It is normal for an older child to envy the younger one who replaced him (in his eyes), until this little baby came along all the attention went to him! So maybe if he starts acting like lil bro, he will get the same attention as he does? Some of this you cannot do anything about, but when enteracting with the baby, make sure you include the older one as much as you can. The older one has to learn to share but let him be the one to do it. He also has to learn to respect someone elses space. If he cannot be around the little one without hitting him, then he needs removed from the area and put in another room to play. Altho hitting and tantrums are normal at this age, you still want to discourage it as much as possible, yet respect the rights of the older child too. Reward the good behavior and ignore as much as possible the bad. I think they call this sibling rivalry! LOL
Instead of focusing on showing him you are mad, time outs, ignoring , go the opposite way , he was your baby he is feeling usurped, its very hard on a child, he sees the baby getting most of the attention and he feels left out,so give him some one to one time, let Dad have the baby you do some special things with him, and get Dad to also do the same at 4 year old there are some great ball games and fun those guys can have together. Focus on his positive side and praise him when you see him doing something right.This happens a lot when a new Baby arrives its part of a normal feeling for a child but tough on them lots of attention and hugs will work ...
There could be more than just "jealousy" going on here. Have you discussed his behaviour at school in detail with his teacher - how does he interact with adults, how he interacts with peers, does he eat normally, does he use the washroom at school, is he overly reserved or hyperactive. If the teacher has any concerns, please let us know. - just wondering ....