Dirac alanı için kuantum boşluk enerjisi
Küçük Resim Yok
Tarih
2021
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Trakya Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu çalışmada; geri zeminde var olan kütlesiz Dirac Alanı'nın içine yerleştirilmiş paralel plakalar ve küresel kabuğun Casimir enerjisi yeniden hesaplanacaktır. Dirac alanı için, MIT veya "bag" sınır koşulunu uyularak, elde edilen modların toplamı göz önüne alınarak, modların toplamı yöntemi ile hem paralel plakalar hemde küresel kabuk için, renormalize edilmiş Casimir enerji elde edilmiştir. Kuantum boşluk enerjisi sonsuz bir nicelliği temsil eder, onu sonluya dönüştermek için birinci problemde üstel fonksiyonlarının özelliklerini ve ikinci problemde zeta fonksiyonu kullanılmıştır. Bu dönüşme regülarizasyon denir. Kuantum boşluk enerjisinin regülarizasyondan sonra bazı ıraksak katkılar hala mevcut olmaktadır, kuantum boşluk enerjisi üzerine bu katkıları çıkartmak için renormalizasyonu yapılmıştır. "Heat Kernel" katsayıları kullanılarak renormalizasyon gerçekleştirilmiştir. İki plaka arasında Dirac alanı için çekici ve küresel kabuk itici Casimir kuvvetini elde edilmiştir. Elde edilen sonuçlar, literatür ile uyumludur. Regülarizasyon ve renormalizasyon yöntemleri göz önüne alındığında; elimizde, yegâne bir matematiksel teknik bulunmadığından, farklı kuantum alanları için farklı geometrideki kuantum boşluk enerjisi çalışmaları bize yeni gelişmeler sunacaktır. Bu çalışmadan kazanılan birikimle eş merkezli iki küre arasındaki Dirac alanının Casimir etkisi gelecekte tartışılacaktır.
In this thesis it was recalculated the Casimir energy between two parallel plates and for the spherical shell placed in the ground state of Dirac field. The renormalized Casimir energy was obtained for Dirac field for both parallel planes and spherical shell by the mode summation method. Therefore, during the calcultaions it was used the mode summation function while the field obeys the MIT or "bag" boundary condition. The vacuum energy represents an infinite quantity therefore for the first problem were used the properties of the exponential function to transform that quantity into finite; whereas for the second problem was used zeta function. This transformation is called regularization. After the regularization of vacuum energy in spherical shell geometry some divergent contributions still appear. Hence upon vacuum energy, it was done the renormalization to eleminate these contributions. Renormalization is done by using heat kernel coefficients. Casimir force for Dirac field between two parallel planes is founded to be attractive and in spherical shell repulsive. The results obtained are compatible with previous calculations by many researchers. There is no unique mathematical technique in concern with the regularization and renormalization methods, hence the studies upon quantum vacuum energy for different quantum fields in different geometries will provide us with new outcomes. With the conclusions provided by this study, in the future will be discussed the Casimir effect between two concentric spheres.
In this thesis it was recalculated the Casimir energy between two parallel plates and for the spherical shell placed in the ground state of Dirac field. The renormalized Casimir energy was obtained for Dirac field for both parallel planes and spherical shell by the mode summation method. Therefore, during the calcultaions it was used the mode summation function while the field obeys the MIT or "bag" boundary condition. The vacuum energy represents an infinite quantity therefore for the first problem were used the properties of the exponential function to transform that quantity into finite; whereas for the second problem was used zeta function. This transformation is called regularization. After the regularization of vacuum energy in spherical shell geometry some divergent contributions still appear. Hence upon vacuum energy, it was done the renormalization to eleminate these contributions. Renormalization is done by using heat kernel coefficients. Casimir force for Dirac field between two parallel planes is founded to be attractive and in spherical shell repulsive. The results obtained are compatible with previous calculations by many researchers. There is no unique mathematical technique in concern with the regularization and renormalization methods, hence the studies upon quantum vacuum energy for different quantum fields in different geometries will provide us with new outcomes. With the conclusions provided by this study, in the future will be discussed the Casimir effect between two concentric spheres.
Açıklama
Yüksek Lisans
Anahtar Kelimeler
Fizik ve Fizik Mühendisliği, Physics and Physics Engineering
