泛函积分方法与黑洞背景下物质能量密度涨落的研究

发布时间：2018-05-04 00:40

本文选题：sine-Gordon-Thirring模型 + 泛函积分　；参考：《四川师范大学》2010年硕士论文

【摘要】： 通常可采用两种方法研究一维非线性量子场论模型的统计物理性质,即:Bethe ansatz方法或泛函积分方法。第一种方法可以给出精确解,但是这种方法只能研究低维物理模型。泛函积分方法可以应用于任何非线性系统,并根据微扰理论得到物理模型的近似解。本文根据泛函积分方法研究了一维量子sine-Gordon-Thirring模型的统计物理性质。首先,使用微扰和变分泛函积分方法分析了模型的相结构和相的稳定性质;其次研究了黑洞背景和非对易时空中费米物质的能量密度涨落,对非对易时空中的费米物质能量密度涨落和黑洞内部引力场的扰动进行了分析。然后,本文研究了标量场和玻色Thirring模型的能量密度涨落,并在相同黑洞背景下与费米场的能量密度涨落进行了比较。最后,根据热核泛函积分方法,研究了黑洞背景中费米场和玻色场的能量密度涨落,并与泛函积分方法得到的结果进行了比较。本文的创新工作如下: 1、利用泛函积分方法推导了一维sine-Gordon-Thirring模型的等效势和自由能,并在强、弱耦合情况下研究了模型的相结构和稳定性质。 2、在黑洞背景下推导了sine-Gordon-Thirring模型的自由能与等效势,计算了弱耦合和强耦合情况下费米物质的能量密度,分析了引力场扰动对费米物质能量密度涨落的影响。 3、计算了标量场和玻色Thirring模型的能量密度涨落,并与相同黑洞背景下的费米场能量密度涨落进行了比较。 4、根据热核泛函积分方法计算了黑洞背景下玻色场与费米场的能量密度涨落,并与变分泛函积分方法得到的结果进行了对比。
[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.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2010
【分类号】：P145.8

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