$ϕ^n$ trajectory bootstrap
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912234645487616 |
|---|---|
| author | Li, Wenliang |
| author_facet | Li, Wenliang |
| contents | We perform an extensive bootstrap study of Hermitian and non-Hermitian theories based on the novel analytic continuation of $\langleϕ^n\rangle$ or $\langle(iϕ)^n\rangle$ in $n$. We first use the quantum harmonic oscillator to illustrate various aspects of the $ϕ^n$ trajectory bootstrap method, such as the large $n$ expansion, matching conditions, exact quantization condition, and high energy asymptotic behavior. Then we derive highly accurate solutions for the anharmonic oscillators with the parity invariant potential $V(ϕ)=ϕ^2+ϕ^{m}$ and the $\mathcal{PT}$ invariant potential $V(ϕ)=-(iϕ)^{m}$ for a large range of integral $m$, showing the high efficiency and general applicability of this new bootstrap approach. For the Hermitian quartic and non-Hermitian cubic oscillators, we further verify that the non-integer $n$ results for $\langleϕ^n\rangle$ or $\langle(iϕ)^n\rangle$ are consistent with those from the wave function approach. In the $\mathcal{PT}$ invariant case, the existence of $\langle(iϕ)^n\rangle$ with non-integer $n$ allows us to bootstrap the non-Hermitian theories with non-integer powers, such as fractional and irrational $m$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05778 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $ϕ^n$ trajectory bootstrap Li, Wenliang High Energy Physics - Theory Statistical Mechanics High Energy Physics - Lattice Nuclear Theory Quantum Physics We perform an extensive bootstrap study of Hermitian and non-Hermitian theories based on the novel analytic continuation of $\langleϕ^n\rangle$ or $\langle(iϕ)^n\rangle$ in $n$. We first use the quantum harmonic oscillator to illustrate various aspects of the $ϕ^n$ trajectory bootstrap method, such as the large $n$ expansion, matching conditions, exact quantization condition, and high energy asymptotic behavior. Then we derive highly accurate solutions for the anharmonic oscillators with the parity invariant potential $V(ϕ)=ϕ^2+ϕ^{m}$ and the $\mathcal{PT}$ invariant potential $V(ϕ)=-(iϕ)^{m}$ for a large range of integral $m$, showing the high efficiency and general applicability of this new bootstrap approach. For the Hermitian quartic and non-Hermitian cubic oscillators, we further verify that the non-integer $n$ results for $\langleϕ^n\rangle$ or $\langle(iϕ)^n\rangle$ are consistent with those from the wave function approach. In the $\mathcal{PT}$ invariant case, the existence of $\langle(iϕ)^n\rangle$ with non-integer $n$ allows us to bootstrap the non-Hermitian theories with non-integer powers, such as fractional and irrational $m$. |
| title | $ϕ^n$ trajectory bootstrap |
| topic | High Energy Physics - Theory Statistical Mechanics High Energy Physics - Lattice Nuclear Theory Quantum Physics |
| url | https://arxiv.org/abs/2402.05778 |