When you use second quantization (a quantum theory with the ability to create or destroy particles), the notion of particle identity evaporates. Second quantization is a crucial element of the most fundamental theories.
If you’re using a quantum theory without using second quantization, you follow certain rules—symmetrization or antisymmetrization—that make it look like what you said. Symmetrization and antisymmetrization are also a part of theories with second quantization, but they no longer look like that.
When you use second quantization (a quantum theory with the ability to create or destroy particles), the notion of particle identity evaporates. Second quantization is a crucial element of the most fundamental theories.
If you’re using a quantum theory without using second quantization, you follow certain rules—symmetrization or antisymmetrization—that make it look like what you said. Symmetrization and antisymmetrization are also a part of theories with second quantization, but they no longer look like that.