December 30, 2009
Checking for new eprints, three papers by P. J. Cote and M. A. Johnson caught my attention: (A) New perspectives on classical electromagnetism (arXiv:0903.4104v2), (B) On the peculiarity of the Coulomb gauge (arXiv:0906.4752v1), (C) Groupthink and the blunder of the gauges (arXiv:0912.2977v1). The main point of these papers seems to be that the exploitation of gauge freedom in electromagnetism is questionable. Specific objections are raised to steps in standard derivations using Lorentz and Coulomb gauges. For example, the title of paper B refers to the non-locality of potentials in the Coulomb gauge and some remarks on the matter quoted from J. D. Jackson’s classic textbook.
The papers themselves border on crankery, which is a bit alarming since the authors are affiliated with the army, but are at least wrong in instructive ways. Electromagnetism is manifestly gauge invariant and there are no genuine causality problems in the Coulomb gauge since the non-local potentials are not physically meaningful quantities in and of themselves. Read the rest of this entry »
December 29, 2009
Condensed matter physics provides mathematical analogies with particle physics. Quasiparticles, i.e. particle-like excitations of a given ground state, often share many physical properties with more fundamental particles. Among the many attempts to find deeper insights into the Standard Model is the exportation of analogies in the other direction: from condensed-matter physics to fundamental physics. Here’s one such line of work:
I. Schmelzer. A condensed matter interpretation of SM fermions and gauge fields. arXiv:0908.0591
Abstract: We present the bundle Aff(3) x C x /(R^3), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each C x /(R^3) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space Aff(3) x C (Z^3). This space allows a simple physical interpretation as a phase space of a lattice of cells in R^3. We find the SM SU(3)_c x SU(2)_L x U(1)_Y action on Aff(3) x C x /(R^3) to be a maximal anomaly-free special gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations. The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with Z_2-degenerated vacuum state. We construct anticommuting fermion operators for the resulting Z_2-valued (spin) field theory. A metric theory of gravity compatible with this model is presented too.
A recent follow up paper focuses on neutrinos:
I. Schmelzer. Neutrinos as pseudo-acoustic ether phonons. arXiv:0912.3892
Abstract: Recently [arXiv:0908.0591] the author has proposed a condensed matter model which gives all fermions and gauge fields of the standard model of particle physics. In the model, the inertness of right-handed neutrinos is explained by an association with translational symmetry. We argue that this association may be used as well to explain the small neutrino masses. They appear to be pseudo-Goldstone particles associated with an approximate translational symmetry of a subsystem. Then we propose to explain the masslessness of SU(3)_c x U(1)_em with an unbroken SU(3)x U(1) gauge symmetry of the model. We also detect a violation of a necessary symmetry property in the lattice Dirac equation and present a fix for this problem.
December 29, 2009
After a busy few months it’s time to resurrect this blog from the blog graveyard. Like I hope at the end of every year, I hope I’ll have more spare time next year!