The term transformation theory refers to a procedure and a "picture" used by
Paul Dirac
Paul Adrien Maurice Dirac ( ; 8 August 1902 – 20 October 1984) was an English mathematician and Theoretical physics, theoretical physicist who is considered to be one of the founders of quantum mechanics. Dirac laid the foundations for bot ...
in his early formulation of
quantum theory, from around 1927.
This "transformation" idea refers to the changes a quantum state undergoes in the course of time, whereby its vector "moves" between "positions" or "orientations" in its
Hilbert space
In mathematics, a Hilbert space is a real number, real or complex number, complex inner product space that is also a complete metric space with respect to the metric induced by the inner product. It generalizes the notion of Euclidean space. The ...
.
[Prugovecki, Eduard (2006). ''Quantum Mechanics in Hilbert Space'', Second edition (Dover Books on Physics) Paperback. .] Time evolution, quantum transitions, and symmetry transformations in
quantum mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
may thus be viewed as the systematic theory of abstract, generalized rotations in this space of
quantum state
In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a prediction for the system ...
vectors.
Remaining in full use today, it would be regarded as a topic in the mathematics of Hilbert space, although, technically speaking, it is somewhat more general in scope. While the terminology is reminiscent of rotations of vectors in ordinary space, the Hilbert space of a quantum object is more general and holds its entire quantum state.
(The term further sometimes evokes the
wave–particle duality
Wave–particle duality is the concept in quantum mechanics that fundamental entities of the universe, like photons and electrons, exhibit particle or wave (physics), wave properties according to the experimental circumstances. It expresses the in ...
, according to which a
particle
In the physical sciences, a particle (or corpuscle in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass.
They vary greatly in size or quantity, from s ...
(a "small" physical object) may display either particle or wave aspects, depending on the observational situation. Or, indeed, a variety of intermediate aspects, as the situation demands.)
References
Foundational quantum physics
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