论文标题
在经典背景上创建粒子的概率
Inclusive probability of particle creation on classical backgrounds
论文作者
论文摘要
严格构造了具有二次非组织汉密尔多亚人的玻色子和费米恩场的量子理论。观测值代数的表示由哈密顿对角线化程序给出。制定了在有限时间存在统一动力学的足够条件，并得出了进化运算符的矩阵元素的明确公式。特别是，这给出了明确定义的一环有效作用的表达。紫外线和红外发散是通过该理论的哈密顿量的能量临界值正规化的。可能的无限粒子产生受相应的反绝热项的调节。得出了检测器记录的粒子$ n_d $的平均数量和概率$ w（d）$记录检测器的粒子的明确公式。事实证明，这些数量允许正规化删除限制，在此限制下，$ n_d $是有限的，$ w（d）\ in [0,1）$。例如，考虑了中性玻色子场的理论，该理论具有哈密顿量和非组织源的固定二次部分。在有限的时间演变中，该源从真空中产生的颗粒的平均数量以及记录创建粒子的包含概率。得出了创建颗粒平均密度的红外和紫外线渐近物。特殊情况下，考虑具有经典电流的量子电动力学。得出了平均光子数量的紫外线和红外渐近线。发现了由绝热驱动电流产生的平均光子数量的渐近数。
The quantum theories of boson and fermion fields with quadratic nonstationary Hamiltoanians are rigorously constructed. The representation of the algebra of observables is given by the Hamiltonian diagonalization procedure. The sufficient conditions for the existence of unitary dynamics at finite times are formulated and the explicit formula for the matrix elements of the evolution operator is derived. In particular, this gives the well-defined expression for the one-loop effective action. The ultraviolet and infrared divergencies are regularized by the energy cutoff in the Hamiltonian of the theory. The possible infinite particle production is regulated by the corresponding counterdiabatic terms. The explicit formulas for the average number of particles $N_D$ recorded by the detector and for the probability $w(D)$ to record a particle by the detector are derived. It is proved that these quantities allow for the regularization removal limit and, in this limit, $N_D$ is finite and $w(D)\in[0,1)$. As an example, the theory of a neutral boson field with stationary quadratic part of the Hamiltonian and nonstationary source is considered. The average number of particles produced by this source from the vacuum during a finite time evolution and the inclusive probability to record a created particle are obtained. The infrared and ultraviolet asymptotics of the average density of created particles are derived. As a particular case, quantum electrodynamics with a classical current is considered. The ultraviolet and infrared asymptotics of the average number of photons are derived. The asymptotics of the average number of photons produced by the adiabatically driven current is found.
