I have used pbrt to render my scene. I have specified the viewing angle in the scene file and on rendering it with pbrt I see the image from that specific viewing angle. I want to know if there exists a way by which I can rotate the scene rendered by pbrt using my mouse in real time
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No.
To see if it is even possible, render a scene and time how ling it takes. In order to get it real-time you will need pbrt to render at least a few frames a second, preferably 60!
I don't think this is going to happen in 2016.
Alternatively you will need something like an OpenGL representation to perform the real-time interaction and then the rendered scene can only be displayed over the top (once the rendering has been finished). the frustums need to match in order for you to do this otherwise what the user interacts with will not be the same as what they see rendered.
If your editing the scene file, it sounds like your not in coding land and so the only possibility is to write some program that can display the scene (in GL) and update the scene file information to be the same as the current camera and render using pbrt. Its all going to take a long time (pbrt needs to parse the file each time, and re-buffer all the geometry) since supplying the file means pbrt won't save anything from the previous state and so will have to construct acceleration structures etc as well as rendering the scene. Each frame!
Even in code pbrt is not going to give you great performance. It's not designed for that, more to be a physically accurate path tracer (as the name suggests). In order to get anything remotely near real-time, you'll need some bad ass acceleration structures and better command of the light model you are using. If you really are interested your probably need to write your own renderer. Look into Metropolis Light Transport (MLT) and Vertex connect merge (VCM), which are much more refined/efficient models using Monte Carlo method.
Plus some pretty decent hardware with lots of cores, or a decent gfx card if wish to employ SIMD through Cuda or equivalent.
[EDIT] Also note that the pbrt renderer, is based on a book "Physically Based Rendering (From Theory to Implementation)" ISBN-13: 978-0123750792. Which outlines how to implement your own version of pbrt.