The isolated, uniformly moving electron: Selfintersecting SU(2) Yang-Mills center vortex loop and Louis de Broglie’s hidden thermodynamics

Abstract

We propose that the one-fold selfintersecting center-vortex loop, being the stable excitation in the confining phase of SU(2) Yang-Mills thermodynamics of scale Λ ∼ 0.5 MeV, after an electric-magnetically dual interpretation of this theory represents the electron/positron. Our argument invokes recent results on the physics of a strongly and spherically perturbed 't Hooft-Polyakov monopole, the role of the central spatial region in a Harrington-Shepard (HS) (anti)caloron, the latter's deformation towards maximally non-trivial holonomy and subsequent dissociation into a pair of a screened BPS monopole and antimonopole, the energydensity of the deconfining thermal ground state, and the critical temperature T c for the deconfining-preconfining transition. We estimate the typical spatial extent of the selfintersection region and the monopole core size, implying that the electron/positron, judged by its Compton wave length, is anything but a point particle. Our results support and elucidate the ideas of Louis de Broglie on the thermodynamics of an isolated particle.

The Isolated Electron: De Broglie’s Hidden Thermodynamics, SU(2) Quantum Yang-Mills Theory, and a Strongly Perturbed BPS Monopole

“…The present article's purpose is a model of the electron along the lines proposed in [49] with more precise inputs from SU(2) Yang-Mills thermodynamics and relying on the work in [37]. This model posits the electron to be represented by a one-fold self-intersecting spatial center-vortex loop immersed into the confining phase.…”

“…The remainder of this paper is intended to corroborate and explain the above-sketched model of the electron in more quantitative terms, thereby considering a few (rather small) corrections to the results obtained in the simplified treatment of [49] where complete ground-state dominance of the deconfining thermodynamics within the intersection region was assumed. Since our derivations heavily rest on a grasp of the phase structure of an SU(2) Yang-Mills theory we will briefly review it in Section 2.…”

“…Based on [49] we would now like to perform an improved estimate of the radius R 0 associated with the region of self-intersection. The idea is to prescribe at T 0 , where deconfining SU(2) thermodynamics does not exert any pressure, that the rest mass of the quantum particle electron,…”

“…In writing Equation (19), Equation (9) of [49] and Equations (13) and (14) were used. Interactions between the monopole and deconfining SU(2) thermodynamics (caloron and anticaloron centers [33] invoking energy transfer from quasi-particle excitations to the monopole which partially radiates this energy back into the Yang-Mills plasma) will effectively introduce spatial fluctuations of temperature T about the equilibrium value T 0 , but they won't change the energy content of the overall system.…”

Quantum Field Theory

“…In this context, I do share the opinion voiced in [26] that an understanding of the micro(quantum)structure of gravitational solitons, such as Schwarzschild black holes, will benefit from a deeper understanding of the nature of ordinary elementary particles such as the electron. Such a link could rest on the notion of spatially confined and quantum-stabilised phases of thermal gauge theory [5,8,27], and I do believe that fundamental problems such as the information paradox of black hole thermodynamics will find their resolution when faced from a vantage point within this more fundamental layer of reality, when compared to what the SMPP and our present theory of gravitation, together with its various strategies of quantisation, are able to provide: both, the SMPP and present approaches to quantum gravity are field or string theories quantised 'after the fact' when quantum behaviour is likely to emerge from classical Euclidean gauge theory (see above). Based on these deeper insights, it may well turn out, as Roger Penrose supposes [28], that the unitary evolution of a pure quantum state in interaction with a black hole is hampered by state reduction due to strong gravitational field interference in the vicinity of the black hole's horizon or its singularity, and hence that information cannot be conserved as a matter of principle.…”