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Is there any theory in which every particle can be further subdivided into any number of particles and the total number of particles any where in the space time are infinity in theory and only due to practical constraints that we are capable of observing the known particles in the current World.

Also could you please explain the nature of the two widely accepted theories which explain the small scale and large scale universe which are QP and GR repectively in the current context of the question.

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You may consider every excited state of an atom $\Psi_n$ as another particle. Then their number may be infinite even in this simple example. The higher energy of the system, the higher $n$.

In QFT each particle has occupation numbers. During reactions some occupation numbers decrease, some other increase. Factually QFT equations are the balance equations governing the occupation numbers while interactions.

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In answer to your question, experimental data up to now have given us a number of particles that can be incorporated in the general framework of String Theory, which is a theory that also incorporates the quantization of Gravity.

String Theory does not allow an infinite number of particles if you think of them as being nested like russian dolls, more and more composite. It allows for a mathematical description of the Standard Model which incorporates particles we have seen, also predicts new particles but not in the nested form you are suggesting.

There are many types of infinities: The energy levels of a potential well are infinite, but at some point the distinction of the levels becomes trivial energetically.

At the moment we believe that quarks and leptons are the real "atoms" , i.e. non composite, components of nature.

If these experimental facts are contradicted by new data, it will be a big revolution in theory, including string theory which is aiming at being the theory of everything.

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