Action is the integral of the Lagrangian; as before, this critical point is typically a minimum, so this is called the "principle of least action"::formula_30We get the solution to the dynamics problem (up to a factor of formula_31) from the statics problem by Wick rotation, replacing formula_26 by formula_33 and the spring constant formula_28 by the mass of the rock formula_35::formula_36:formula_37==Both thermal/quantum and static/dynamic==Taken together, the previous two examples show how the path integral formulation of quantum mechanics is related to statistical mechanics.
: formula_38Мы получили решение динамической задачи (с точностью до множителя formula_39) из решения статической при помощи поворота Вика, заменив formula_4 на formula_3, formula_42 на formula_43, и коэффициент упругости formula_36 на массу камня formula_45:: formula_46: formula_47* Wick rotation — a blog introduction* A Spring in Imaginary Time — a worksheet in Lagrangian mechanics illustrating how replacing length by imaginary time turns the parabola of a hanging spring into the inverted parabola of a thrown particle