- Toward Quantum Fields: Scalar and Spinor Fields
Thus far we have encountered classical fields such as the electromagnetic field and the current and density fields of fluids and so on. Now we explore the idea that any classical field equations, such as Maxwell’s equations, wave equations and so on, are obtainable as the equations of motion of a suitable Lagrangian/Hamiltonian. This would be particularly useful in investigating the nature of the quantum mechanical version of these theories as the machinery for studying quantum mechanics using Hamiltonians, and as we shall see Lagrangians as well, is quite well developed. We start with the wave equation for a scalar field.