This book is based on the analysis of canonical commutation
relations (CCRs) and their possible deformations. In light of the
recent interest on PT-quantum mechanics, the author presents a
special deformed version of the CCRs, and discusses the
consequences of this deformation both from a mathematical side, and
for its possible applications to physics. These include the
analysis of several non self-adjoint Hamiltonians, a novel view to
the position and momentum operators, and a general approach to
compute path integrals and transition probabilities using the
so-called bi-coherent states. The book is meant for researchers and
is also suited for advanced students. It can be used as a gentle
introduction to some delicate aspects in functional analysis and in
quantum mechanics for non self-adjoint observables.
General
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