This paper explores the quantum structure of electromagnetic fields in space-time varying materials, addressing the challenges posed by frequency and energy conservation violations. The authors propose a Hamiltonian for these systems and show that quantum field operators evolve according to classical equations in the Heisenberg picture. They discuss the unique quantum phenomenon of photon-pair creation, which is similar to Hawking's radiation from black holes. The paper introduces a new set of annihilation operators to account for negative frequencies, which are essential for understanding the quantum processes in these media. The authors derive the Hamiltonian and show how it governs the time evolution of the field operators, leading to spontaneous emission of radiation. The study highlights the central role of negative frequencies and the creation of photon pairs in these systems, providing a quantum mechanical description of space-time varying materials.This paper explores the quantum structure of electromagnetic fields in space-time varying materials, addressing the challenges posed by frequency and energy conservation violations. The authors propose a Hamiltonian for these systems and show that quantum field operators evolve according to classical equations in the Heisenberg picture. They discuss the unique quantum phenomenon of photon-pair creation, which is similar to Hawking's radiation from black holes. The paper introduces a new set of annihilation operators to account for negative frequencies, which are essential for understanding the quantum processes in these media. The authors derive the Hamiltonian and show how it governs the time evolution of the field operators, leading to spontaneous emission of radiation. The study highlights the central role of negative frequencies and the creation of photon pairs in these systems, providing a quantum mechanical description of space-time varying materials.