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Hello! If you have a Lagrangian (say of a scalar field) depending only on the field and its first derivative and you want to calculate the ground state configuration, is it necessary a constant value? I read about Spontaneous symmetry breaking having this Lagrangian $$L= \frac{1}{2}(\partial_\mu \phi)^2-\frac{1}{2}m^2\phi^2-\frac{\lambda}{4!}\phi^4$$ and they say that to get the lowest energy configuration you set ##\phi## to be a constant and work from there. In the case of a particle it makes sense that a motionless particle would have less energy that a moving one at a point. but is this obvious for fields? Can't a complicate configuration bring the energy lower than a constant value? Thank you!