本文選題：sine-Gordon-Thirring模型 + 泛函積分�。� 參考：《四川師范大學》2010年碩士論文

【摘要】： 通�？刹捎脙煞N方法研究一維非線性量子場論模型的統(tǒng)計物理性質,即:Bethe ansatz方法或泛函積分方法。第一種方法可以給出精確解,但是這種方法只能研究低維物理模型。泛函積分方法可以應用于任何非線性系統(tǒng),并根據微擾理論得到物理模型的近似解。 本文根據泛函積分方法研究了一維量子sine-Gordon-Thirring模型的統(tǒng)計物理性質。首先,使用微擾和變分泛函積分方法分析了模型的相結構和相的穩(wěn)定性質;其次研究了黑洞背景和非對易時空中費米物質的能量密度漲落,對非對易時空中的費米物質能量密度漲落和黑洞內部引力場的擾動進行了分析。然后,本文研究了標量場和玻色Thirring模型的能量密度漲落,并在相同黑洞背景下與費米場的能量密度漲落進行了比較。 最后,根據熱核泛函積分方法,研究了黑洞背景中費米場和玻色場的能量密度漲落,并與泛函積分方法得到的結果進行了比較。 本文的創(chuàng)新工作如下: 1、利用泛函積分方法推導了一維sine-Gordon-Thirring模型的等效勢和自由能,并在強、弱耦合情況下研究了模型的相結構和穩(wěn)定性質。 2、在黑洞背景下推導了sine-Gordon-Thirring模型的自由能與等效勢,計算了弱耦合和強耦合情況下費米物質的能量密度,分析了引力場擾動對費米物質能量密度漲落的影響。 3、計算了標量場和玻色Thirring模型的能量密度漲落,并與相同黑洞背景下的費米場能量密度漲落進行了比較。 4、根據熱核泛函積分方法計算了黑洞背景下玻色場與費米場的能量密度漲落,并與變分泛函積分方法得到的結果進行了對比。
[Abstract]:In general, two methods can be used to study the statistical physical properties of one-dimensional nonlinear quantum field theory models, that is, the ansatz method or the functional integral method. The first method can give the exact solution, but this method can only study the low dimensional physical model. The functional integral method can be applied to any nonlinear system and the approximate solution of the physical model is obtained according to the perturbation theory. In this paper, the statistical physical properties of one-dimensional quantum sine-Gordon-Thirring model are studied by functional integral method. Firstly, the phase structure and phase stability of the model are analyzed by using perturbation and variational functional integral methods, and then the energy density fluctuations of Fermi matter in black hole background and noncommutative space-time are studied. The fluctuation of Fermi matter energy density and the disturbance of gravitational field in black hole are analyzed. Then, the energy density fluctuations of the scalar field and the Boson Thirring model are studied, and the energy density fluctuations of the scalar field and the Boson Thirring model are compared with those of the Fermi field under the same black hole background. Finally, based on the thermonuclear functional integral method, the energy density fluctuations of the Fermi field and the boson field in the black hole background are studied and compared with the results obtained by the functional integration method. The innovative work of this paper is as follows: 1. The equivalent potential and free energy of one-dimensional sine-Gordon-Thirring model are derived by using functional integral method, and the phase structure and stability of the model are studied under strong and weak coupling. 2. Under the background of black hole, the free energy and equivalent potential of sine-Gordon-Thirring model are derived, the energy density of Fermi matter under weak coupling and strong coupling is calculated, and the influence of gravitational field disturbance on the fluctuation of Fermi mass energy density is analyzed. 3. The energy density fluctuations of the scalar field and the boson Thirring model are calculated and compared with those of the Fermi field in the same black hole background. 4. The energy density fluctuations of boson field and Fermi field in black hole background are calculated according to the thermonuclear functional integral method, and the results are compared with those obtained by variational functional integral method.
【學位授予單位】：四川師范大學
【學位級別】：碩士
【學位授予年份】：2010
【分類號】：P145.8

【參考文獻】

相關期刊論文 前10條

1 顏駿,陶必友;二維Dilaton引力模型中的帶電Sine-Gordon孤子解[J];高能物理與核物理;2003年09期

2 顏駿,王順金;泛函積分方法于Dicke模型中的臨界溫度和集體激發(fā)譜[J];量子光學學報;1999年03期

3 李鵬,董會寧;d維正規(guī)格子上圖論因子的機算方案[J];四川大學學報(自然科學版);2002年02期

4 袁敏;;量子Heisenberg磁性薄膜熱動力學性質的研究[J];四川大學學報(自然科學版);2007年02期

5 顏駿;王濤;鄒伯夏;;泛函積分與sine-Gordon-Thirring模型的統(tǒng)計平均值[J];四川師范大學學報(自然科學版);2011年02期

6 俞允強,馬欖,陳時;宇宙常數與宇宙年齡問題[J];天體物理學報;1997年01期

7 陳時,俞允強;宇宙常數和星系團[J];天體物理學報;1997年03期

8 沈有根,陳大明;1+1維黑洞背景時空中的熵[J];天文學報;1999年01期

9 許伯威,陳志堅,丁國輝,章豫梅;sine-Gordon系統(tǒng)中的相圖[J];物理學報;1995年02期

10 陳洪,鄭瑞倫;量子Heisenberg薄膜臨界點的變分累積展開研究[J];物理學報;2000年02期

，

本文編號：1840837