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Name:  
Miloslav Znojil  
Reviewer number:  
9689  
Email:  
znojil@ujf.cas.cz  
Item's zblNumber:  
DE 017 290 069  
Author(s):  
maslov, V. P.:  
Shorttitle:  
A new representation of the Hamiltonian operator for bosons and fermions. Quantization of free energy and dependence of Landau criterion on temperature.  
Source:  
Math. Notes 68, No. 6, 800802 (2000); translation from Mat. Zametki 68, No. 6, 945947 (2000), in Russian.  
Classification:  
 
Primary Classification:  
 
Secondary Classification:  
 
Keywords:  
many particle Hamiltonians; bosonic and fermonic Fock space; creation and annihilation operators; entropy operator; free energy operator; thermodynamic limit; phase transition; condensate; Landau criterion of the loss of superfluidity;  
Review:  
Three pages of short notes on three subjects covered by the title and by the three recent papers by the author (plus his two older books). This means that the text (the majority of which are formulae) forms an extended abstract by itself. Its main theorem states that in terms of the (either bosonic or fermionic) creation and annihilation operators one can introduce a densitylike functional and an ''averaged" operator H in such a way that the projection of H on the pertaining Fock space coincides with the usual partial differential Hamiltonian of the system. The subsequent commentary (adding, in the similar spirit, an entropy and free energies) is split in the weak and stronginteraction parts. Curiously enough, the paper was originally presented in Russian (I was told by my Russian friends that such a practice has also some pecuniary benefits)] but the text concerning the latter case [including the operator representation of the free energies (8) and related discussion] appears only in its ''translated" English update where one misses (for compensation?) the explicit halfpage form of the equation which determines the k=1 solutions (6) and, via the loss of reality of its eigenvalues, describes the Landau's boundary of the domain of the superfluidity (hence, interested people and the specialists should rather read both the language mutations).  
Remarks to the editors:  