The term transformation theory refers to a procedure used by P. A. M. Dirac in his early formulation of quantum theory, from around 1927. Paul Adrien Maurice Dirac, (August 8, 1902 - October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ... Fig. ...

The term is related to the famous wave-particle duality, according to which a particle (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. In physics, wave-particle duality holds that light and matter can exhibit properties of both waves and of particles. ... A particle is Look up Particle in Wiktionary, the free dictionary In particle physics, a basic unit of matter or energy. ...

This "transformation" idea also refers to the changes a physical object may undergo in the course of time, whereby it may "move" between "positions" in its Hilbert "space".

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 motion in ordinary space, the Hilbert space of a quantum object is more general, and holds its entire quantum state. In mathematics, a Hilbert space is an inner product space that is complete with respect to the norm defined by the inner product. ... A quantum state is any possible state in which a quantum mechanical system can be. ...