English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In QCD with $N_c$ colors the anti-symmetric valence quark color space singletstate $\sim \epsilon_{i_1\cdots i_{N_c}} |i_1,\cdots, i_{N_c}\rangle$ of theproton corresponds to the reduced density matrix $\rho_{ij}=(1/N_c)\delta_{ij}$ for a single color degree of freedom. Its degenerate spectrum ofeigenvalues, $\lambda_i=1/N_c$, the purity $\mathrm{tr}~\rho^2 = 1/N_c$, andthe von~Neumann entropy $S_\mathrm{vN}=\log(N_c)$ all indicate maximalentanglement of color. On the other hand, for $N_c\to\infty$ the spatial wavefunction of the proton factorizes into valence quark wave functions determinedby a mean field (E. Witten, Nucl. Phys. B 160 (1979) p. 57) where there is noentanglement of spatial degrees of freedom. A model calculation at $N_c=3$using a simple three quark model light-front wave function by Brodsky andSchlumpf, predicts percent level entanglement of spatial degrees of freedom.Using light-cone perturbation theory we also derive the density matrixassociated with the four parton $|qqqg\rangle$ Fock state. Tracing out thequarks, we construct the reduced density matrix for the degrees of freedom ofthe gluon, which encodes its entanglement with the sources. Our expressionsprovide the dependence of the density matrix on the soft cutoff $x$ for thegluon light-cone momentum, and on the collinear and ultraviolet regulators.Numerical results obtained in a simple approximation indicate strongerentanglement for the gluon (with $x_g < \langle x_q\rangle$) than for quarks inthe three quark Fock state.

Quark and gluon entanglement in the proton on the light cone at intermediate $x$