1. Markets consist of agents. Molecules consist of atoms.

2. Agents interact between themselves. Atoms interact between themselves.

3. Everything that markets do, the interacting agents do. Everything that molecules do, the interacting atoms do.

4. Dynamics of markets are determined by a principle of maximization (e.g. the trade maximization principle). Dynamics of molecules is determined by a principle of maximization (e.g. the least action principle).

5. Uncertainty and probability is an inherent important property of the market behavior. The same is valid for dynamics of molecules.

And this is still far from a complete enumeration of coincidences and analogies between the economic and physical systems.

It is widely-known that presently, advanced mathematical methods are applied in describing the dynamics of complex economic systems much less frequently than in physics. As far as the difference in the level of the penetration of formal mathematical methods into economics and physics is concerned, it is possible with reasonable caution to assert that this difference does not lie in the fact that in principle, mathematics cannot be widely used in economics by its very nature. Instead, physics has proven to be the more developed science mathematically in modern times for a variety of historical and technological reasons. This has been the situation for the past 300 years. Beautiful mathematical models have been created in physics during this time frame to describe dynamic phenomena in many-particle systems. Unfortunately, the same cannot be said for economic theory. It is obvious to me that, things being as they are, the correct conclusion for us now must not be to preserve the status quo. Nor should economists urgently develop their own unique mathematical calculations to describe economic phenomena, independent of physics. After all, why re-invent the wheel? All that is needed is to make use of some of the most salient and staggering achievements of humanity at the present time by borrowing from theoretical physics. These can be put to use for the good of the development of economic science and the global economy. This book is one of the many steps in the right direction along the proper road. Hopefully I am not wrong, although there is always that chance. There is no doubt that it will be a long road to this accomplishment, and most certainly not a fast one.

I am well aware that the very idea of using methods of theoretical physics, especially quantum mechanics, for describing economic phenomena must cause a healthy dose of skepticism from the physicists. Therefore, I emphasize that the discussion deals with the fact that only the mathematic framework of theoretical models of the respective physical systems are transferred to the physical economic models.

I incorporate into economics only the formal structural aspects of physical theories. First of all are the equations of motion for the many-particle systems, which just by themselves must not be too rigidly attached to real physical microscopic objects. Equations – they are just equations and nothing more, and if they are a beneficial descriptive tool in another science, why not make use of them? I repeat that this is just a useful mathematical object which can and should be used as a theoretical tool where it can provide benefit. For instance, in quantum mechanics wave functions and the Schrödinger equations have been successfully used for the incorporation of the uncertainty and probability principle into physics. Why, then, can we not then apply the same mathematical apparatus to the analogous uncertainty and probability principle in economic theory for purposes of mathematical description?