further points of discussion

1.we discussed the possibilty of whether all canonical transformations can be represented by rotations of phase space and reasoned that in general it cannot.the reasoning follows the lines of symplectic structure of the poisson brackets which implies that canonical transformations cannot be
in general represented by rotations of phase space.
2.the second pair of maxwell equations
3. we saw that quantum mechanics is a field theory in some sense.this is because we can always obtain the klein-gordon equation (which describes quantum mechanics) from an action which can be said to describe a classical field theory in 0+1 dimension.
4.some discussions on path integrals