# Fundamental Spacetime Representations of Quantum Antenna Systems
## 1 Introduction
Even though the data to be transmitted are encoded into time signals, in general, the quantum antenna system is much more complex than its time excitation method. There is a need, then, to understand the complex and multifaceted nature of the spatiotemporal structure of the radiation field emitted by a generic quantum system at a very broad level. This paper is a contribution toward this goal. The classical theory of controlled radiation has been extensively studied and developed in applied electromagnetics [27, 28, 33, 34, 35]. On the other hand, the general theory of quantum antennas has not been investigated in depth so far, in spite of the publication in recent years of a number of reports and proposals about the subject, not restricted only to quantum wireless communications but also involving other topics as well, e.g., see [15, 16, 17, 18, 19, 20, 21]. Some of the main conceptual and philosophical hurdles that a viable theory of quantum antennas need to overcome include, though by no means are restricted to, the following issues:  
1. Understanding what is meant by _quantum radiation_. 2. Understanding the role played by particle emission dynamics in light of the wave-particle duality characteristic of quantum phenomena. Understanding the complex role played by quantum fields, propagators, and Green's functions in quantum radiation. * Understanding the role played by many-particle states/interactions in quantum radiation processes. It should be noted that these conceptual and technical issues are still considered difficult open research fields in both foundational and applied research as they have not been resolved even within standard quantum field theory itself. For instance, it is still not clear what the ultimate meaning of \"particle\" in quantum fields is [36; 37]; questions about the nature of quantum excitations in interacting field theories have been asked in the past [38] and are still being investigated up to date [39]. Therefore, there is a need to re-examine the subject of quantum antennas at a very general and fundamental level, that of developing possible foundations for the topic that may help illuminate current and future open theoretical problems on one hand, and to help devise and evolve new genera of quantum systems and applications on the other hand. A viable candidate for such foundational approach, we believe, is to formulate the entire problem of quantum antennas and quantum radiation using a relativistic spacetime formalism (QFT in this case). Our intended goals in the present article include a wide spectrum. Most of these objectives are research related and can be classified as part of the emerging area of quantum antenna theory within both quantum physics and quantum engineering. Yet, additionally, other aspects in our work are pedagogical, relating to the wish to reach a wide multidisciplinary audience. We summarize these two flavors of our main goals as follows:  
* Primary research objectives of the present article: 1. Generalizing the concept of antennas beyond acoustic and electromagnetic antennas, the two concepts that have dominated the field so far, by demonstrating how relativistic QFT can be used to formulate a single and unified concept of \"quantum radiators\" valid for a large number of possible radiation processes in nature. 2. Providing a concrete illustration of some of the potential algorithmic capabilities of the spacetime formalism of quantum antennas by constructing various possible candidates for radiation pattern functions and gains in the case of the quantum (spin-0) Klein-Gordon q-antennas. * Secondary (pedagogical) objectives of the present article: 1. Introducing new applications of fundamental theory (here relativistic quantum mechanics) to different audiences, e.g., quantum engineering and quantum technology research. 2.