In Dirac's hole theory the vacuum state is generally believed to be the state of minimum energy. However it has recently been shown that this is not the case. In [1] it was shown that energy can be extracted from the hole theory vacuum state through the application of an electric field so that the final state has less energy than the vacuum state. In this paper we will confirm the results of [1] by calculating the change in the energy of the vacuum state due to its interaction with a specific electric field. It will be shown that the final state has less energy than the original vacuum state.
Generalized Dirac equation containing vacuum-mass contribution is introduced. The vacuum-mass contribution arises due to the coupling of quantum mechanical matter field with the vacuum field. Vacuum stress energy tensor arises in the Scalar-Tensor Field equation (Extended Einstein's Field equation), implies a mass like corrections to the newly formulated Dirac equation. Apart from the inertial mass of the electron, generalized Dirac equation proposed here, contains a mass-term as a result of vacuum field coupling.
We compute the entanglement entropy of a free massive Dirac field between two causally disconnected open charts in de Sitter space. We first derive the Bunch-Davies vacuum mode functions of the Dirac field. We find there exists no supercurvature mode for the Dirac field. We then give the Bogoliubov transformation between the Bunch-Davies vacuum and the open chart vacua that makes the reduced density matrix diagonal. We find that the Dirac field becomes more entangled than a scalar field as $m^2/H^2$ becomes small, and the difference is maximal in the massless limit.
Nonperturbative vacuum polarization effects are explored for a supercritical Coulomb source with $Z>Z_{cr}$ in 1+1 D. Both the vacuum charge density $ρ_{vac}(x)$ and vacuum energy $E_{vac}$ are considered. It is shown that in the overcritical region the behavior of vacuum energy could be significantly different from perturbative quadratic growth up to decrease reaching large negative values.
We study the relations of the positive frequency mode functions of Dirac field in 4-dimensional Minkowski spacetime covered with Rindler and Kasner coordinates, and describe the explicit form of the Minkowski vacuum state with the quantum states in Kasner and Rindler regions, and analytically continue the solutions. As a result, we obtain the correspondence of the positive frequency mode functions in Kasner region and Rindler region in a unified manner which derives vacuum entanglement.
We study the vacuum polarization of planar charged Dirac fermions by a strong Coulomb potential. Induced vacuum charge density is calculated and analyzed at the subcritical and supercritical Coulomb potentials for massless and massive fermions. For the massless case the induced vacuum charge density is localized at the origin when the Coulomb center charge is subcritical while it has a power-law tail when the Coulomb center charge is supercritical. The finite mass contribution into the induced charge due to the vacuum polarization is small and insignificantly distorts the Coulomb potential onl…
A remarkable quantitative agreement is found between the non-Markovian quantum kinetic approach and the time-dependent Dirac equation approach for a large region of Keldysh parameter, in the investigation of electron-positron pair production in the electric fields which is spatially homogeneous and envelope pulse shaped. If a sub-critical bound potential is immersed in this background field, the TDDE results show that the creation probability will be enhanced by the bound states resonance by two orders of magnitude. We also establish a computing resources greatly saved TDDE formalism for spati…
Based on the original combination of analytical methods, computer algebra tools and numerical calculations, proposed recently in Refs. [1]-[3], the non-perturbative vacuum polarization effects in the 2+1 D supercritical Dirac-Coulomb system with $Z > Z_{cr,1}$ are explored. Both the vacuum charge density $ρ_{VP}(\vec{r})$ and vacuum energy $\mathcal{E}_{VP}$ are considered. The main result of the work is that in the overcritical region $\mathcal{E}_{VP}$ turns out to be a rapidly decreasing function $\sim - η_{eff}\, Z^3/R\, $ with $η_{eff}>0 $ and $R$ being the size of the external Coulomb so…
Non-perturbative vacuum polarization effects are explored for a supercritical Dirac-Coulomb system with $Z > Z_{cr,1}$ in 2+1 D, based on the original combination of analytical methods, computer algebra and numerical calculations, proposed recently in Refs. [1]-[3]. Both the vacuum charge density $ρ_{VP}(\vec{r})$ and vacuum energy $\mathcal{E}_{VP}$ are considered. Due to a lot of details of calculation the whole work is divided into two parts I and II. Taking account of results, obtained in the part I [4] for $ρ_{VP}$, in the present part II the evaluation of the vacuum energy $\mathcal{E}_{…
The effect of vacuum polarization of charged massive fermions in an Aharonov-Bohm (AB) potential in 2+1 dimensions is investigated. The causal Green's function of the Dirac equation with the AB potential is represented via the regular and irregular solutions of the two-dimensional radial Dirac equation. It is shown that the vacuum current density contains the contribution from free filled states of the negative energy continuum as well as that from a bound unfilled state, which can emerge in the above background due to the interaction of the fermion spin magnetic moment with the AB magnetic fi…
Some effects of vacuum polarization in QED due to the presence of field sources are investigated. We focus on effects with no counter-part in Maxwell electrodynamics. The the Uehling interaction energy between two stationary point-like charges is calculated exactly in terms of Meijer-G functions. Effects induced on a hydrogen atom by the vacuum polarization in the vicinity of a Dirac string are considered. We also calculate the interaction between two parallel Dirac strings and corrections to the energy levels of a quantum particle constrained to move on a ring circumventing a solenoid.
An explicit construction is given of field operators satisfying the free Dirac equation. The quantum expectation of these field operators forms a spinor which satisfies the original Dirac equation. The current operators are defined as pair correlation functions. Explicit expressions in terms of creation and annihilation operators are obtained. A small example shows that all relevant quantities are mathematically well-defined.
Study of spin states in vacuum pair production via the Dirac-Heisenberg-Wigner formalism
State Key Laboratory for Tunnel Engineering, China University of Mining and Technology（中国矿业大学隧道工程国家重点实验室）；School of Science, China University of Mining and Technology（中国矿业大学理学院）
In certain special circumstances, such as in the vicinity of a black hole or in a uniformly accelerating frame, vacuum fluctuations appear to give rise to a finite-temperature environment. This effect, currently without experimental confirmation, can be interpreted as a manifestation of quantum entanglement after tracing out vacuum modes in an unobserved region. In this work, we identify a class of experimentally accessible quantum systems where thermal density matrices emerge from vacuum entanglement. We show that reduced density matrices of lower-dimensional subsystems embedded in $D$-dimens…
Stochastic Theory of Relativistic Particles Moving in a Quantum Field: II. Scalar Abraham-Lorentz-Dirac-Langevin Equation, Radiation Reaction and Vacuum Fluctuations
Creation of charged fermion pair from a vacuum in the so-called supercritical Coulomb potential is examined for the case when created pair moves in one plane. In which case the quantum dynamics of charged massive or massless fermions can be described by the two-dimensional Dirac Hamiltonians with a Coulomb potential. These Hamiltonians are singular and require the additional definition in order for them to be treated as self-adjoint quantum-mechanical operators. We construct the self-adjoint two-dimensional Dirac Hamiltonians with a Coulomb potential and determine the quantum-mechanical states…
We analyze the simulation of Dirac neutrino oscillations using quantum walks, both in vacuum and in matter. We show that this simulation, in the continuum limit, reproduces a set of coupled Dirac equations that describe neutrino flavor oscillations, and we make use of this to establish a connection with neutrino phenomenology, thus allowing to fix the parameters of the simulation for a given neutrino experiment. We also analyze how matter effects for neutrino propagation can be simulated in the quantum walk. In this way, important features, such as the MSW effect, can be incorporated. Thus, th…
