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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We investigate the electromagnetic form factor $F(q^2)$ of the meson by usingthe solvable $\phi^{3}$ scalar field model in $(1+1)$ dimensions. As thetransverse rotations are absent in $(1+1)$ dimensions, the advantage of thelight-front dynamics (LFD) with the light-front time $x^+ = x^0 + x^3$ as theevolution parameter is maximized in contrast to the usual instant form dynamics(IFD) with the ordinary time $x^0$ as the evolution parameter. In LFD, theindividual $x^+$-ordered amplitudes contributing to $F(q^2)$ are invariantunder the boost, i.e., frame-independent, while the individual $x^0$-orderedamplitudes in IFD are not invariant under the boost but dependent on thereference frame. The LFD allows to get the analytic result for the one-looptriangle diagram which covers not only the spacelike ($q^{2}<0$) but alsotimelike region ($q^{2}>0$). Using the analytic results, we verify that thereal and imaginary parts of the form factor satisfy the dispersion relations inthe entire $q^{2}$ space. Comparing with the results in $(3+1)$ dimensions, wediscuss the transverse momentum effects on $F(q^2)$ . We also discuss thelongitudinal charge density in terms of the boost invariant variable $\tilde z= p^+ x^-$ in LFD.

Light-front dynamic analysis of the longitudinal charge density using the solvable scalar field model in (1+1) dimensions