Question: What is involved in the study of Quantum mechanics?
About the article "Quantum mechanics", section "Abstract".

Candidate passages:
In theoretical physics, supersymmetric quantum mechanics is an area of research where mathematical concepts from high-energy physics are applied to the field of quantum mechanics. 
The application of the new quantum theory to electromagnetism resulted in quantum field theory, which was developed starting around 1930.
Quantum field theory has driven the development of more sophisticated formulations of quantum mechanics, of which the one presented here is a simple special case.
Path integral formulation Phase space formulation of Quantum Mechanics, Weyl quantization & geometric quantization quantum field theory in curved spacetime axiomatic, algebraic and constructive quantum field theory C* algebra formalism Generalized Statistical Model of Quantum Mechanics On a different front, von Neumann originally dispatched quantum measurement with his infamous postulate on the collapse of the wavefunction, raising a host of philosophical problems.
Over the intervening 70 years, the "problem of measurement" became an active research area and itself spawned some new formulations of quantum mechanics.
Relative state/Many-worlds interpretation of quantum mechanics Decoherence Consistent histories formulation of quantum mechanics Quantum logic formulation of quantum mechanics A related topic is the relationship to classical mechanics.
Any new physical theory is supposed to reduce to successful old theories in some approximation.
For quantum mechanics, this translates into the need to study the so-called classical limit of quantum mechanics.
Also, as Bohr emphasized, human cognitive abilities and language are inextricably linked to the classical realm, and so classical descriptions are intuitively more accessible than quantum ones.
In particular, quantization, namely the construction of a quantum theory whose classical limit is a given and known classical theory, becomes an important area of quantum physics in itself.
Finally, some of the originators of quantum theory (notably Einstein and Schrödinger) were unhappy with what they thought were the philosophical implications of quantum mechanics.
In particular, Einstein took the position that quantum mechanics must be incomplete, which motivated research into so-called hidden-variable theories.
The issue of hidden variables has become in part an experimental issue with the help of quantum optics.
de Broglie–Bohm–Bell pilot wave formulation of quantum mechanics Bell's inequalities Kochen–Specker theorem  
In mathematics and physics the CCR and CAR algebras arise from the study of canonical commutation relations in bosonic and fermionic quantum mechanics.
They are used in mathematical formulations of quantum statistical mechanics and quantum field theory. 
Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems.
In quantum mechanics a statistical ensemble (probability distribution over possible quantum states) is described by a density operator "S", which is a non-negative, self-adjoint, trace-class operator of trace 1 on the Hilbert space "H" describing the quantum system.
This can be shown under various mathematical formalisms for quantum mechanics.
One such formalism is provided by quantum logic. 
A symmetric, informationally complete, positive operator valued measure (SIC-POVM) is a special case of a generalized measurement on a Hilbert space, used in the field of quantum mechanics.
A measurement of the prescribed form satisfies certain defining qualities that makes it an interesting candidate for a "standard quantum measurement," utilized in the study of foundational quantum mechanics.
Furthermore, it has been shown that applications exist in quantum state tomography and quantum cryptography.