Content deleted Content added
Reaper1945 (talk | contribs) No edit summary |
Johnjbarton (talk | contribs) →top: the formulation generalizes the principle not the concept of action. |
||
Line 2:
{{about|a formulation of quantum mechanics|integrals along a path, also known as line or contour integrals|line integral}}
{{Quantum mechanics|cTopic=Formulations}}
The '''path integral formulation''' is a description in [[quantum mechanics]] that generalizes the [[
This formulation has proven crucial to the subsequent development of [[theoretical physics]], because manifest [[Lorentz covariance]] (time and space components of quantities enter equations in the same way) is easier to achieve than in the operator formalism of [[canonical quantization]]. Unlike previous methods, the path integral allows one to easily change [[coordinates]] between very different [[canonical coordinates|canonical]] descriptions of the same quantum system. Another advantage is that it is in practice easier to guess the correct form of the [[Lagrangian (field theory)|Lagrangian]] of a theory, which naturally enters the path integrals (for interactions of a certain type, these are ''coordinate space'' or ''Feynman path integrals''), than the [[Hamiltonian (quantum mechanics)|Hamiltonian]]. Possible downsides of the approach include that [[unitarity]] (this is related to conservation of probability; the probabilities of all physically possible outcomes must add up to one) of the [[S-matrix]] is obscure in the formulation. The path-integral approach has proven to be equivalent to the other formalisms of quantum mechanics and quantum field theory. Thus, by ''deriving'' either approach from the other, problems associated with one or the other approach (as exemplified by Lorentz covariance or unitarity) go away.<ref>{{harvnb|Weinberg|2002|loc=Chapter 9.}}</ref>
| |||