By V. N. Popov, V. S. Yarunin (auth.)

Material debris, electrons, atoms, molecules, engage with each other by way of electromagnetic forces. that's, those forces are the reason for their being mixed into condensed (liquid or strong) states. In those condensed states, the movement of the debris relative to each other proceeds in orderly style; their person homes in addition to the electrical and magnetic dipole moments and the radiation and absorption spectra, as a rule fluctuate little by means of comparability with their homes within the unfastened country. Exceptiotls are the unique so-called collective states of condensed media which are shaped below section transitions of the second one sort. The collective states of topic are characterised to a excessive measure by means of the micro-ordering that arises end result of the interplay among the debris and that's damaged down by means of chaotic thermal movement lower than heating. Examples of such pheonomena are the superfluidity of liquid helium, and the superconductivity and ferromagnetism of metals, which exist in simple terms at temperatures under the severe temperature. At low temperature states the debris don't convey their person features and behavior themselves as a unmarried entire in lots of respects. They circulation alongside capillaries in ordered type and create an undamped present in a conductor or a macroscopic magnetic second. during this regard the fabric acquires unique homes that aren't often inherent to it.

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48) to the case when there exist anomalous Green's functions has, apart from the trivial one, non-trivial solutions for the anomalous Green's functions which are below the phase transition point. The possibility of partial summation is quite general for diagramatic perturbation theory, and is valid both for statistical physics and for relativistic field theory. 27) is not obeyed. FUNCTIONAL INTEGRALS IN QUANTUM THEORY 29 number of particles, momentum, kinetic energy and pressure. To begin with, we consider the Bose system.

Note that differentiation with respect to a (or a*) of any element of the diagram apart from firstorder vertices is equivalent to joining an incoming (or outgoing) line to this element. For example: 42 CHAPTER 2 - r= x -r ---r o - - =0. Therefore, differentiation of any diagram with respect to a (or a*) is equivalent to joining to the diagram incoming (or outgoing) arrows in all possible ways. We consider the diagrams for the pressure p = -Q/V. Contributions to the expression for p are provided by the constant Co, the pressure Po of the ideal Bose gas and the sum of all the connected vacuum diagrams.

N are the potentials of the ideal and non-ideal systems. We have Q, = -PoV. n = -pV. where Po. 56) we obtain the formula Pic . 1 ~ P = Po + ~V£.. 57) i expressing the pressure p in terms of the pressure Po and the sum of the contributions of the vacuum diagrams. 57) is also true for Fermi systems. 54) for the Bose system in that there is a sign change and the boson frequencies 0) = 21tnT are replaced by the fermion frequencies (2n +1)1tT. The above perturbation theory coincides with the temperature-diagram technique set forth, for example, in the book [2].