Question about quantization of scalar field

[martyf]

Why the quantization of scalar field resolves the energy negative problem that exist in the klein-gordon equation?

 

[olgranpappy]

Because the time dependence of the scalar fields is not related to the energy of the particles as it was in single particle quantum mechanics.

 

[Entropia]

The quantization of scalar fields resolves the energy negative problem in the Klein-Gordon equation by introducing the concept of discrete energy levels. In classical physics, energy is considered to be continuous and can take on any value. However, in quantum mechanics, energy is quantized and can only exist in discrete levels. This means that the energy of a system can only take on specific values, rather than a continuous range.

In the Klein-Gordon equation, the energy negative problem arises because the equation allows for negative energy states. This is problematic because it goes against the fundamental principles of quantum mechanics, where energy must be positive. By quantizing the scalar field, we restrict the energy levels to only positive values, thus resolving the energy negative problem.

Furthermore, the quantization of scalar fields also leads to the concept of antiparticles, which have the same mass as particles but opposite charge. This allows for a more complete description of particle interactions and eliminates the need for negative energy states.

In summary, the quantization of scalar fields resolves the energy negative problem in the Klein-Gordon equation by introducing discrete energy levels and the concept of antiparticles, which are both fundamental principles in quantum mechanics.