Is work done when you carry a book across the room at a constant velocity

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Work is not done when you carry an object forward. You may have learnt that carrying an object and moving horizontally at a constant velocity has no work done. The truth is, there is a slight amount of work done due to overcoming air resistance in the horizontal direction.

"No" according to the work energy theorem about work is done when there is a change in final and initial velocity. But if I use Work = Force x displacement, even though the velocity is constant there is still some displacement done by the (constant) force acting on it.

a physical change is being made.

ok yes, but what is the question? as soon as you ask the actual question i will answer it. : )