Abstract

First, the case of (0 + 1)-dimensional nonequilibrium quantum mechanics is analyzed using the Yukawa model in external scalar field \({{\phi }_{{{\text{cl}}}}}(t) = \frac{m}{{{\lambda }}} + \frac{{{\alpha }}}{{{\lambda }}}t\) as an example. It is shown that the exact fermion propagators do not change with time, and the growth of bosonic propagators is determined by the contribution to the quantum mean of field \(\phi \) and corresponds to the so-called “tadpole” diagrams. After that, the Yukawa theory of the interacting massive Dirac field and massless real scalar field in the (1 + 1)-dimensional Minkowski space with the signature (+1, –1) is examined. In this theory, a classical current is first calculated, and then quantum corrections for the Dirac field in an external coordinate-dependent scalar field with Yukawa interaction are determined. The response of fermion pair generation to an external bosonic field that linearly depends on the coordinate is studied.

中文翻译：

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QM和QFT中强标量场的衰减

摘要

首先，使用Yukawa模型在外部标量场\（{{\ phi __ {{\ text {cl}}}}}}（t）= \中分析（0 +1）维非平衡量子力学的情况以frac {m} {{{\ lambda}}} + \ frac {{{\ alpha}}} {{{\ lambda}}} t \）为例。结果表明，确切的费米子传播者不随时间而改变，和玻色子传播者的生长是通过向场量子平均值的贡献来确定\（\披\）并且对应于所谓的“ ta”图。此后，研究了（1 + 1）维Minkowski空间中具有签名（+1，–1）的相互作用的大Dirac场和无质量实标量场的Yukawa理论。在此理论中，首先计算经典电流，然后确定具有Yukawa相互作用的外部坐标依赖标量场中Dirac场的量子校正。研究了费米子对的生成对线性依赖于坐标的外部波场的响应。