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

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.