Revisiting canonical quantization of radiation: the role of the vacuum field

Abstract

Canonical quantization has conventionally been adopted as a necessary procedure for the description of the quantum radiation field by analogy between quantum-mechanical oscillators and field oscillators. In this paper we provide the physical basis for the formal quantization of the radiation field interacting with matter in the presence of the vacuum field, taken here as a solution of classical Maxwell equations. Just as the canonical particle operators x^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{x}$$\\end{document}, p^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{p}$$\\end{document} have been shown to be the response functions of the particle to this field, here we derive the creation and annihilation operators a^†\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{a}^{\\dagger }$$\\end{document}, a^\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{a}$$\\end{document}, with [a^,a^†]=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[\\hat{a},\\hat{a}^{\\dagger }]=1$$\\end{document}, as an expression of the field’s response to this interaction. The results obtained shed new light on the physical meaning of the description of light in terms of operators and suggest that neither matter nor radiation are quantized in isolation.