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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A system consisting of a point particle coupled to gravity is investigated.The set of constraints is derived. It was found that a suitable superpositionof those constraints is the generator of the infinitesimal transformations ofthe time coordinate $t\equiv x^0$ and serves as the Hamiltonian which gives thecorrect equations of motion. Besides that, the system satisfies the mass shellconstraint, $p^\mu p_\mu - m^2 = 0$, which is the generator of the worldsheetreparametrizations, where the momenta $p_\mu$, $\mu=0,1,2,3$, generateinfinitesimal changes of the particle's position $X^\mu$ in spacetime.Consequently, the Hamiltonian contains $p_0$, which upon quantization becomesthe operator $- i \partial/\partial T$, occurring on the r.h.s. of theWheeler-DeWitt euqtion. Here the role of time has the particle coordinate $X^0\equiv T$, which is a distinct concept than the spacetime coordinate $x^0\equiv t$. It is also shown how the ordering ambiguities can be avoided if aquadratic form of the momenta is cast into the form that instead of the metriccontains the basis vectors.

On the Coupling of Relativistic Particle to Gravity and Wheeler-DeWitt Quantization