This negative sign is why our world exists as it does, especially what is called the stability of matter.

Matter is essentially made of what are called fermions, which are described by a mathematical object called a Spinor, like the Dirac field.

A spinor differs from a vector in that after being rotated spatially by 360 degrees, it returns to itself with a negative sign. The unique mathematical behavior of the spinor is what causes the Pauli principle and Fermi statistics, which characterize electrons.

In the image is what is called the Feynman propagator, which consists of the vacuum expectation value of two fields at two different spacetime points or the probability of a particle propagating between these two points. Without this negative sign, relativity, causality, and particle physics based on perturbation theory, which in turn consists of Feynman propagators, would collapse.

In fact, studying why the world's matter is stable due to the behavior of fermions is not easy and it took a long time for some of the most prominent scientists of the twentieth century, namely Walter Thirring and Elliot Lieb, and led to very interesting research.

From Mr. Osama