红外灾变的Carleman算子刻画及其奇异性
Characterization of Infrared Catastrophe by The Carleman Operator and Its Singularity
摘要：
本文讨论了量子场论中由红外突变引起的一些数学问题。IR突变在算子理论中被描述和研究，其特征在于Carleman算子。利用这些表征，我们还研究了红外突变下基态的不存在性。本文从数学和固体物理的角度出发，将本文的理论应用于描述非相对论性电子与声子或极化激元量子场耦合的模型的哈密顿量。
英文摘要：
This paper addresses some mathematical problems arising from the infrared (IR) catastrophe in quantum field theory. IR catastrophe is formulated and studied in operator theory, characterized by the Carleman operator. Non-existence of ground state under IR catastrophe is also investigated with the help of the characterization. The theory presented in this paper is applied to the Hamiltonian of the model describing a non-relativistic electron coupled with a quantum field of phonons or polaritons in the light of mathematics as well as solid state physics.
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