Stability and decay of the Dirac vacuum in external gauge fields

2003

With the aid of a Fermi-Walker chart associated with an orthonormal frame attached to a time-like curve in spacetime, a discussion is given of relativistic balance laws that may be used to construct models of massive particles with spin, electric charge and a magnetic moment, interacting with background electromagnetic fields and gravitation described by non-Riemannian geometries. A natural generalisation to relativistic Cosserat media is immediate.

The geometric properties of General Relativity are reconsidered as a particular nonlin- ear interaction of fields on a flat background where the perceived geometry and coordi- nates are “physical” entities that are interpolated by a patchwork of observable bodies with a nonintuitive relationship to the underlying fields. This more general notion of gauge in physics opens an important door to put all fields on a similar standing but requires a careful reconsideration of tensors in physics and the conventional wisdom surrounding them. The meaning of the flat background and the induced conserved quantities are discussed and contrasted with the “observable” positive definite energy and probability density in terms of the induced physical coordinates. In this context, the Dirac matrices are promoted to dynamic proto-gravity fields and the keeper of “phys- ical metric” information. Independent sister fields to the wavefunctions are utilized in a bilinear rather than a quadratic lagrangian in these fields. This construction greatly enlarges the gauge group so that now proving causal evolution, relative to the physical metric, for the gauge invariant functions of the fields requires both the stress-energy conservation and probability current conservation laws. Through a Higgs-like coupling term the proto-gravity fields generate a well defined physical metric structure and gives the usual distinguishing of gravity from electromagnetism at low energies relative to the Higgs-like coupling. The flat background induces a full set of conservation laws but results in the need to distinguish these quantities from those observed by recording devices and observers constructed from the fields.

viXra, 2009

Einstein's equivalence principle implies that Newton's gravity force has no local objective meaning. It is an inertial force, i.e. a contingent artifact of the covariantly tensor accelerating (non-zero g's) Local Non-Inertial Frame (LNIF i) detector. ii Indeed, Newton's gravity force disappears in a locally coincident non-accelerating (zero g) Local Inertial Frame (LIF iii). The presence or absence of tensor spacetime curvature is completely irrelevant to this fact. In the case of an extended test body, these remarks apply only to the Center of Mass (COM). Stresses across separated parts of the test body caused by the local objective tensor curvature are a logically independent separate issue. Garbling this distinction has generated not-even-wrong critiques of the equivalence principle among "philosophers of physics" and even among some venerable confused theoretical physicists. Non-standard terms coupling the spin-connection to the commutator of the Dirac matrices and to the Lorentz group Lie algebra generators are conjectured.

Physical Review D, 2009

We consider the behavior of massive Dirac fields on the background of a charged de Sitter black hole. All black hole geometries are taken into account, including the Reissner-Nordström-de Sitter one, the Nariai case, and the ultracold case. Our focus is at first on the existence of bound quantum mechanical states for the Dirac Hamiltonian on the given backgrounds. In this respect, we show that in all cases no bound state is allowed, which amounts also to the nonexistence of normalizable time-periodic solutions of the Dirac equation. This quantum result is in contrast to classical physics, and it is shown to hold true even for extremal cases. Furthermore, we shift our attention on the very interesting problem of the quantum discharge of the black holes. Following the Damour-Deruelle-Ruffini approach, we show that the existence of level crossing between positive and negative continuous energy states is a signal of the quantum instability leading to the discharge of the black hole, and in the cases of the Nariai geometry and of the ultracold geometries we also calculate in WKB approximation the transmission coefficient related to the discharge process.

General Relativity and Gravitation

We aim to give a mathematical and historical introduction to the 1932 paper "Dirac equation in the gravitational field I" by Erwin Schrödinger on the generalization of the Dirac equation to a curved spacetime and also to discuss the influence this paper had on subsequent work. The paper is of interest as the first place that the well-known formula g μν ∇ μ ∇ ν + m 2 + R/4 was obtained for the 'square' of the Dirac operator in curved spacetime. This formula is known by a number of names and we explain why we favour the name 'Schrödinger-Lichnerowicz formula'. We also aim to explain how the modern notion of 'spin connection' emerged from a debate in the physics journals in the period 1929-1933. We discuss the key contributions of Weyl, Fock and Cartan and explain how and why they were partly in conflict with the approaches of Schrödinger and several other authors. We reference and comment on some previous historical accounts of this topic.

