Let's talk about general relativity first. In GR, the gravitational field is described as the geometric effect of space-time, and gravity is determined by the energy dynamics tensor, which is equivalent to Einstein tensor describing the geometric form of space-time. It can be seen that the gravitational field is different from the traditional field theory, and it does not depend on a certain space-time background (or GR is a background-independent theory). As for the field in quantum field theory, it needs to be discussed in different situations: 1. One is the Quantum Field Theory (QFT) that everyone usually discusses. It depends on the space-time background and can be said to be a quantized classical field. The quantization here needs to consider renormalization methods, such as QED, which is the most successful example. A very important reason why the gravitational field is difficult to be quantized is that it cannot be renormalized directly, which is related to the properties of GR. Of course, not all QFT without gravity can be renormalized, such as the four fermions theory. . But now there is a theory that can describe the weak interaction well, and Weinberg, Salam and others have realized the electric weak unity. 2. There is topological quantum field theory (TQFT). Some correlation functions of this theory do not depend on the measurement of space-time manifold, but it has only a limited number of global degrees of freedom and no local degrees of freedom. Simply put, the difference with QFT is that QFT tends to be "object-oriented", while t QFT is more "relationship-oriented". The relatively advanced progress in this field needs to be described by high-dimensional category theory. A theory related to TQFT is Loop Quantum Gravitation Theory (LQG), which is different from string theory in that it attempts to directly quantize GR. However, instead of using the traditional quantization scheme, we separate the regular variables from the background to realize regular quantization, but this will change the regular variables themselves. In addition, even if LQG is background-independent to some extent, it still needs a specific spatio-temporal topology, and it is difficult to transition to the traditional GR, so there are still many problems. . Other theories, such as scaling relativity (which does not seem to satisfy gauge symmetry), Verlinde entropy force theory (which is not as accurate as dark matter theory), noncommutative geometry and so on. Some people are very optimistic about noncommutative geometry, but for the grand unified theory including gravity, people have used almost all the geometry in mathematics, and there are still many problems that cannot be solved. Algebra? It is said that both string theory and LQG use category theory, but the mathematical tools seem to be insufficient.