Is it theoretically possible to genetically alter humans so that they could live off solar energy like plants? What biological and physiological changes would have to be made?
The basic problem is explained in http://what-if.xkcd.com/17/; there is simply not enough surface area on the average human (or cow) to provide the energy and nutrition needed for a high energy mammalian lifestyle.
This can be addressed in two ways:
Plants can be made more efficient. Current plant life uses solar energy relatively inefficiently, with only a small percentage being converted into actual usable sugars or creating oxygen. While there would be a lot of obstacles to creating plants with efficiencies rivalling high end solar cells (mostly to do with heat rejection), the idea of plants which can convert 5% or more of the incoming solar energy would have lots of advantages, even in traditional applications like agriculture.
Become a symbiont in free space. Since plants are limited in their collecting area by gravity, the ability of a human to carry an acre of photosynthesizing surface will be quite limited on Earth. IF the human is symbiotically paired with a "hyperplant", the plant part can shelter the person inside, and extend its leaves into free space to collect energy, as well as circulate sap for heat control like a giant radiator
Free floating human plant symbionts in orbit would make a great far future setting. Just add water....
Yes, it exists in the fantasy world. Or something close to it. In the Wings Series by Aprilynne Pike, the main character is sort of a human-plant hybrid, though she is called a faerie. Females of her species bloom for one quarter a year (spring faeries bloom in spring, etc), where a flower blossoms on their backs, and if a male of that species is around a blooming female, his body produces pollen on his hands. Faeries need to be in the sun as much as possible, and they only eat fruits and vegetables.
I suppose if you want it to be purely science-fiction, you could try splicing human and plant DNA? Biologically, the change in DNA would do your work for you, but physiologically, you might have to deal with flowers and pollen (how would such hybrids mate) and more basically, the fact that chlorophyll may be produced by the body, causing certain parts of the body to turn green. Then, you'd have to see if the chlorophyll in the body is enough to power the person completely with just water, sunlight and CO2, or if he needs extra nourishment, in which case, a non-vegetarian diet might not agree with him.