A unified treatment of the 2 × 2 analog of the Freudenthal-Tits magic square of Lie groups is given, providing an explicit representation in terms of matrix groups over composition algebras.Mathematics Subject Classification. 22E46, 17A35, 15A66.
Representations of SO(4, 2) are constructed using 4 × 4 and 2× 2 matrices with elements in H ⊗ C and the known isomorphism between the conformal group and SO(4, 2) is written explicitly in terms of the 4 × 4 representation. The Clifford algebra structure of SO(4, 2) is briefly discussed in this language, as is its relationship to other groups of physical interest.
The double slit experiment provides a classic example of both
interference and the effect of observation in quantum physics. When particles
are sent individually through a pair of slits, a wave-like interference pattern
develops, but no such interference is found when one observes which
“path” the particles take. We present a model of interference,
dephasing, and measurement-induced decoherence in a one-dimensional version of
the double-slit experiment. Using this model, we demonstrate how the loss of
interference in the system is correlated with the information gain by the
measuring apparatus/observer. In doing so, we give a modern account of
measurement in this paradigmatic example of quantum physics that is accessible
to students taking quantum mechanics at the graduate or senior undergraduate
levels.
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