Applied Physics and Mathematics Annotation << Back WHAT EXACTLY IS A PHOTON? THE NATURE OF RADIATION QUANTA AND COSMOLOGICAL REDSHIFT. PART 1 A.V. KUKUSHKIN This is Part 1 which is introductory in both physical and mathematical sense. The first section of this part concerns the design of the physical foundation for creating a mathematical model of the classical photon field within the framework of relativistic physics. The second section discusses the modification of the tensor algebra within the Minkowski space. It is shown that such a modification becomes possible when the Minkowski space is identified as complex through the recognition of the time unit vector of the 4-dimensional standard basis of the rectangular Cartesian system as an imaginary vector. The article analyzes all the consequences for tensor algebra and terminology which arise in theory after the introduction of an imaginary directional unit (imaginary vector) into mathematics. For example, a new concept of a vector quantity is proposed which now becomes complex. Special cases of a complex vector are an ordinary real (space-like) vector, an imaginary (time-like) vector, and a zero (isotropic) vector. Keywords: magnitude of the imaginary unit vector, complex Minkowski space, imaginary vector, complex vector, photon beam. DOI: 10.25791/pfim.04.2025.1339 Pp. 22-48.