Is this a sign of jealousy or what?

My boyfriend doesn't like PDA much, especially at school. We've been dating 4 months and he's only held my hand or kissed me a few times at school. But whenever I'm talking to another guy at school he'll come up to me and put his arm around me. I definitely like it a lot. It makes me think he's saying "I hope you know this is MY girl..." without actually saying it. But is this honestly a sign of jealousy or just a coincidence?