On the connection between Hamilton and Lagrange formalism in Quantum Field Theory

Understand

The connection between the Hamilton and the standard Lagrange formalism is established for a generic Quantum Field Theory with vanishing vacuum expectation values of the fundamental fields.

• The Effective Actions in both formalisms are the same if and only if the fundamental fields and the momentum fields are related by the stationarity condition.
• These momentum fields in general differ from the canonical fields as defined via the Effective Action.
• By means of functional methods a systematic procedure is presented to identify the full correlation functions, which depend on the momentum fields, as functionals of those usually appearing in the standard Lagrange formalism.