**Subject:** Further Problems in the Standard Model

**Date:** Sat, 2 May 2009 02:18:00 EDT

This is a good review of Lewis H. Ryder’s “Quantum Field Theory”, (CUP, 196, 2nd. ed., softback). Here, Horst Eckardt points out several basic problems with the standard approach to spin in relativistic quantum mechanics. In ECE theory the problem is approached from the point of view of geometry, and ECE has the advantage of being generally covariant. It was shown in papers 129 and 130 that the fermion spin can be developed with the Pauli matrices only, and without the Dirac sea and negative energy. These complications in Ryder begin in chapter two, and the book becomes progressively more abstruse as it introduces the various and interminable obscurities of twentieth century physics, quantum electrodynamics, gauge theory, and finally supersymmetry. String theory further compounds this non Baconian obscurity with yet more unobservables. A further problem i sthat teh book is written in non SI units. I restored all the units in “The Enigmatic Photon”, but ECE has now evolved far beyond the twentieth century, into the more enlightened sixteenth century of Bacon and Shakespeare.

Today on “labour day” I read the chapter on the Dirac equation. The introduction of the 4×4 matrices is tightly connected with the properties of the Lorentz group which leads to massive complications. In the ECE approach this reference is not needed because the ECE wave equation is generally covariant. This is a further hint that the theory is self-consistent and superior due to Occam’s razor. On page 44 the Dirac anti-particles are derived from the negative square root of the energy equation. This can be omitted by arguments of classical field theory as you introduced. There is an additional argument anywhere that the eigenvalues of the eigen value equations (2.140) are plus/minus 1, which is a different argument for negative energies. I suppose that this comes from the different phase factors in (2.136) which we do not have in ECE theory. Probably one can nullify this argument by the hint that in ECE no gamma matrices are used. Another interesting point is the Spin operator introduced in (2.169). The group theoretical background must be generalized further to the Poicare group to come to any results, but as Ryder writes, even these are not satisfactory, and a huge mathematical apparatus is built up to proceed. However this problem is of practical relevance, it pertains to relativistic quantum-chemical calculations where it is not clear how to define the relativistic spin. Key point is that eq. (2.166) has to be fulfilled, the spin commutator has to represent a Lie group. This seems barely be possible with the gamma matrices, but I suppose that it is fulfilled for the Dirac spin matrices when the Spin vector operator is defined as

S = ( sigma_1, sigma_2, sigma_3)

and the physical spin is its expectation value. If this is true, it would justify a further paper in my opinion, where the “relativistic spin problem” is solved.

Horst