Gruppentheorie by Ludwig Baumgartner

By Ludwig Baumgartner

This booklet used to be digitized and reprinted from the collections of the collage of California Libraries. It used to be made from electronic pictures created throughout the libraries’ mass digitization efforts. The electronic pictures have been wiped clean and ready for printing via automatic methods. regardless of the cleansing method, occasional flaws should still be current that have been a part of the unique paintings itself, or brought in the course of digitization. This booklet and millions of others are available on-line within the HathiTrust electronic Library at www.hathitrust.org.

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By Ludwig Baumgartner

This booklet used to be digitized and reprinted from the collections of the collage of California Libraries. It used to be made from electronic pictures created throughout the libraries’ mass digitization efforts. The electronic pictures have been wiped clean and ready for printing via automatic methods. regardless of the cleansing method, occasional flaws should still be current that have been a part of the unique paintings itself, or brought in the course of digitization. This booklet and millions of others are available on-line within the HathiTrust electronic Library at www.hathitrust.org.

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Thus, as was mentioned in Sec. 2-2, the microscopic theory does not solve the problem of the identification of the parameters in the functional integral. We write Po,Eq. (2-57), as an expansion in the neighborhood of T o , Eq. (2-58), the point at which the free theory becomes unstable.

Another parameter appearing in the theory is a cutoff. One has to introduce either a lower limit on the length scale over which the order parameter field can vary, or an upper limit to the wave number of the Fourier components of the field. Otherwise, infinities are incurred in the calculation of the various correlation functions, as is the case in quantum field theory. In relativistic quantum field theory a special procedure has to be introduced to define the finite part of the various quantities.

D T H E O R Y . T l l E RESORMALIZATIOK GROUP. A N D CRITICAL. PIIENOMENA REFERENCES 1. D. Mukamel, Physical Review Letters, 34,482 (1975). 2. B. I. Halperin, T. C. Lubensky and S. K. Ma, Physical Review Letters, 32, 292 (1974). 3. S. Coleman and E. Weinberg, Physical Review, D7, 1888 (1973). 4. I. M. Gelfand and A. M. Yaglom, Journal of Mathematical Physics, 1, 48 (1960); E. J. 1967). See also the reviews by S. Albeverio and R. Hbegh-Krohn, Oslo University preprint ISBN-82-553-0193-3 (1974) and F.

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