Related papers: The Dirac Sea for the Non-Separable Hilbert Spaces

We study the Fock quantization of a free Dirac field in 2+1-dimensional backgrounds which are conformally ultrastatic, with a time-dependent conformal factor. As it is typical for field theories, there is an infinite ambiguity in the Fock…

This article examines Hilbert spaces constructed from sets whose existence is incompatible with the Countable Axiom of Choice (CC). Our point of view is twofold: (1) We examine what can and cannot be said about Hilbert spaces and operators…

We use 1+1 dimensional large N Gross-Neveu models as a laboratory to derive microscopically effective Lagrangians for positive energy fermions only. When applied to baryons, the Euler-Lagrange equation for these effective theories assumes…

The Fock quantization of free fields propagating in cosmological backgrounds is in general not unambiguously defined due to the non-stationarity of the spacetime. For the case of a scalar field in cosmological scenarios it is known that the…

We construct the coherent states in the sense of Gilmore and Perelomov for the fermionic Fock space. Our treatment is from the outset adapted to the infinite-dimensional case. The fermionic Fock space becomes in this way a reproducing…

We extend to a non-Hermitian fermionic quantum field theory with PT symmetry our previous discussion of second quantization, discrete symmetry transformations, and inner products in a scalar field theory [arXiv:2006.06656]. For…

The tetrad gauge invariant theory of the free Dirac field in two special moving charts of the de Sitter spacetime is investigated pointing out the operators that commute with the Dirac one. These are the generators of the symmetry…

The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions under which a change of the coefficient fields…

Analyzing the constraint structure of electrodynamics, massive vector bosons, Dirac fermions and electrodynamics coupled to fermions, we show that Dirac quantization method leads to appropriate creation-annihilation algebra among the Forier…

A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…

We consider introducing the Dirac sea in a quantum cellular automata model of fermions in discrete spacetime which approximates the Dirac equation in the continuum limit. However, if we attempt to fill up the `negative' energy states, we…

A spinor theory on a space with linear Lie type noncommutativity among spatial coordinates is presented. The model is based on the Fourier space corresponding to spatial coordinates, as this Fourier space is commutative. When the group is…

We study a formal extension of the Dirac equation in the framework of a non-commutative two-sheeted space-time. It is shown that this approach naturally extends the classical Dirac theory by doubling the number of fermionic states, which…

This work is devoted to incorporating into QFT the notion that particles and hence the particle states should be localizable in space. It focuses on the case of the Dirac field in 1+1 dimensional flat spacetime, generalizing a recently…

The Dirac wave function in a curved spacetime is usually defined as a quadruplet of scalar fields. It can alternatively be defined as a four-vector field. We describe these two representations in a common geometrical framework and we prove…

In terms of the relational approach to space-time geometry and physical interactions, we show that the Dirac equation for a free fermion in the momentum representation can be obtained starting from a binary system of complex relations…

Using properties of the determinant line bundle for a family of elliptic boundary value problems, we explain how the Fock space functor defines an axiomatic quantum field theory which formally models the Fermionic path integral. The 'sewing…

In this survey article, we explain a few ideas behind the fermionic projector approach and summarize recent results which clarify the connection to quantum field theory. The fermionic projector is introduced, which describes the physical…

We summarize a recent work on the subject title. The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions…

The Dirac's formalism for constrained systems is applied to the analysis of time-dependent Hamiltonians in the extended phase space. We show that the Lewis invariant is a reparametrization invariant and we calculate the Feynman propagator…