Scholarlink

Abstract <p>A complete set of solutions of the scalar field equation on the background of three-dimensional flat space-time with a single extracted point (impurity) is obtained. The defect is described within the technique of Laplacian self-adjoint extension, in which the impurity is identified with a delta-like singularity. It is shown that in the case of two spatial dimensions, the existence of a single bound state in self-adjoint extensions, which raises no objections at the level of quantum mechanics, corresponds to unphysical states in quantum field theory. The physical states are isolated, and an exact expression for the renormalized Hadamard function is obtained. As an example, the renormalized vacuum expectation value of the field squared <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\langle\phi^{2}(x)\rangle_{\textrm{ren}}\)</EquationSource> <!--BPhysMGU2570323Grats-m3--> </InlineEquation> is computed. It is shown that the toy model can be regarded as a first approximation to the extended issue of field effects in locally flat conical spaces, as well as in the cosmic-string background.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Pointlike Interaction in (\(\boldsymbol{2+1}\))-Dimensional Space-Time

  • 期刊论文

  • 发表日期：

    2025年12月1日

查看全文
  • Yu. V. Grats,
  • P. A. Spirin

摘要

Abstract

A complete set of solutions of the scalar field equation on the background of three-dimensional flat space-time with a single extracted point (impurity) is obtained. The defect is described within the technique of Laplacian self-adjoint extension, in which the impurity is identified with a delta-like singularity. It is shown that in the case of two spatial dimensions, the existence of a single bound state in self-adjoint extensions, which raises no objections at the level of quantum mechanics, corresponds to unphysical states in quantum field theory. The physical states are isolated, and an exact expression for the renormalized Hadamard function is obtained. As an example, the renormalized vacuum expectation value of the field squared \(\langle\phi^{2}(x)\rangle_{\textrm{ren}}\) is computed. It is shown that the toy model can be regarded as a first approximation to the extended issue of field effects in locally flat conical spaces, as well as in the cosmic-string background.