to a principal bundle, which in the present case is the frame bundle. Differences between points on the fiber correspond to the symmetries of the system. The spinor bundle has two distinct generators of its symmetries: the total angular momentum and the