**1.** The Law of Laws (LL; see **Posts 3, 4**) is a machine, generating particular single-particle laws dependent upon the behavior of wave field *χ* under spacetime transformations. Because *χ* is self-imaging and propagates in extra dimensions, each such law brings with it the prospect of new physics. Already we have seen in **Posts 6** and **7** how, taking *χ* to be a Dirac spinor, the Dirac equation in 4 + 2 and 4 + 2 + 2 dimensions resolves long-standing questions about neutrino mass and the family problem. In this and the next post I want draw attention to implications of the LL for astrophysics and cosmology. This means asking the LL to give us propagation laws for vector and tensor (boson) representations of * χ*.

The most efficient way to deal with boson fields in general is via the seemingly magical Dirac-Clifford matrices and associated algebra. There are fifteen such matrices—fifteen being also, not accidentally, the number of rotations in a space of 4 + 2 dimensions. They, together with the unit matrix, form a set of sixteen linearly independent matrices, Γ* _{i }*,

Specifically, for massive, charge neutral fields ( *p *_{5} = 0 ) we get one scalar equation for the Higgs particle (Klein-Gordon); one 4-vector equation for the *Z *^{0 }boson (Maxwell-Proca); and one pseudo-scalar equation for a new boson we call* Z *^{5 }.

Similarly, for charged fields ( *p *_{5} = ± *m* * _{e} c *) we get 4-vector equations for the

The new pseudoscalar bosons *Z *^{5 }and ^{ }*W *^{5 }have the same masses as the *Z *^{0 }and W ^{±}, respectively: * m _{z}* = 91.2 GeV /

In a recent issue of Physical Review Letters (Volume **118**, p. 191102, published 9 May, 2017) Alessandro Cuoco, Michael Krämer and Michael Korsmeier find that the recently observed excess of antiprotons in cosmic rays is explainable in terms of the annihilation of dark-matter particles with masses of about 80 GeV / *c* ^{2}. Intriguingly, this just happens to be the mass of the *W *^{5} particle. Unfortunately, as the *W *^{5} is stable, it can have nothing to do with the creation of antiprotons; and even if it could annihilate, it could not yield an antiproton without violating conservation of baryon number.

**2.** Applying this same procedure for massless fields ( *p *_{5 }= *p *^{6}_{ }= _{ }0 ), we obtain: two 4-vector equations in the Maxwell *F _{μ ν}* tensor, one of them inhomogeneous, the other homogeneous (the Bianchi relation); one inhomogeneous pseudoscalar equation and one homogeneous 4-vector equation in the pseudovector

** **