Classical electron mass renormalization (original) (raw)
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The renormalized electron mass in non-relativistic quantum electrodynamics
Journal of Functional Analysis, 2007
This work addresses the problem of infrared mass renormalization for a scalar electron in a translation-invariant model of non-relativistic QED. We assume that the interaction of the electron with the quantized electromagnetic field comprises a fixed ultraviolet regularization and an infrared regularization parametrized by σ > 0. For the value p = 0 of the conserved total momentum of electron and photon field, bounds on the renormalized mass are established which are uniform in σ → 0, and the existence of a ground state is proved. For |p| > 0 sufficiently small, bounds on the renormalized mass are derived for any fixed σ > 0. A key ingredient of our proofs is the operatortheoretic renormalization group using the isospectral smooth Feshbach map. It provides an explicit, finite algorithm that determines the renormalized electron mass at p = 0 to any given precision.
Nonperturbative Description Of The Mass And Charge Renormalization In Quantum Electrodynamics
In this paper the nonperturbative analysis of the spectrum for one-particle excitations of the electronpositron field (EPF) is considered in the paper. A standard form of the quantum electrodynamics (QED) is used but the charge of the "bare" electron e0 is supposed to be of a large value (e0 ≫ 1). It is shown that in this case the quasi-particle can be formed with a non-zero averaged value of the scalar component of the electromagnetic field (EMF). Self-consistent equations for the distribution of charge density in the "physical" electron (positron) are derived. A variational solution of these equations is obtained and it defines the finite renormalization of the charge and mass of the electron (positron). It is found that the coupling constant α0 between EPF and EMF and mass m0 of the "bare" electron can be connected with the observed values of the fine structure constant α and the mass of the "physical" electron m as follows (h = c = 1): 2
monopolar electron, 2019
In this paper, a particular attempt for unification shall be indicated in the proposal of a third kind of relativity in a geometric form of quantum relativity, which utilizes the string modular duality of a higher dimensional energy spectrum based on a physics of wormholes directly related to a cosmogony preceding the cosmologies of the thermodynamic universe from inflaton to instanton. In this way, the quantum theory of the microcosm of the outer and inner atom becomes subject to conformal transformations to and from the instanton of a quantum big bang or qbb and therefore enabling a description of the macrocosm of general relativity in terms of the modular T-duality of 11-dimensional supermembrane theory and so incorporating quantum gravity as a geometrical effect of energy transformations at the wormhole scale. Part 1 of this article series includes: Introduction; The Electromagnetic Mass Energy and the [v/c] 2 Velocity Ratio Distribution; The Extension of Newton's Law in Relativistic Momentum & Energy and the Magnetopolar Self-Interaction of the Electron; and Frequency permutation states in the monopolar velocity distribution.
A quantum field theory of the extended electron
In the first part ͑Secs. I and II͒ of this paper, starting from the Pauli current, we obtain the decomposition of the nonrelativistic field velocity into two orthogonal parts: ͑i͒ the ''classical'' part, that is, the velocity w ϭp/m in the center of mass ͑c.m.͒, and ͑ii͒ the ''quantum'' part, that is, the velocity V of the motion of the c.m. frame ͑namely, the internal ''spin motion'' or Zitterbewegung͒. By inserting such a complete, composite expression of the velocity into the kinetic-energy term of the nonrelativistic classical ͑i.e., Newtonian͒ Lagrangian, we straightforwardly get the appearance of the so-called quantum potential associated, as it is known, with the Madelung fluid. This result provides further evidence of the possibility that the quantum behavior of microsystems is a direct consequence of the fundamental existence of spin. In the second part ͑Secs. III and IV͒, we fix our attention on the total velocity vϭwϩV, now necessarily considering relativistic ͑classical͒ physics. We show that the proper time entering the definition of the four-velocity v for spinning particles has to be the proper time of the c.m. frame. Inserting the correct Lorentz factor into the definition of v leads to completely different kinematical properties for v 2 . The important constraint p v ϭm, identically true for scalar particles but just assumed a priori in all previous spinning-particle theories, is herein derived in a self-consistent way.
