Renormalized Poincar\'e algebra for effective particles in quantum field theory
Phys.Rev. D65 (2002) 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...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
19.10.2001
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Subjects | |
Online Access | Get full text |
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Summary: | Phys.Rev. D65 (2002) 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. |
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DOI: | 10.48550/arxiv.hep-th/0110185 |