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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.

Mathematics --- Mathematical physics --- Quantum mechanics. Quantumfield theory --- quantumfysica --- toegepaste wiskunde --- wiskunde --- fysica --- Commutation relations (Quantum mechanics) --- Bosons.

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Partial differential operators --- Commutation relations (Quantum mechanics) --- Representations of Lie groups --- Lie groups --- Representations of groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Differential operators --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Commutative algebra --- Quantum theory --- Partial differential operators. --- Representations of Lie groups. --- Commutation relations (Quantum mechanics). --- Lie, Algèbres de --- Lie, Groupes de --- Opérateurs linéaires --- Opérateurs, Théorie des