1) Consider the Lagrangian for a real-valued Klein-Gordon field: 2 (1) Let's consider Alice and Bob, each in their own unique inertial frame. Does the Klein-Gordon equation of motion remain consistent across both frames? One straightforward answer is that the Klein-Gordon Lagrangian is inherently a Lorentz scalar. That's correct. However, for our pur- poses, let's examine whether the Lorentz transformation acts as a symmetry transformation. If it does, can you identify the conserved current and charge? Moreover, how does this transformation connect to Newton's first law of motion? Observation: To keep the notation as straightforward as possible, reduce your Minkowski space so that it has just one spatial dimension: x' =t, x x. It might be useful to use the Pauli X matrix: x] = 0 It's recom- mendded that you drop the "x" subscript and just refer to this as the o-matrix