Title: Particle creation and energy conditions for a quantized scalar field in the presence of an external, time-dependent, Mamev-Trunov potential Show Chinese title

Title: 粒子产生和能量条件在存在外部时间依赖的马涅夫-特鲁诺夫势的量子标量场中的情况

Abstract: We study the behavior of a massless, quantized, scalar field on a two-dimensional cylinder spacetime as it responds to the time-dependent evolution of a Mamev-Trunov potential of the form $V(x,t) = 2 \xi \delta(x) \theta(-t)$. We begin by constructing mode solutions to the classical Klein-Gordon-Fock equation with potential on the whole spacetime. For a given eigen-mode solution of the IN region of the spacetime ($t<0$), we determine its evolution into the OUT region ($t>0$) through the use of a Fourier decomposition in terms of the OUT region eigen-modes. The classical system is then second quantized in the canonical quantization scheme. On the OUT region, there is a unitarily equivalent representation of the quantized field in terms of the OUT region eigen-modes, including zero-frequency modes which we also quantize in a manner which allows for their interpretation as particles in the typical sense. After determining the Bogolubov coefficients between the two representations, we study the production of quanta out of the vacuum when the potential turns off. We find that the number of "particles" created on the OUT region is finite for the standard modes, and with the usual ambiguity in the number of particles created in the zero frequency modes. We then look at the renormalized expectation value of the stress-energy-tensor on the IN and OUT regions for the IN vacuum state. We find that the resulting stress-tensor can violate the null, weak, strong, and dominant energy conditions because the standard Casimir energy-density of the cylinder spacetime is negative. Finally, we show that the same stress-tensor satisfies a quantum inequality on the OUT region. Show Chinese abstract

Abstract: 我们研究了在二维圆柱时空上，质量为零的量子标量场对Mamev-Trunov势随时间变化演化的行为，其形式为$V(x,t) = 2 \xi \delta(x) \theta(-t)$。 我们首先构建整个时空上的经典Klein-Gordon-Fock方程与势的模解。 对于时空IN区域的一个给定本征模解（$t<0$），我们通过使用OUT区域本征模的傅里叶分解，确定其在OUT区域（$t>0$）中的演化。 然后在规范量子化方案中对经典系统进行二次量子化。 在OUT区域，存在一种与OUT区域本征模相关的量子场的单位等价表示，包括零频模，我们以一种允许它们被解释为典型粒子的方式对其进行量子化。 在确定了两种表示之间的Bogolubov系数后，我们研究了当势关闭时真空中量子的产生。 我们发现，对于标准模来说，OUT区域上“粒子”的数量是有限的，而零频模中产生的粒子数量则存在通常的不确定性。 然后我们研究了IN真空态下IN区域和OUT区域的应力-能量张量的重整化期望值。 我们发现，由于圆柱时空的标准卡西米尔能量密度为负，所得应力张量可能会违反零、弱、强和主导能量条件。 最后，我们证明了相同的应力张量在OUT区域满足量子不等式。