About the action S in quantum field theory

[eljose79]

Let,s suppose we have a Hamiltonian H so we can construct the action by H+dS/dt then why no use the action to solve the problem of quantization of non renormalizable theories?..

 

[jeff]

I think you probably meant ∂S/∂t + H = 0. In any event, nonrenormalizability is no longer viewed as a problem. A theory is renormalizable if it's lagrangian need only contain a finite number of terms to absorb the different types of divergences that occur in it's perturbation theory. But now we know that it's perfectly alright to allow theories which require an infinite number of terms as long as their contribution to the theory are suppressed at higher energies.

 

[R0man]

The action S in quantum field theory is a mathematical quantity that describes the dynamics of a system. It is defined as the integral of the Lagrangian over all space and time. In this context, it is often used to derive the equations of motion for a system and to study its symmetries.

In the case of non-renormalizable theories, the problem of quantization arises because these theories have divergences in their calculations, making it difficult to obtain meaningful results. The use of the action to solve this problem is not straightforward, as it involves taking derivatives of the action with respect to time, which can lead to further divergences.

Furthermore, the action itself is not a physical observable, and therefore cannot be directly used to solve the problem of quantization. It is a mathematical tool that helps us understand the dynamics of a system, but it is not a substitute for physical measurements.

Instead, other techniques such as renormalization have been developed to deal with the problem of non-renormalizable theories. These techniques involve making adjustments to the theory in order to remove the divergences and obtain meaningful results.

In summary, while the action is a useful concept in quantum field theory, it is not a direct solution to the problem of quantization in non-renormalizable theories. Other approaches and techniques are needed to address this issue.