Berry phase and the U(1) gauge symmetry

I discussed Berry phase back in February, (Berry or Pancharatnam-Berry or Quantum phase) from a vector / density matrix point of view, but I thought it would be nice to describe Berry phase from the point of view of the U(1) gauge symmetry of quantum mechanics. From a density matrix point of view, the U(1) [...]

Mass Survives 1 Year

This blog celebrated its 1st nominal birthday today with a new monthly record for view:

Views of the blog have increased month to month at a rate of about 20 page views per day per month. I don’t own a watch and hate to have to deal with time periods less than around two weeks. So [...]

Cubic Matrix Models, Quarks and Leptons

Lee Smolin recently put up an arXiv article, Matrix universality of gauge and gravitational dynamics, 0803.2926. The first sentence of the abstract is “A simple cubic matrix model is presented,which has truncations that, it is argued, lead at the classical level to a variety of theories of gauge fields and gravity.” A cubic matrix model [...]

MUBs, nilpotents and idempotents of Clifford algebras

Kea recently wrote about Rowland’s being banned on arXiv. Rowland’s efforts are kind of similar to mine except that he works with the nilpotents (BB = 0) of a Clifford algebra while I work with the idempotents (BB = B). Some years ago, I had a conversation with Hestenes and discussed these things, and he [...]

The Neutral Point of View

One finds a fairly diverse collection of characters hanging around the Crossroads Mall Chess Club, (which I sometimes inaccurately refer to as the “Overlake Mall Chess Club”). Mostly it’s men who love chess, or are retired or otherwise have too much time on their hands. In my case, it’s a love of watching others play [...]

MUBs and the 0.7 Anomaly in QPC conductance

Thank Nanoscale for bringing to my attention a long standing puzzle in mesocopic scale condensed matter physics, the “0.7 anomaly”. The problem is the behavior of the conductance (inverse of resistance) for a quantum point contact (QPC). Two experimental papers showing the effect are 0706.0792 and cond-mat/0005082, which see. Shot noise decreases at the 0.7 [...]

Book Review: River Run Red; The Fort Pillow Massacre, Andrew Ward

The Fort Pillow Massacre dates to April 12, 1864, the fourth year of the American Civil War, on the banks of the Mississippi river in west Tennessee. I bought this 530 page hardback by Andrew Ward at Half Price Books at a bit of a steal for $3 or so:

The book is peculiarly interesting in [...]

Quarks, leptons and generations!

I’ve finally just now figured out how to combine the quark / lepton weak hypercharge and weak isospin quantum numbers with the generation numbers. This should allow the Koide mass formula to be extended to the quarks!
The weak hypercharge and weak isospin quantum numbers for the elementary fermions are:
, with the quantum numbers for the [...]

Pascal’s Triangle and Lisi’s E8 Quantum Numbers

Suppose we have an object X composed of three spin-1/2 fermions, R, G, and B. I should mention that “spin-1/2″ means SU(2) here, in particular the usual 2-dimensional Pauli spin. The three fermions can each have spin +- 1/2, what spin states can object X have? This is a problem learned in undergraduate quantum mechanics; [...]