  The crucial step towards quantum field theory is in some respects analogous to the corresponding quantization in quantum mechanics, namely by imposing commutation relations, which leads to operator valued quantum fields. The starting point is the classical Lagrangian formulation of mechanics, which is a so-called analytical formulation as opposed to the standard version of Newtonian mechanics. A generalized notion of momentum (the conjugate or canonical momentum) is defined by setting \(p = \partial L/\partial\dot{q}\), where \(L(q, \dot{q})\) is the Lagrange function, or Lagrangian. Here \(\dot{q}\equiv dq/dt\). The Lagrangian defines the theory, so it has no a-priori definition. The special case of the Newtonian theory is described by \(L = T - V\) (\(T\) is the Newtonian kinetic energy and \(V\) the potential).  This fact can be motivated by looking at the special case of a Lagrange function with a potential \(V\) which depends only on the position so that (using Cartesian coordinates) \(\partial L/\partial\dot{x} = (\partial/\partial\dot{x})(m\dot{x}^2 /2) = m\dot{x} = p_x\).  Under these conditions the generalized momentum coincides with the Newtonian mechanical momentum. In classical Lagrangian field  theory one associates with the given field \(\phi\) a second field, namely the conjugate field