-д хадгалсан:
| Үндсэн зохиолч: | |
|---|---|
| Формат: | Recurso digital |
| Хэл сонгох: | |
| Хэвлэсэн: |
Zenodo
2026
|
| Нөхцлүүд: | |
| Онлайн хандалт: | https://doi.org/10.5281/zenodo.19960577 |
| Шошгууд: |
Шошго нэмэх
Шошго байхгүй, Энэхүү баримтыг шошголох эхний хүн болох!
|
Агуулга:
- <p>This work presents an effective field theory extension of nonrelativistic quantum mechanics incorporating a higher-dimensional coupling between a scalar field and the Kretschmann scalar <span class="katex"><span class="katex-mathml">K=RμνρσRμνρσK = R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}</span><span class="katex-html"><span class="base"><span class="mord mathnormal">K</span><span class="mrel">=</span></span><span class="base"><span class="mord"><span class="mord mathnormal">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">μν</span><span class="mord mathnormal mtight">ρ</span><span class="mord mathnormal mtight">σ</span></span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mord"><span class="mord mathnormal">R</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">μν</span><span class="mord mathnormal mtight">ρ</span><span class="mord mathnormal mtight">σ</span></span></span></span></span></span></span></span></span></span></span>. Starting from a covariant action with quadratic curvature invariants and a dimension-8 operator suppressed by a cutoff scale <span class="katex"><span class="katex-mathml">Λ\Lambda</span><span class="katex-html"><span class="base"><span class="mord">Λ</span></span></span></span>, we derive a modified Klein–Gordon equation and perform a controlled weak-curvature nonrelativistic reduction.</p> <p>The resulting effective Schrödinger equation contains the standard Newtonian gravitational potential together with a curvature-squared correction proportional to <span class="katex"><span class="katex-mathml">K/Λ4K/\Lambda^4</span><span class="katex-html"><span class="base"><span class="mord mathnormal">K</span><span class="mord">/</span><span class="mord">Λ<span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span></span></span></span></span></span></span>. In Schwarzschild spacetime, this induces a distinct tidal potential scaling as <span class="katex"><span class="katex-mathml">1/r61/r^6</span><span class="katex-html"><span class="base"><span class="mord">1/</span><span class="mord"><span class="mord mathnormal">r</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">6</span></span></span></span></span></span></span></span></span></span>, making the effect sensitive to strong gravitational curvature rather than the integrated potential.</p> <p>We compute the leading energy shifts and derive phenomenological constraints on the EFT cutoff scale, finding consistency with current observational bounds for <span class="katex"><span class="katex-mathml">Λ≳1012−1014 GeV\Lambda \gtrsim 10^{12} - 10^{14}\,\text{GeV}</span><span class="katex-html"><span class="base"><span class="mord">Λ</span><span class="mrel amsrm">≳</span></span><span class="base"><span class="mord">1</span><span class="mord">0<span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">12</span></span></span></span></span></span></span><span class="mbin">−</span></span><span class="base"><span class="mord">1</span><span class="mord">0<span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">14</span></span></span></span></span></span></span><span class="mord text"><span class="mord">GeV</span></span></span></span></span>. Extensions to time-dependent curvature are also discussed, showing that the same operator structure leads to parametrically driven quantum corrections.</p> <p>This paper provides a systematic and self-consistent EFT framework for exploring curvature-squared corrections to quantum dynamics in gravitational backgrounds.</p>