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Hamiltonian mechanics electromagnetic field 
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#1
Jan1912, 01:49 PM

P: 321

1. The problem statement, all variables and given/known data
Let (V(x,t) , A(x,t)) be a 4vector potential that constructs the electromagnetic field (in gaussian Units) by E(x,t) = ∇V(x,t)  (1/c)δ_{t}A(x,t) , B = ∇xA , (x,t) elements of R^{3}xR^{t} Consider the lagrangian L=.5mv^{2}  eV(x,t) + (ev/c)(dot)A(x,t) a) compute and interpret the Eulerlagrange equatinons of motion for this system b) determine the hamiltonian c) determine hamilton's equations of motion. Are they gauge invariant? 2. Relevant equations 3. The attempt at a solution 3 simple questions about this, and hopefully not too stupid of questions when i apply the eulerlagrange equations do i take the curl of A or the gradient? if gradient what does that mean to take the ∇A? is there only one equation of motion because i fail to see the other possibility if there is one. Otherwise i can solve the rest thanks 


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