The Monopolar Quantum Relativistic Electron: An Extension of the Standard Model & Quantum Field Theory (Part 2), 2019
In this paper, a particular attempt for unification shall be indicated in the proposal of a third kind of relativity in a geometric form of quantum relativity, which utilizes the string modular duality of a higher dimensional energy spectrum based on a physics of wormholes directly related to a cosmogony preceding the cosmologies of the thermodynamic universe from inflaton to instanton. In this way, the quantum theory of the microcosm of the outer and inner atom becomes subject to conformal transformations to and from the instanton of a quantum big bang or qbb and therefore enabling a description of the macrocosm of general relativity in terms of the modular T-duality of 11-dimensional supermembrane theory and so incorporating quantum gravity as a geometrical effect of energy transformations at the wormhole scale. Part 2 of this article series includes: The Mass Distribution for the Quantum Relativistic Classical Electron; Electromagnetic Mass Distribution for the Quantum Relativistic Electrodynamic Electron; The bare rest mass of the electron in the Coulombic charge quantum and the mensuration calibration in the alpha fine structure; The M-Sigma conformal mapping onto {meo/me} 2 in the ß 2 distribution; The Planck-Stoney Bounce in conformal supermembrane cosmology; and The charge radius for the proton and neutrinos in quantum relativity. We set Constant A in Amec = μoe 2 /8πc 2 Re for Aß 2 = 1/√[1-ß 2 ]-1 from: c 2 (m-mec) = μoe 2 v 2 /8πRe = mecc 2 (1/√[1-ß 2 ]-1) = mecv 2 A with a total QR monopolar mass m = mec/√(1-[v/c] 2)
The Monopolar Quantum Relativistic Electron: An Extension of the Standard Model & Quantum Field Theory (Part 3) , 2019
In this paper, a particular attempt for unification shall be indicated in the proposal of a third kind of relativity in a geometric form of quantum relativity, which utilizes the string modular duality of a higher dimensional energy spectrum based on a physics of wormholes directly related to a cosmogony preceding the cosmologies of the thermodynamic universe from inflaton to instanton. In this way, the quantum theory of the microcosm of the outer and inner atom becomes subject to conformal transformations to and from the instanton of a quantum big bang or qbb and therefore enabling a description of the macrocosm of general relativity in terms of the modular T-duality of 11-dimensional supermembrane theory and so incorporating quantum gravity as a geometrical effect of energy transformations at the wormhole scale. Part 3 of this article series includes: A Mapping of the Atomic Nucleus onto the Thermodynamic Universe of the Hyperspheres; The Higgsian Scalar-Neutrino; & The Wave Matter of de Broglie. We consider the universe's thermodynamic expansion to proceed at an initializing time tps=fss at lightspeed for a light path x=ct to describe the hypersphere radii as the volume of the inflaton made manifest by the instanton as a lower dimensional subspace and consisting of a summation of a single spacetime quantum with a quantized toroidal volume 2π²rweyl and where rweyl=rps is the characteristic wormhole radius for this basic building unit for a quantized universe (say in string parameters given in the Planck scale and its transformations). At a time tG, say so 18.85 minutes later, the count of space time quanta can be said to be 9.677x10 102 for a universal 'total hypersphere radius' of about rG=3.391558005x10 11 meters and for a G-Hypersphere volume of so 7.69x10 35 cubic meters from N{2π 2 .rps 3 } = Volume = 2π2.RHk3.
In this paper, a particular attempt for unification shall be indicated in the proposal of a third kind of relativity in a geometric form of quantum relativity, which utilizes the string modular duality of a higher dimensional energy spectrum based on a physics of wormholes directly related to a cosmogony preceding the cosmologies of the thermodynamic universe from inflaton to instanton. In this way, the quantum theory of the microcosm of the outer and inner atom becomes subject to conformal transformations to and from the instanton of a quantum big bang or qbb and therefore enabling a description of the macrocosm of general relativity in terms of the modular T-duality of 11-dimensional supermembrane theory and so incorporating quantum gravity as a geometrical effect of energy transformations at the wormhole scale.
Prespacetime Journal, 2019
In this paper, a particular attempt for unification shall be indicated in the proposal of a third kind of relativity in a geometric form of quantum relativity, which utilizes the string modular duality of a higher dimensional energy spectrum based on a physics of wormholes directly related to a cosmogony preceding the cosmologies of the thermodynamic universe from inflaton to instanton. In this way, the quantum theory of the microcosm of the outer and inner atom becomes subject to conformal transformations to and from the instanton of a quantum big bang or qbb and therefore enabling a description of the macrocosm of general relativity in terms of the modular T-duality of 11-dimensional supermembrane theory and so incorporating quantum gravity as a geometrical effect of energy transformations at the wormhole scale. Part 5 of this article series includes: Quark-Lepton Unification in XL-Boson Class HO(32) SEWg-SEW.G.
Un-renormalized classical electromagnetism
Annals of Physics, 2006
This paper follows in the tradition of direct-action versions of electromagnetism having the aim of avoiding a balance of infinities wherein a mechanical mass offsets an infinite electromagnetic mass so as to arrive at a finite observed value. Given that, in this respect the direct-action approached ultimately failed because its initial exclusion of self-action was found to be untenable in the relativistic domain, this paper continues the tradition considering instead a version of electromagnetism wherein mechanical action is excluded and self-action is retained. It is shown that the resulting theory is effectively interacting due to the presence of infinite forces. A vehicle for the investigation is a pair of classical point charges in a positronium-like arrangement for which the orbits are found to be selfsustaining and naturally quantized.