20世纪以来 ，量子力学和相对论的发展对经典物理学来说是颠覆性的。 Dirac将这两种理论结合发表了相对论量子力学的运动方程，并且根据得到的负能解预言了正电子的存在。 Heisenberg根据正电子的预言发现真空是不稳定的，这也符合不确定性原理关于真空的认知。因此，在强电磁场的作用下，由于真空中虚粒子的涨落，会产生诸如真空极化、真空双折射和真空中物质的产生等效应。虽然真空在外加电场的作用下产生正负电子对在理论上很早被预测了，但是其临界场强很高（1018V/m），并且产生几率受场强的指数抑制，因此无法通过现有的实验条件去实现。随着激光技术的发展，相信在不久的将来将会实现在实验室中对产生。

激光的强度是随空间和时间变化的，因此本论文将采用在空间上为高斯型、在时间上为单脉冲的Sauter型电场模型。主要内容如下：

       1、我们研究了单脉冲对称电场下不同空间尺度对正负电子对产生的影响。首先，在不同产生机制下，空间尺度的影响程度是不一样的，空间尺度对多光子机制影响较小，对Schwinger机制影响较大。其次，在空间尺度对动量谱的影响上，随着脉冲宽度的增加，达到准均匀电场对应的空间尺度也在增加，然而与在较大的空间尺度不同的是，在较小的空间尺度下动量谱的范围并不是随脉冲宽度的增加而增加，与此同时，约化粒子数密度最大时对应的空间尺度减小直至不变。最后，在空间对约化粒子数的影响上，随着脉冲宽度的增加，约化粒子数先降低再增加，降低时不是线性的关系，但是在增长过程中逐渐转变为线性关系；约化粒子数最小值对应的脉冲宽度随着空间尺度的增加而减小直至不变；脉冲宽度不变时，约化粒子数随空间尺度的增加而增加直至不变；而归一化约化粒子数在空间尺度λ > 50λC时基本不变，也就是说空间尺度λ > 50λC时，空间尺度虽然对动量谱有所影响，但是对粒子产生的影响程度没有变化，而且在脉冲宽度较大时归一化约化粒子数与空间尺度的关系不变。

       2、我们研究了单脉冲非对称电场下不同空间尺度对正负电子对产生的影响，并与对称脉冲的影响进行了对比。首先，在动量分布方面，对称脉冲和非对称脉冲的下降脉冲宽度相同时，空间尺度越小时产生的粒子的动量谱在上升阶段的契合度在下降脉冲宽度越小时越高。其次，在约化粒子数方面，下降脉冲宽度相同的非对称脉冲和对称脉冲的约化粒子数与空间尺度的关系在变化趋势上是相同的，而且当上升脉冲与下降脉冲的正负电子对产生机制都是Schwinger机制时，非对称脉冲电场产生的正负电子对在粒子数的数值上是以非对称脉冲电场的上升脉冲、下降脉冲的脉冲宽度大小为脉冲宽度大小的两个对称电场模型的1/2。最后，非对称脉冲的上升脉冲宽度和下降脉冲宽度在数值上交换后对产生的粒子数没有影响。

          Since 20th century, the development of quantum mechanics and relativity is subversive to classical physics. Dirac published the equation of motion for the relativistic quantum mechanics based on these two theories，and predicted the existence of positrons based on the resulting negative energy solution. Heisenberg found that the vacuum is unstable based on the prediction of positrons, which is consistent with the Uncertainty Principle. Many effects, such as vacuum polarization, vacuum birefringence and the production of matter in vacuum, will be found in strong electromagnetic field due to the fluctuation of virtual particles in vacuum. Although the generation of electron positron pair in vacuum under the action of external electric field has been predicted in theory for a long time, its critical field strength is very high (1018V / m), and the generation probability is exponentially suppressed by the field strength, so it can not be realized under the existing experimental conditions. With the development of laser technology, it will be realized in the laboratory in the near future.

The intensity of the laser changes with space and time. Therefore, this paper will adopt electric field model which is Gauss type in space and Sauter type of single pulse in time. The main contents are as follows:

          1. We have studied the effect of the creation of vacuum electron and positron pairs in a single electric field pulse which is symmetric in different spatial scales. First of all, the degree of effect of the spatial scale is different in different mechanisms. The spatial scale has less influence on the multiphoton mechanism than the Schwinger mechanism. Secondly, as for the effect of spatial scale on momentum spectrum, the spatial scale corresponding to the quasihomogeneous electric field increases with the increase of pulse width. However, compared with larger spatial scales, the range of momentum spectrum does not increase with the increase of pulse width in smaller spatial scales. When the reduced particle number density is maximum, the corresponding spatial scale decreases until it remains unchanged with the increase of pulse width. Finally, as for the effect of spatial scale on the reduced particle number, as the pulse width increases, the reduced particle number decreases at first and then increases, the relationship is not linear when the reduced particle number decreases, but it changes to a linear relationship gradually when the reduced particle number increases. With the increase of the spatial scale, the pulse width corresponding to the minimum value of the reduced particle number decreases until it remains unchanged. When the pulse width is constant, the reduced particle number increases with the increase of the spatial scale until it stays the constant. When the spatial scale λ > 50λC, the normalized reduced particle number is basically unchanged,in other words,the spatial scale has an effect on the momentum spectrum but not on the degree of the impact of the creation of particle, and the relationship between the normalized reduced particle number and the spatial scale remains unchanged when the pulse width is large.

          2. We have studied the effect of the creation of vacuum electron and positron pairs in a single electric field pulse which is asymmetric in different spatial scales, and compared with the effect of symmetric pulses. First, in terms of momentum distribution, when the falling pulse width of symmetric pulses and asymmetric pulses is the same, the smaller the falling pulse width, the higher the fit of the momentum spectrum during the rising phase in the smaller spatial scale. Secondly, in terms of the reduced particle number, the relationship between the reduced particle number and the spatial scale is same variation trend when the asymmetric pulse and the symmetric pulse with the same width of the falling pulse, and the number of particles of the asymmetric pulse electric field is half of the number of particles of the two symmetric electric field models with the values of the pulse width are the same as the values of the rising pulse and the falling pulse of the asymmetric pulse width when both the generation mechanism of the rising pulse and the falling pulse are the Schwinger mechanism. Finally, the number of particles will be the same if we exchange the values of the rising pulse width and the falling pulse width of the asymmetric pulse.