quantum field theory - Is space-time a special form of energy?

I know space-time can be influenced by matter and energy, so it must be somehow mingled in with the mix of it all, but does space-time have a fundamental particle? Can we make a little bit of space-time with enough energy? Might the Planck length & time quantize space-time?

Answer

The Einstein field equations relate matter to the deformation of spacetime, i.e.

$$\underbrace{R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R}_{\text{geometry}} = \underbrace{8\pi G T_{\mu\nu}}_{\text{matter}}$$

However, $T_{\mu\nu}=0$ does not imply a trivial solution. A non-trivial solution such as the Schwarzschild metric which describes a spherical body, e.g. a black hole is a solution for a totally vanishing stress-energy tensor. However, as indicated in another answer, we may associate a mass to the solution,

$$M=\frac{R}{2G}$$

in natural untis where $R$ is the Schwarzschild radius (distance from the center to the event horizon) and $G$ is the four-dimensional gravitational constant. As expected, in the limit $M\to 0$ $g_{\mu\nu}$ reduces to,

$$\mathrm{d}s^2 = \mathrm{d}t^2 - \mathrm{d}x^2 -\mathrm{d}y^2 - \mathrm{d}z^2$$

which is flat ($R^{a}_{bcd}=0$) Minkowski spacetime, as expected.

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Does spacetime have a fundamental particle?

Spacetime itself is a manifold, and we do not associate a particle which literally comprises spacetime. However, the graviton is a gauge boson of spin $2$ which is believed to act as the mediator of gravitation which is represented or interpreted as the deformation of spacetime.