the mathematical expression of a core quantum mechanical principle

Known as the path integral, the path integral is the mathematical expression of a core quantum mechanical principle: Anything that can happen does happen.

an integral where the function to be integrated is evaluated along a path or curve

In mathematics, a path integral (also known as a line integral) is an integral where the function to be integrated is evaluated along a path or curve.

as being the sum of all paths through an infinite space–time

The path integrals are usually thought of as being the sum of all paths through an infinite space–time.

mathematical objects that can be considered as generalizations to an infinite number of variables, represented by paths, of usual integrals

Path integrals are mathematical objects that can be considered as generalizations to an infinite number of variables, represented by paths, of usual integrals.

an analytic continuation of a method for summing up all possible random walks

The Schrödinger equation is a diffusion equation with an imaginary diffusion constant, and the path integral is an analytic continuation of a method for summing up all possible random walks.

powerful tools for the study of quantum mechanics

Path integrals are powerful tools for the study of quantum mechanics.

a canonical vector-based navigation strategy used by a diverse array of both flying and walking animals, potentially including Drosophila

Path integration is a canonical vector-based navigation strategy used by a diverse array of both flying and walking animals, potentially including Drosophila.

the integral of a functional over a space of curves Path integral formulation by Richard Feynman of quantum mechanics

Path integral may refer to: Line integral, the integral of a function along a curve Functional integration, the integral of a functional over a space of curves Path integral formulation by Richard Feynman of quantum mechanics

a highly conserved, self-motion-based navigation strategy

Path integration (PI) is a highly conserved, self-motion-based navigation strategy.

a probabilistic algorithm to generate a Euclidean scalar field configuration

The path integral defines a probabilistic algorithm to generate a Euclidean scalar field configuration.

as the 'sum of histories' of all paths through an infinite space–time

The path integrals are described as the 'sum of histories' of all paths through an infinite space–time.

a more intuitive understanding , of quantum mechanics especially in quantum field theory and particle physics

Path integrals provide a more intuitive understanding of quantum mechanics, especially in quantum field theory and particle physics.

the natural formulation of the laws which rule the global and stochastic evolutions

Differential equations constitute the appropriate expressions of some deterministic and local physical laws, while the path integrals (belonging to Quantum Mechanics) are the natural formulation of the laws which rule the global and stochastic evolutions.

a sum over all possibilities

A path integral is a sum over all possibilities.