This is a collection of essays based on lectures that author has
given on various occasions on foundation of quantum theory,
symmetries and representation theory, and the quantum theory of the
superworld created by physicists. The lectures are linked by a
unifying theme: how the quantum world and superworld appear under
the lens of symmetry and supersymmetry.
In the world of ultra-small times and distances such as the
Planck length and Planck time, physicists believe no measurements
are possible and so the structure of spacetime itself is an unkown
that has to be first understood. There have been suggestions
(Volovich hypothesis) that world geometry at such energy regimes is
non-archimedian and some of the lectures explore the consequences
of such a hypothesis.
Ultimately, symmetries and supersymmetries are described by the
representation of groups and supergroups. The author's interest in
representation is a lifelong one and evolved slowly, and owes a
great deal to conversations and discussions he had with George
Mackey and Harish-Chandra. The book concludes with a retrospective
look at these conversations.
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