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Can someone explain to me how the concept of particle is defined in lattice QCD?

Here are the reasons why it seems problematic to me:

1) Lattice QCD is based on functional-integral formulation of QFT, which does not contain any operators in the Hilbert space. In particular, it does not contain the particle creation and destruction operators.

2) It is a non-perturbative theory with confinement, which means that one cannot define particles though the LSZ reduction based on assumption that asymptotic states are free particle states (quarks and gluons).

References in which these things are explained would be highly desirable.

Also, if one knows a simpler toy model of a non-perturbative definition of particles in interacting QFT, that might be even more interesting.

Here are the reasons why it seems problematic to me:

1) Lattice QCD is based on functional-integral formulation of QFT, which does not contain any operators in the Hilbert space. In particular, it does not contain the particle creation and destruction operators.

2) It is a non-perturbative theory with confinement, which means that one cannot define particles though the LSZ reduction based on assumption that asymptotic states are free particle states (quarks and gluons).

References in which these things are explained would be highly desirable.

Also, if one knows a simpler toy model of a non-perturbative definition of particles in interacting QFT, that might be even more interesting.

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