Dr. Michio Kaku is a theoretical physicist, best-selling author, and popularizer of science. A fascinating exploration of the science of the impossible.
Dear Dr.I am writing to you because I need your help in terms of a question in one of your books “ quantum field theory : a modern introduction” I tried my best to get the answer but I could not unluckily get it. If you do me a favor to give me the correct answer it would be appreciated you.Many thanks in advance1.Since the action principle must be satisfied in the new coordinates then pq ̇-H must be equal to PQ ̇-H ̃ up to a total derivative that is up to some arbitrary function F ̇. show that without losing any generality we can take F to be one of four functions given by :F_1(q,Q,t) ,F_2(q,P,t) ,F_3(p,Q,t) or F_4(p,P,t).2.If we choose F= F_1 (q,Q,t) then prove that p = (∂F_1)/( ∂q) ,P=-∂F/∂Q and H ̃=H+F ̇_1 .3.What are the analogous relations for the other three F_i function.
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