Being a noob to the Green Lantern lore, I noticed in his 2011 movie that he was only able to manifest physical expressions of his power through his ring, such as a physical sword, a car, a track, a ray of light etc. Is there any case where he has invoked fear, pestilence, hypnosis or some other non-physical expression through his ring?
No, the green Oan power rings are not limited to generating purely physical manifestations or what are known as light-constructs by the Corps.
However, emotional control (fear) or hypnosis (mind-control) are not necessarily able to be created using the Green Ring. Other color rings may have such emotional control powers (yellow rings can generate fear; violet rings are capable of limited mind control)
They can generate electromagnetic phenomena such as heat or light, and can create any radiation known to the Book of Oa. They may also project this as energy weapons, beams of force, or radiation streams.
They can manipulate all of the fundamental forces and manipulate the fabric of space time.
They are able to generate space-time disruptions such as worm-holes shortening journey which would otherwise take months, even at faster-than-light speeds.
The rings seen in the Green Lantern movies did not appear as powerful as the ones used in the comics (or perhaps the writers weren't truly aware of how powerful they can be in the right hands).
Capabilities of the Power Ring
Green Lantern rings are very complex devices carved psionically from the material of the prime Power Battery on Oa. They function by creating psychoplasmic constructs comprised of an energy similar to that of the Source. These devices are capable of a number of features little known by non-ring wielders:
The constructs are based in light and do not generate heat nor sound unless unless the wielder wishes it. The emerald energy can be used in a variety of ways, usually it is shaped to form objects of varying degrees of complexity depending on the willpower, creativity, and intelligence of the user. The ring is capable of creating any form of radiation and its effects, including such signature and specific signatures such as kryptonite.
There are virtually no limits to the energy constructs the power ring can create, whether giant green boxing gloves or high tech robotic equipment. Some wielders choose a diversity of forms to create while others go for the tried and true.
While there is a psychological advantage of creating an imposing energy construct to unnerve a foe, creativity can only go so far. A strong will is needed to back up that power. Distractions can cause a ring wielder to break concentration and weaken the energy construct. Fear is the greatest enemy of a Green Lantern. Control is needed to wield the power ring effectively. -- Green Lantern Corps
More about Green Lantern Power Rings in my answer to Why do some Green Lanterns talk to their rings when giving a command?.
For the sake of readability, all panels are linked to but not included, as it would distort the bullet lists.
Current power set
As Thaddeus' answer explains, the rings are not limited to producing constructs. Common non-constructs these days include:
- instant translation between languages
- flight and life support (maintaining an adapted pressure, oxygen etc)
- scanning of materials or beings
- instant access to database, and instant databases updates (with new features like shapeshifter detection or lethal force being unlocked)
The above are today's Green Lantern power set; and while the occasional enthusiast writer may pull a stunt with some ring feat never seen before (teleportation of ringless Hal through Kyle's body comes to mind), most of it tries to stay relatively grounded.
Previous power set (now more or less abandoned by writers)
In the past, the 60s notably, cheesy comics used the "most powerful weapon in the universe"/"can do anything you want to" gimmick to inject Green Lantern with whatever crossed the writer's mind at that time (it's true for almost all heroes). For instance, the ring has been shown to be able to...
- read/alterate minds and memories, see Can Green Lantern power rings be used for mind-reading and/or memory alteration? (disclaimer: one of the answers there is mine)
- phase through walls
- shapeshifting other people, into other people or animals (Pieface is later turned into a monkey, then a seagull)
- turn walls into live feeds (arguably this one could be covered by today's hacking feature)
- make ring-images of Hal Jordan (who can later on power him up - conservation of energy much?)
- make the wearer turn invisible
- shrink the wearer (I wouldn't be surprised if enlarging him was also a thing)
All those spanning no more than a dozen issues in total (early Showcase and Green Lantern runs), which is to say how quickly stuff could get
weird creative back then.