Path integral formulation of quantum mechanics using functional integration, due to Richard Feynman
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The Duru–Kleinert transformation, named after İsmail Hakkı Duru and Hagen Kleinert, is a mathematical method for solving path integrals of physical systems with singular potentials, which is necessary for the solution of all atomic path integrals due to the presence of Coulomb potentials (singular like ).
Richard Feynman's path integral formulation of quantum mechanics is based on a stationary-action principle, using path integrals.
Stephen Hawking and Leonard Mlodinow, in the popular scientific book The Grand Design, take a philosophical position to support a view of the universe as a multiverse, and define it in the book as model-dependent realism which along with a sum-over-histories approach (see Path integral formulation of Quantum mechanics) to the universe as a whole, is used to claim that M-theory is the only candidate for a complete theory of the universe.
1989, he developed a Wick-rotated version of Richard Feynman's quantum path integral formalism for analyzing performance degradation in large-scale computer systems and packet networks.
The method achieves the same result as Richard Feynman's use of trajectories in the path integral formulation – the mapping of the initial wavefunction through time – however, instead of using Feynman's 'all possible paths' between two points, it employs at most one path.
He is known for developing the path integral formulation of the Fermionic field, inventing Grassmann integration for this purpose.