At what level of theory? Is the planet still a solid ball with 99.9% of its mass unused in its depths? Are humans still 50-100 kg masses of biological metabolism, and not, say, programs being simulated on small computers? Not trying to be pretentious, but I think the question needs to be more specific.
Here's two soft limits.
The solar power incident on the earth is on the order of 10^17 watts -- harnessing more than this means creating structures much larger than the earth, at which point it's not really "the same planet" (most of the surface area would have to be non-planet). Humans metabolize on the order of 10^2 watts, just like desktop computers. So, 10^17/10^2 = 10^15 humans, one quadrillion,
Suppose instead the earth uses an energy source much more powerful than its surface solar power (e.g. fusion power). Then one limit is how much heat can be produced without temperature reaching impossible levels. Basically, heat rejection is by thermal radiation into space (no conduction); the power goes as T^4 [1]. Right now we're rejecting on the order of 10^17 W (same as the solar input -- it's balanced), at about 300 Kelvin. So without changing the surface environment drastically, we can't really go above 10^17 W. But if we're willing to do drastic terraforming -- living in underground air-conditioned chambers with Herculean heat pumps everywhere, leading to an uninhabited surface hotter than molten iron (the Great Radiator), you could push the limit above that. At a surface temperature of 3000 Kelvin (~2700 C), that's 10 times what it is now, so the thermal radiation would be 10^4 times = 10,000 times larger. We could reject 10^21 W, enough to power 10^19 humans. (Which would comprise 0.01% of the earth's entire mass! Bit like Hong Kong really.)
Organic (CNHO) chemicals aren't in the slightest dependent on petroleum, it is only a passing quirk of the early 21st-century economy that oil and natural gas byproducts are the most common chemical feedstocks. CNHO atoms are everywhere on earth, and they're not going anywhere (mass doesn't leave the earth, for the most part). Basic organic chemistry building-blocks, e.g. ethylene, are not much more difficult to obtain from biological matter (e.g. ethanol) than from oil/gas. Organic chemistry -- insecticides, plastics, pharma, what have you -- isn't going anywhere, and this is all a silly misunderstanding from confused Malthusians.
...aquifers...
...artificial irrigation...
There's no theoretical limit to artificial irrigation (well there is, but it's ludicrous). In refutation: nuclear or solar powered ocean desalination plants, with aqueducts, large pipes, or underground canals piping freshwater inland -- thousands of miles if need be. Elementary, existing technology, and I think not too far from economic feasibility even today. Desalination is already economic (if not directly competitive with natural freshwater sources, when they are available) -- lots of it in the Middle East, Southeast Asia. Aqueducts are ancient technology.
...phosphorus fertilizers...
Nothing stopping us from recycling phosphorus -- it's not like we're flinging it off the earth into space. The whole earth is a closed cycle for chemicals -- water, CNOH, trace minerals, all of them sustainable. Since the issue is framed as "maximum theoretical", well, in the limit we can ion-exchange phosphorus out of the seas -- the ultimate repository for "used" phosphorus. (Although in the nearer term there's more simple resolutions, like preventing runoff waste, recovery from sewers/rivers, mining new types of phosphorus minerals, etc.)
But the green revolution is totally unsustainable.
Ignorance is totally unsustainable. Please conserve.
Here's two soft limits.
The solar power incident on the earth is on the order of 10^17 watts -- harnessing more than this means creating structures much larger than the earth, at which point it's not really "the same planet" (most of the surface area would have to be non-planet). Humans metabolize on the order of 10^2 watts, just like desktop computers. So, 10^17/10^2 = 10^15 humans, one quadrillion,
Suppose instead the earth uses an energy source much more powerful than its surface solar power (e.g. fusion power). Then one limit is how much heat can be produced without temperature reaching impossible levels. Basically, heat rejection is by thermal radiation into space (no conduction); the power goes as T^4 [1]. Right now we're rejecting on the order of 10^17 W (same as the solar input -- it's balanced), at about 300 Kelvin. So without changing the surface environment drastically, we can't really go above 10^17 W. But if we're willing to do drastic terraforming -- living in underground air-conditioned chambers with Herculean heat pumps everywhere, leading to an uninhabited surface hotter than molten iron (the Great Radiator), you could push the limit above that. At a surface temperature of 3000 Kelvin (~2700 C), that's 10 times what it is now, so the thermal radiation would be 10^4 times = 10,000 times larger. We could reject 10^21 W, enough to power 10^19 humans. (Which would comprise 0.01% of the earth's entire mass! Bit like Hong Kong really.)
http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law