Theoretical and Mathematical Physics, 2009

The authors dedicate this article to one of the mathematical and physical giants of the XX-th centuryacademician Prof. Nikolai N. Bogolubov in memory of his 100th Birthday with great appreciation to his brilliant talent and impressive impact to modern nonlinear mathematics and quantum physics

arXiv (Cornell University), 2023

2019

To a gravitating ball we want to associate a Dirac particle in the Minkows-ki spacetime but having all the information of the original spacetime in the wave function of the particle. Hope is that something nontrivial will come out to relate the mass generation by Higgs mechanism to the ADM mass. Investigation in this matter was due actually long time ago: soon after the proof of the positive mass theorem if not towards the end of 70s. It is neither desirable nor necessary to obtain a solution of the exact Dirac equation and our particle does not satisfy it exactly in the setting of quantum electrody-namics. The physical Dirac equation has interaction terms in it and to get benefit from it at present we have to use Higgs mechanism. Dirac spinor we are associating with the spacetime has an imaginary magnetic field when the particle is at rest. It is therefore not strictly an U(1) theory. In future we shall try to incorporate more complicated groups hoping to explain away the imaginary part as a component of a non-electromagnetic gauge potential. We also search for a particle event, decay or interaction, that can be potentially easy to explain according to the Gravity is All philosophy. Salam-Weinberg theory is very complicated involving too many particles. In these notes we collect the materials in one place for the benefit of potential researchers and students who are interested in the Gravity is All project and who are appreciative for the need of a multi-discipline preparation and collaboration for settling the questions on unification. The notes have also the purpose of justifying further the Step I described in the first report posted for the Gravity is All project. Easier staffs in the beginning are for the prerequisite of interdisciplinary studies. Aim is to attract the researchers in PDE to the subject assuming they get lost and disinterested because of the too early introduction of quantization or premature and non-rigourous manipulation with the expansion of the Greens functions or 8-8 mathematics. Harder staff starting from the end of Section 5 are mostly open issues. The main point is that a deeper study is possible that has the prospect of showing the unification of GR and QFT. In this note we shall not cover topics related to wave packets, propagators, quantization and fermion-antifermion systems.

Physical Review D, 2006

We investigate the quantum motion of a neutral Dirac particle bouncing on a mirror in curved spacetime. We consider different geometries: Rindler, Kasner-Taub and Schwarzschild, and show how to solve the Dirac equation by using geometrical methods. We discuss, in a first-quantized framework, the implementation of appropriate boundary conditions. This leads us to consider a Robin boundary condition that gives the quantization of the energy, the existence of bound states and of critical heights at which the Dirac particle bounces, extending the well-known results established from the Schrödinger equation. We also allow for a nonminimal coupling to a weak magnetic field. The problem is solved in an analytical way on the Rindler spacetime. In the other cases, we compute the energy spectrum up to the first relativistic corrections, exhibiting the contributions brought by both the geometry and the spin. These calculations are done in two different ways. On the one hand, using a relativistic expansion and, on the other hand, with Foldy-Wouthuysen transformations. Contrary to what is sometimes claimed in the literature, both methods are in agreement, as expected. Finally, we make contact with the GRANIT experiment.

Gravitation and Cosmology

As a consequence of the Poincare-Weyl gauge theory of gravity, the space-time possesses the geometric structure of Cartan-Weyl CW 4 space with curvature and torsion 2-forms and a Weyltype nonmetricity 1-form. The Dirac field β(x) appears as an essential additional geometric component with respect to the metric tensor. The conformal theory of gravity coupled with β(x) in the exterior form formalism is considered. At an early stage of the universe evolution, we consider these field equations for the spatially flat FRW metric, assuming the densities of ordinary matter and dark matter to be very small. Then the field equations can be expressed in terms of the metric tensor and β(t) only and have an exponentially diminishing solution for β(t), which can explain an exponential decrease of dark energy (the energy of physical vacuum) as a function of time as a consequence of field dynamics in the ultra-early Universe.