Effective potentials and Bogoliubov’s quasi-averages |
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Authors: | D V Peregoudov |
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Institution: | (1) State Institute for Radio Engineering, Electronics, and Automation (Technical University), Moscow, Russia |
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Abstract: | The effective potential method, used in quantum field theory to study spontaneous symmetry violation, is discussed from the
point of view of Bogoliubov’s quasi-averaging procedure. It is shown that the effective potential method is a disguised type
of this procedure. The catastrophe theory approach to the study of phase transitions is discussed and the existence of the
potentials used in that approach is proved from the statistical point of view. It is shown that in the case of broken symmetry,
the nonconvex effective potential is not a Legendre transform of the generating functional for connected Green’s functions.
Instead, it is a part of the potential used in catastrophe theory. The relationship between the effective potential and the
Legendre transform of the generating functional for connected Green’s functions is given by Maxwell’s rule. A rigorous rule
for evaluating quasi-averaged quantities within the framework of the effective potential method is established.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 1, pp. 149–161, October, 1997. |
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