Search results
Results from the WOW.Com Content Network
The path integral formulation is a description in quantum mechanics that generalizes the stationary action principle of classical mechanics.It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude.
In a path integral, the field Lagrangian, integrated over all possible field histories, defines the probability amplitude to go from one field configuration to another. In order to make sense, the field theory should have a well-defined ground state, and the integral should be performed a little bit rotated into imaginary time, i.e. a Wick ...
Functional integration is a collection of results in mathematics and physics where the domain of an integral is no longer a region of space, but a space of functions. Functional integrals arise in probability, in the study of partial differential equations, and in the path integral approach to the quantum mechanics of particles and fields.
Quantum Field Theory. McGraw-Hill. ISBN 9780070320710. R.J. Rivers (1990). Path Integral Methods in Quantum Field Theories. Cambridge University Press. V.P. Nair (2005). Quantum Field Theory A Modern Perspective. Springer. There are some review article about applications of the Schwinger–Dyson equations with applications to special field of ...
Statistical field theory. In theoretical physics, statistical field theory (SFT) is a theoretical framework that describes phase transitions. [1] It does not denote a single theory but encompasses many models, including for magnetism, superconductivity, superfluidity, [2] topological phase transition, wetting [3][4] as well as non-equilibrium ...
In Schwinger's approach, the action principle is targeted towards quantum mechanics. The action becomes a quantum action, i.e. an operator, . Although it is superficially different from the path integral formulation where the action is a classical function, the modern formulation of the two formalisms are identical. [4]
Double-well potential. The so-called double-well potential is one of a number of quartic potentials of considerable interest in quantum mechanics, in quantum field theory and elsewhere for the exploration of various physical phenomena or mathematical properties since it permits in many cases explicit calculation without over-simplification.
In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. [1] The terms path integral, curve integral, and curvilinear integral are also used; contour integral is used as well, although that is typically reserved for line integrals in the complex plane. The function to be integrated may be a ...