ABSTRACT
The procedure we described for the case of a single degree of freedom can be extended immediately to the case of a finite number of degrees of freedom. All the results obtained are directly applicable to a system with n degrees of freedom, provided it is understood that the symbol q should be interpreted as a vector with n components, q = { q 1 … q n } $ q=\{q_{1}\ldots q_{n}\} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315369723/48d43afe-85b0-4e2b-a932-df2bd1af07be/content/inline-math3_154.tif"/> . For example, a Green’s function can be defined as G k 1 , k 2 ⋯ , k N ( t 1 , t 2 , … t N ) = 0 | T q k 1 ( t 1 ) q k 2 ( t 2 ) … q k N ( t N ) | 0 . $$ \begin{aligned} G_{k_{1},k_{2}\dots , k_{N}}( t_{1},\,t_{2},\,\ldots \,t_{N} )= \left\langle {0|T\left[ q_{k_{1}}(t_{1})\,q_{k_{2}}(t_{2})\,\ldots q_{k_{N}}(t_{N})\right]|0}\right\rangle \ . \end{aligned} $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315369723/48d43afe-85b0-4e2b-a932-df2bd1af07be/content/math3_36.tif"/>
