PATH INTEGRATION Meaning and
Definition
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Path integration is a mathematical technique used in physics to calculate the values of certain physical quantities by integrating along a particular path in a multidimensional space. It is based on the concept of a path integral, which is the sum of all possible trajectories of a particle or a system of particles between two points in space and time.
In the context of quantum mechanics, path integration is used to calculate the probability amplitude of a particle to move between two points by summing over all possible paths. This method is particularly useful for systems with a large number of degrees of freedom, where traditional methods of solving differential equations become impractical.
Path integration also finds applications in various areas of theoretical physics, such as quantum field theory and statistical mechanics. In quantum field theory, it is used to calculate the correlation functions of quantum fields, which describe the interactions between particles. In statistical mechanics, path integration is employed to compute the partition function, which determines the equilibrium properties of a system.
Overall, path integration is a powerful mathematical tool in physics that allows for the calculation of physical quantities by summing over all possible paths. It provides a comprehensive understanding of the behavior of quantum systems and has proven to be an essential tool in advancing our knowledge of the fundamental laws of nature.
Etymology of PATH INTEGRATION
The term "path integration" in physics and mathematics has its roots in the broader concept of integration. The word "integration" comes from the Latin word "integrare", which means "to make whole". It emerged in the 17th century and initially referred to the process of finding the area under a curve, which involved summing infinitesimally small sections of the graph.
The addition of the word "path" to integration arose in the context of understanding the motion of particles in quantum mechanics. The concept of a "path" or trajectory became crucial in quantum mechanical models that emphasized the wave-particle duality, where particles were described by wavefunctions.
In the 1940s, Richard Feynman, a renowned theoretical physicist, introduced his formulation of quantum mechanics known as the "Feynman path integral" or "path integral formulation".
