**Part 1**

**Theoretical Fundamentals: Problem of Observables** 

**1** 

*Ukraine* 

**Description of Field States with Correlation** 

Modern physics deals with the consistent quantum concept of electromagnetic field. Creation and annihilation operators allow describing pure quantum states of the field as excited states of the vacuum one. The scale of its changes obliges to use statistical description of the field. Therefore the main object for full description of the field is a statistical operator (density matrix). Field evolution is reflected by operator equations. If the evolution equations are formulated in terms of field strength operators, their general structure coincides with the Maxwell equations. At the same time from the point of view of experiments only reduced description of electromagnetic fields is possible. In order to analyze certain physical situations and use numerical methods, we have the necessity of passing to observable quantities that can be measured in experiments. The problem of parameters, which are necessary for non-equilibrium electromagnetic field description, is a key one for building the field kinetics whenever it is under discussion. The field kinetics embraces a number of physical theories such as electrodynamics of continuous media, radiation transfer theory, magnetic hydrodynamics, and quantum optics. In all the cases it is necessary to choose physical quantities providing an adequate picture of non-equilibrium processes after transfer to averages. It has been shown that the minimal set of parameters to be taken into account in evolution equations included binary correlations of the field. The corresponding theory can be built in terms of one-particle density matrices, Wigner distribution functions, and conventional simultaneous correlation functions of field operators. Obviously, the choice depends on traditions and visibility of phenomenon description. Some methods can be connected due to relatively simple relations expressing their key quantities through one another. The famous Glauber's analysis (Glauber, 1966) of a quantum detector operation had resulted in using correlation functions including positiveand negative-frequency parts of field operator amplitudes in the quantum optics field. Herewith the most interesting properties of field states are described with non-simultaneous correlation functions. Various approaches in theoretical and experimental research into field

Our starting point is investigation of the Dicke superfluorescence (Dicke, 1954) on the basis of the Bogolyubov reduced description method (Akhiezer & Peletminskii, 1981). It paves the way to constructing the field correlation functions. We can give a relaxation process picture in different orders of the perturbation theory. The set of correlation functions providing a

**1. Introduction**

correlations are compared in the present chapter.

**Functions and Measurements** 

Sergiy Lyagushyn and Alexander Sokolovsky *Oles' Honchar Dnipropetrovs'k National University* 

**in Quantum Optics** 
