Constant term in Lagrangian Why can we always drop any constant term in a Lagrangian density in quantum field theory?
This issue is somehow related to the constant term being some kind of cosmological constant.
Can you please explain this issue?
 A: You can drop a constant term in the Lagrangian because it doesn't affect the Euler-Lagrange equations, and therefore the equations of motion are the same.
A constant term does have an effect in the actual value of, say, the Hamiltonian (and the rest of Noether charges). But you can only measure differences in energies, and therefore a constant term in the Hamiltonian is again irrelevant (the same can be said about all the scalar Noether charges; if a charge has a Lorentz index then the constant term vanishes by symmetry). In other words, a constant term doesn't affect predictions of conserved operators.
If you include gravity, then a constant term becomes relevant, and you cannot drop it. But the quantisation program doesn't specify a canonical way to choose a constant term: we must resort to experiments to measure it (in other words, the cosmological constant, like most parameters in a theory, cannot be predicted but is an input to the model instead). Or put it another way: if you consider gravity, then the vacuum energy is no longer irrelevant, but it is still arbitrary: no theory can predict its value (as far as we now today).
