NDLI: Born Level Bound States

Content Provider	Springer Nature Link
Author	Hoyer, Paul
Copyright Year	2017
Abstract	Bound state poles in the S-matrix of perturbative QED are generated by the divergence of the expansion in $$\alpha $$ . The perturbative corrections are necessarily singular when expanding around free, $$\mathcal{O}\left( \alpha ^0 \right) $$ in and out states that have no overlap with finite-sized atomic wave functions. Nevertheless, measurables such as binding energies do have well-behaved expansions in powers of $$\alpha $$ (and $$\log \alpha $$ ). It is desirable to formulate the concept of “lowest order” for gauge theory bound states such that higher order corrections vanish in the $$\alpha \rightarrow 0$$ limit. This may allow to determine a lowest order term for QCD hadrons which incorporates essential features such as confinement and chiral symmetry breaking, and thus can serve as the starting point of a useful perturbative expansion. I discuss a “Born” (no loop, lowest order in $$\hbar $$ ) approximation. Born level states are bound by gauge fields which satisfy the classical field equations. Gauss’ law determines a distinct field $$A^0({\varvec{x}})$$ for each instantaneous position of the charges. A Poincaré covariant boundary condition for the gluon field leads to a confining potential for $$q\bar{q}$$ and qqq states. In frames where the bound state is in motion the classical gauge field is obtained by a Lorentz boost of the rest frame field.
Starting Page	1
Ending Page	7
Page Count	7
File Format	PDF
ISSN	01777963
Journal	Few-Body Systems
Volume Number	58
Issue Number	3
e-ISSN	14325411
Language	English
Publisher	Springer Vienna
Publisher Date	2017-04-03
Publisher Place	Vienna
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Particle and Nuclear Physics Nuclear Physics, Heavy Ions, Hadrons Atomic, Molecular, Optical and Plasma Physics
Content Type	Text
Resource Type	Article
Subject	Atomic and Molecular Physics, and Optics

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