عنوان :
بررسي فازهاي هندسي براي ذرات فرميوني در فضازمان كر
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
ذرات بنيادي و نظريه ميدان ها
محل تحصيل :
اصفهان : دانشگاه صنعتي اصفهان
صفحه شمار :
هشت، 64ص. : 4،0،0
توصيفگر ها :
معادله ديراك , نسبيت عام , متريك كر , فاز بري
تاريخ ورود اطلاعات :
1402/06/11
تاريخ ويرايش اطلاعات :
1402/06/11
كد ايرانداك :
03855101-3fd0-4217-9eb9-cac1edde42bb
چكيده فارسي :
ﺩﺭ ﺍﯾﻦ ﭘﺎﯾﺎﻥ ﻧﺎﻣﻪ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻓﻀﺎﺯﻣﺎﻥ ﺧﻤﯿﺪﻩ ﻭ ﻧﺴﺒﯿﺖ ﻋﺎﻡ، ﻭ ﺑﺎﺯﻧﻮﯾﺴﯽ ﻣﻌﺎﺩﻟﻪ ﺩﯾﺮﺍﮎ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻓﺮﻣﻮﻝ ﺑﻨﺪﯼ ﺗﺘﺮﺍﺩﻫﺎ، ﻭﯾﮋﮔﯽ ﻫﺎﯼ ﻫﻨﺪﺳﯽ ﺣﺮﮐﺖ ﯾﮏ ﺫﺭﻩ ﻓﺮﻣﯿﻮﻧﯽ ﺩﺭ ﻓﻀﺎﺯﻣﺎﻥ ﮐﺮ ﺭﺍ ﻣﺮﻭﺭ ﻣﯽ ﮐﻨﯿﻢ. ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻣﺸﮑﻼﺕ ﺑﺮﺭﺳﯽ ﻧﻈﺮﯾﻪ ﻣﯿﺪﺍﻥ ﺩﺭ ﻓﻀﺎﺯﻣﺎﻥ ﺧﻤﯿﺪﻩ ﻓﺮﻣﻮﻝ ﺑﻨﺪﯼ ﺟﺪﯾﺪﯼ ﺗﺤﺖ ﻋﻨﻮﺍﻥ ﻓﺮﻣﻮﻝ ﺑﻨﺪﯼ ﺷﺒﻪ ﻫﺮﻣﯿﺘﯽ ﺳﺎﺧﺘﻪ ﻣﯽ ﺷﻮﺩ، ﮐﻪ ﺩﺭ ﻓﺼﻞ ﺳﻮﻡ ﻣﺮﻭﺭ ﺷﺪﻩ ﺍﺳﺖ. ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻓﺮﻣﻮﻝ ﺑﻨﺪﯼ ﺷﺒﻪ ﻫﺮﻣﯿﺘﯽ ﺍﺯ ﻫﺎﻣﯿﻠﺘﻮﻧﯽ ﺩﯾﺮﺍﮎ، ﺩﯾﻨﺎﻣﯿﮏ ﺫﺭﺍﺕ ﻓﺮﻣﯿﻮﻧﯽ ﺩﺭ ﻓﻀﺎﺯﻣﺎﻥ ﺧﻤﯿﺪﻩ ﻗﺎﺑﻞ ﺑﺮﺭﺳﯽ ﺍﺳﺖ. ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺣﺪ ﻏﯿﺮﻧﺴﺒﯿﺘﯽ ﻣﻌﺎﺩﻟﻪ ﺩﯾﺮﺍﮎ ﻣﯽ ﺗﻮﺍﻥ ﻣﯿﺪﺍﻥ ﻣﻐﻨﺎﻃﻮﮔﺮﺍﻧﺸﯽ ﺭﺍ ﺗﻌﺮﯾﻒ ﮐﺮﺩ ﮐﻪ ﺍﺯ ﻃﺮﯾﻖ ﺁﻥ ﻓﺎﺯ ﻫﻨﺪﺳﯽ ﻣﻮﺳﻮﻡ ﺑﻪ ﻓﺎﺯ ﺑﺮﯼ ﺩﺭ ﻓﻀﺎﺯﻣﺎﻥ ﺧﻤﯿﺪﻩ ﺑﻪ ﺩﺳﺖ ﻣﯽ ﺁﯾﺪ. ﺩﺭ ﻓﺼﻞ ﺁﺧﺮ ﺫﺭﺍﺕ ﻓﺮﻣﯿﻮﻧﯽ ﺑﺎ ﻓﺮﻣﻮﻝ ﺑﻨﺪﯼ ﺷﺒﻪ ﻫﺮﻣﯿﺘﯽ ﺭﺍ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﺘﺮﯾﮏ ﮐﺮ‑ﻧﯿﻮﻣﻦ‑ﺗﺎﺏ‑ﻧﺎﺕ ﻭ ﯾﮏ ﻣﺘﺮﯾﮏ ﺟﺪﯾﺪ ﺩﺭ ﺣﻀﻮﺭ ﻣﯿﺪﺍﻥ ﺍﺳﮑﺎﻟﺮ، ﺑﺮﺍﯼ ﺍﻭﻟﯿﻦ ﺑﺎﺭ ﺑﺮﺭﺳﯽ ﻣﯽ ﮐﻨﯿﻢ.
چكيده انگليسي :
In this thesis, considering general relativity and Dirac’s equation in the form of tetrads formalism, we tried to express the geometric characteristics of the movement of a fermion particle in Kerr spacetime. First, we described general relativity and its properties and then introduced Kerr’s metric. Next, we extended the Dirac equation to curved spacetime and wrote it as a Schrödinger equation. Considering the problems of investigating field theory in curved spacetime, we introduced a new formulation under the quasi-Hermitian formulation. Using the quasi- Hermitian formulation of the Dirac Hamiltonian, we showed the equation we obtained. In the final step, using the non-relativistic limit of the Dirac equation, we defined the magnetogravitational field, and through that, we extended the quantum geometric phase known as the Berry phase to curved spacetime. Finally, we applied the calculations to the Kerr- Newman-Tab-NUT metrics and the generalization of the Tab-NUT metric.
استاد راهنما :
بهروز ميرزا
استاد داور :
حامد بخشيان , سروش شاكري