| 姓名 |
梅吉莎(Kiersten Meigs)
查詢紙本館藏 |
畢業系所 |
物理學系 |
| 論文名稱 |
(Electromagnetic Waves on Spheres)
|
| 相關論文 | |
| 檔案 |
 [Endnote RIS 格式]
[Bibtex 格式]
 [相關文章]  [文章引用]  [完整記錄]  [館藏目錄]  至系統瀏覽論文 (2030-1-1以後開放)
|
| 摘要(中) |
我們透過分析電磁波的格林函數來研究電磁波在球形時空中的傳播。我們採用純量向量分
解來求解 2 球面上的麥克斯韋方程組，並僅根據純量格林函數表達其解。然後，我們概述了
一種使用 integral-differential operator 從熱核計算相關格林函數的方法，該算子將不同維度
的相應熱核關聯起來，以便所有這些都可以從 1維球體解生成。我們將此方法應用於 2 維
和 3 維球體，並獲得有質量和無質量格林函數的結果。我們注意到，當質量下降到由空間維
度D 確定的某個值以下時，我們的結果顯示出非因果傳播。突出的因果關係問題。 |
| 摘要(英) |
We here study the propagation of electromagnetic waves in spherical spacetimes by analyz-
ing their Green’s functions. We employ a scalar-vector decomposition to solve Maxwell’s
equations on the 2-sphere and write their solutions solely in terms of scalar Green’s func-
tions. We then outline a method for calculating the relevant Green’s functions from their
heat kernels using an integral-differential operator which relates the corresponding heat
kernels in different dimensions, so that all of them may be generated from the 1-sphere
solution. We apply this method to the 2 and 3 dimensional spheres and obtain results
for both the the massive and massless Green’s functions. We note that our results display
acausal propagation when the mass drops below a certain value determined by the spatial
dimension D. In the future, we hope to extend our results to general dimensional spherical
spacetimes and address any outstanding causality issues that remain. |
| 關鍵字(中) |
★ 電磁波
★ 球體
★ 格林函數 |
關鍵字(英) |
★ Electromagnetic Waves
★ Spheres
★ Green′s Functions |
| 論文目次 |
Contents
1 Introduction 1
2 Maxwell’s Equations on R × S2 3
2.1 Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Magnetic Field Fij . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Electric Field F0i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Relation Between Tensor and Scalar Green’s Functions . . . . . . . . . . . . . 11
3 Symmetric Green’s Function from Heat Kernel 13
3.1 Feynman Green’s Function from Heat Kernel . . . . . . . . . . . . . . . . . . . 13
3.2 Symmetric Green’s Function from Feynman Green’s Function . . . . . . . . . 14
4 Green’s Functions from Heat Kernels 15
4.1 Intertwining Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 S3 × R (Einstein Static Universe) Symmetric Green’s Function . . . . . . . . . 16
4.2.1 Massive Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.2.2 Massless Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.3 2+1D Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.3.1 Massive Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.3.2 Massless Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5 Conclusion 21
A Comparison against Feynman Green’s Function in [3] 22
Bibliography 25 |
| 參考文獻 |
Bibliography
[1] Arlen Anderson. “Operator method for finding new propagators from old”. In: Physi-
cal Review D 37.2 (1988), p. 536.
[2] Arlen Anderson and Roberto Camporesi. “Intertwining operators for solving differ-
ential equations, with applications to symmetric spaces”. In: Communications in math-
ematical physics 130 (1990), pp. 61–82.
[3] Roberto Camporesi. “Harmonic analysis and propagators on homogeneous spaces”.
In: Physics Reports 196.1-2 (1990), pp. 1–134.
[4] Marc Casals and Brien C Nolan. “Kirchhoff integral approach to the calculation of
Green’s functions beyond the normal neighborhood”. In: Physical Review D—Particles,
Fields, Gravitation, and Cosmology 86.2 (2012), p. 024038.
[5] Yi-Zen Chu. “A line source in Minkowski for the de Sitter spacetime scalar Green’s
function: Massless minimally coupled case”. In: Journal of Mathematical Physics 55.9
(2014).
[6] Sam R Dolan and Adrian C Ottewill. “On an expansion method for black hole quasi-
normal modes and Regge poles”. In: Classical and Quantum Gravity 26.22 (2009),
p. 225003.
[7] Sam R Dolan and Adrian C Ottewill. “Wave propagation and quasinormal mode ex-
citation on Schwarzschild spacetime”. In: Physical Review D—Particles, Fields, Gravita-
tion, and Cosmology 84.10 (2011), p. 104002.
[8] Abraham I Harte and Theodore D Drivas. “Caustics and wave propagation in curved
spacetimes”. In: Physical Review D—Particles, Fields, Gravitation, and Cosmology 85.12
(2012), p. 124039.
[9] Amos Ori. “private communication (2008) and report (2009)”. available at http://
physics.technion.ac.il/~amos/acoustic.pdf. |
| 指導教授 |
瞿怡仁(Yi-Zen Chu)
|
審核日期 |
2025-1-20 |
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