498
E. Rabinovici
8.3 Unification
8.3.1 Gauge Group Unification [2]
The standard model is unified along the lines that all of its components, the
colour, weak and electromagnetic interactions are described by gauge theories.
They are SU(3) ∗ SU(2) ∗ U(1). The gluons and the photons, the electrons and
the quarks belong to different representations of the product gauge group, it is
natural to attempt to have all of the elementary particles and interactions as a
single representation of a single gauge group. Intermediate algebraic solutions to
this problem have been found. For example the gauge group SU(5) does very
economically unify the known gauge groups. Moreover it predicts that quarks
and leptons can transmute into each other, in particular violating Baryon number
conservation. The proton could decay in such models for example into an positron
and a neutral pion. The original estimates of the half life time of the proton placed
it possibly around 10 31 years. That prediction was within experimental reached and
initiated the construction of very ingenous experiments. Proton decay at that rate
was not found, the lower bound on the proton life time was improved to be 10 35 , thus
invalidating the simplest version of the grand unified group SU(5). In that version
the particles did not all belong to the same representation as one may have wished
based on esthetics. There have been many other attempts since to find an appropriate
unifying group these included SO(10) (which incorporated naturally a right handed
SU(2) singlet neutrino) and exceptional groups such as E(6). This was done with and
without SUSY. Using the renormalization group it was found that in the presence of
SUSY the in teractions may indeed unify in magnitude at a high energy not much
below the planck scale of 10 19 GeV. At such scales it becomes difficult to ignore
quantum gravity. In any case we will not review this vast subject further here.
8.3.2 Extra Dimensions and Unification [3]
The first ideas of unification by increasing the number of dimensions were suggested
in classical field theory by Kaluza and Klein (KK) in the period of the 1920s. At
the time there were two well known interactions, gravity and electromagnetism.
KK suggested that space time is five dimensional rather than four dimensional and
that there is but one fundamental interaction-gravity. In order to be consistent with
observations it was suggested that the five dimensional space time is composed out
of a fifth dimension which is a spatial circle of inverse radius m, and the usual
four dimensional Minkowski component. The radius 1/m should be small enough to
have not been observed yet. The resulting low energy (i.e. energies much lower
than m) five dimensional Lagrangian decomposes into several four dimensional
Lagrangians. They describe, four dimensional gravity, four dimensional Maxwell
electrodynamics and the coupling of a neutral spin zero additional particle. The
E. Rabinovici
8.3 Unification
8.3.1 Gauge Group Unification [2]
The standard model is unified along the lines that all of its components, the
colour, weak and electromagnetic interactions are described by gauge theories.
They are SU(3) ∗ SU(2) ∗ U(1). The gluons and the photons, the electrons and
the quarks belong to different representations of the product gauge group, it is
natural to attempt to have all of the elementary particles and interactions as a
single representation of a single gauge group. Intermediate algebraic solutions to
this problem have been found. For example the gauge group SU(5) does very
economically unify the known gauge groups. Moreover it predicts that quarks
and leptons can transmute into each other, in particular violating Baryon number
conservation. The proton could decay in such models for example into an positron
and a neutral pion. The original estimates of the half life time of the proton placed
it possibly around 10 31 years. That prediction was within experimental reached and
initiated the construction of very ingenous experiments. Proton decay at that rate
was not found, the lower bound on the proton life time was improved to be 10 35 , thus
invalidating the simplest version of the grand unified group SU(5). In that version
the particles did not all belong to the same representation as one may have wished
based on esthetics. There have been many other attempts since to find an appropriate
unifying group these included SO(10) (which incorporated naturally a right handed
SU(2) singlet neutrino) and exceptional groups such as E(6). This was done with and
without SUSY. Using the renormalization group it was found that in the presence of
SUSY the in teractions may indeed unify in magnitude at a high energy not much
below the planck scale of 10 19 GeV. At such scales it becomes difficult to ignore
quantum gravity. In any case we will not review this vast subject further here.
8.3.2 Extra Dimensions and Unification [3]
The first ideas of unification by increasing the number of dimensions were suggested
in classical field theory by Kaluza and Klein (KK) in the period of the 1920s. At
the time there were two well known interactions, gravity and electromagnetism.
KK suggested that space time is five dimensional rather than four dimensional and
that there is but one fundamental interaction-gravity. In order to be consistent with
observations it was suggested that the five dimensional space time is composed out
of a fifth dimension which is a spatial circle of inverse radius m, and the usual
four dimensional Minkowski component. The radius 1/m should be small enough to
have not been observed yet. The resulting low energy (i.e. energies much lower
than m) five dimensional Lagrangian decomposes into several four dimensional
Lagrangians. They describe, four dimensional gravity, four dimensional Maxwell
electrodynamics and the coupling of a neutral spin zero additional particle. The