Boosting QED and QCD bound states in the path integral formalism

Abstract

Wave functions and energy eigenvalues of the path integral Hamiltonian are studied in Lorentz frame moving with velocity $v$. The instantaneous interaction produced by the Wilson loop is shown to be reduced by an overall factor $\sqrt{1-(\frac{v}{c}{)}^2}$. As a result one obtains the boosted energy eigenvalues in the Lorentz covariant form $E= \sqrt{\veP^2+M^2_0}$, where $M_0$ is the c.m. energy, and this form is tested for two free particles and for the Coulomb and linear interaction.Using Lorentz contracted wave functions of the bound states one obtains the scaled parton wave functions and valence quark distributions for large $P$. Matrix elements containing wave functions moving with different velocities strongly decrease with growing relative momentum, e.g. for the time-like formfactors one obtains $F_h(Q_0)\sim (\frac{M_h}{Q_0}{)}^{2n_h}$ with $n_h=1$ and 2 for mesons and baryons, as in the "quark counting rule".

arXiv comment23 pages,one figure,misprints corrected

References in corpus (21)

• The Confinement
• The Feynman-Schwinger representation in QCD
• Hamiltonian Relativistic Two-Body Problem: Center of Mass and Orbit Reconstruction
• The hbar Expansion in Quantum Field Theory
• Perturbative expansions in QCD and analytic properties of alpha_s
• Relativistic path integral and relativistic Hamiltonians in QCD and QED
• Hydrogen Atom in Relativistic Motion
• Spin interactions in mesons in strong magnetic field
• Relativistic theory of string breaking in QCD
• Boosting equal time bound states
• Theory of hadron decay into baryon-antibaryon final state
• Boost operators in Coulomb-gauge QCD: the pion form factor and Fock expansions in phi radiative decays
• QED spectra in the path integral formalism
• Microscopic study of the string breaking in QCD
• Lorentz Contraction of Bound States in 1+1 Dimensional Gauge Theory
• Annihilation range and final-state interaction in the antiproton-proton annihilation into pi-pi+
• The QCD spectrum: mixing, strong decays and the role of sea quarks
• Theory of time-like baryon form factors near thresholds
• Poincaré invariant quantum theory, J. Lab lectures
• The N-Quantum Approximation and Bound States in Motion
• Regge Behavior of DIS Structure Functions

Cited by in corpus (9)

• Field Correlator Method for the confinement in QCD
• Nonperturbative approach to the parton model
• The fundamental scale of QCD
• Proton and neutron form factors with quark orbital excitations
• Strong decays with the boost-corrected wave functions
• Hadron Form Factors with the Boost-Corrected Wave Functions
• Hadron wave functions in high-energy scattering, form factors and strong decays: the effects of the Lorentz contracted form
• Lorentz contraction of the equal-time Bethe-Salpeter amplitude in two-dimensional massless quantum electrodynamics
• Nonperturbative parton distributions and the proton spin problem