Spontaneous symmetry breaking refers to the solution of a system loses some symmetry in its Lagrangian. Consider a Simple Harmonic Oscillator, its lagrangian is time translationally invariant but its solution is periodic in time, thus not time-translational invariant. Is this Spontaneous...
Vectors and covectors transform differently with Jacobian Matrices inverse of each other. However, what is the general coordinate transformation is a simple translation of coordinates, the Jacobian Matrix will be trivially a delta and contains no information of how much the translation is. How...