Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-10-19
Phys.Rev. D65 (2002) 065011
Physics
High Energy Physics
High Energy Physics - Theory
17 pages, 5 figures
Scientific paper
10.1103/PhysRevD.65.065011
Using an expansion in powers of an infinitesimally small coupling constant $g$, all generators of the Poincar\'e group in local scalar quantum field theory with interaction term $g \phi^3$ are expressed in terms of annihilation and creation operators $a_\lambda$ and $a^\dagger_\lambda$ 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 Poincar\'e 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.
Głazek Stanisław D.
Masłowski Tomasz
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