Renormalized Poincaré algebra for effective particles in quantum field theory

Abstract

Using an expansion in powers of an infinitesimally small coupling constant $g$, all generators of the Poincaré group in local scalar quantum field theory with interaction term $g{\varphi }^3$ are expressed in terms of annihilation and creation operators $a_{\lambda }$ and $a_{\lambda }^{†}$ that result from a boost-invariant renormalization group procedure for effective particles. The group parameter $\lambda$ is equal to the momentum-space width of form factors that appear in vertices of the effective-particle Hamiltonians, $H_{\lambda }$. It is verified for terms order 1, $g$, and $g^2$, that the calculated generators satisfy required commutation relations for arbitrary values of $\lambda$. One-particle eigenstates of $H_{\lambda }$ are shown to properly transform under all Poincaré transformations. The transformations are obtained by exponentiating the calculated algebra. From a phenomenological point of view, this study is a prerequisite to construction of observables such as spin and angular momentum of hadrons in quantum chromodynamics.

17 pages, 5 figures

References in corpus (1)

• Dynamics of Effective Gluons

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