本文選題：sine-Gordon-Thirring模型 + 泛函積分��； 參考：《四川師范大學(xué)》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(jì)物理性質(zhì),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(yīng)用于任何非線性系統(tǒng),并根據(jù)微擾理論得到物理模型的近似解。 本文根據(jù)泛函積分方法研究了一維量子sine-Gordon-Thirring模型的統(tǒng)計(jì)物理性質(zhì)。首先,使用微擾和變分泛函積分方法分析了模型的相結(jié)構(gòu)和相的穩(wěn)定性質(zhì);其次研究了黑洞背景和非對易時(shí)空中費(fèi)米物質(zhì)的能量密度漲落,對非對易時(shí)空中的費(fèi)米物質(zhì)能量密度漲落和黑洞內(nèi)部引力場的擾動進(jìn)行了分析。然后,本文研究了標(biāo)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(fèi)米場的能量密度漲落進(jìn)行了比較。 最后,根據(jù)熱核泛函積分方法,研究了黑洞背景中費(fèi)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(jié)果進(jìn)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(dǎo)了一維sine-Gordon-Thirring模型的等效勢和自由能,并在強(qiáng)、弱耦合情況下研究了模型的相結(jié)構(gòu)和穩(wěn)定性質(zhì)。 2、在黑洞背景下推導(dǎo)了sine-Gordon-Thirring模型的自由能與等效勢,計(jì)算了弱耦合和強(qiáng)耦合情況下費(fèi)米物質(zhì)的能量密度,分析了引力場擾動對費(fèi)米物質(zhì)能量密度漲落的影響。 3、計(jì)算了標(biāo)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(fèi)米場能量密度漲落進(jìn)行了比較。 4、根據(jù)熱核泛函積分方法計(jì)算了黑洞背景下玻色場與費(fèi)米場的能量密度漲落,并與變分泛函積分方法得到的結(jié)果進(jìn)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(xué)位授予單位】：四川師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2010
【分類號】：P145.8

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