Complex Klein Gordon Field

Question 1

For what field can we associate a conserved charge with the field?

Answer 1

Only for the complex Klein Gordon Field

Question 2

The Lagrangian density for the complex Klein Gordon Field

Answer 2

L (x) = ∂αφ†(x)∂αφ(x) − 2φ†(x)φ(x).

Question 3

Treating the field and its adjoint as independent fields leads to the same equation for both fields. What equation?

Answer 3

The Klein-Gordon equation

Question 4

Write the continuity equation

Answer 4

partial_mu j^mu = 0