Abstract
In order to derive a measure for the quality of approximate field-theoretical ground states, especially the variational Gaussian approximation, we examine the energy variance ofλφ 4 n+1 and several quantities related to it. Inn<-1 the variance is manifestly finite and can be interpreted in a straightforward manner. Inn>-2, however, the canonical (noncovariant) variance turns out divergent and nonrenormalizable. As a substitute, we propose a closely related covariant and renormalizable quantity and demonstrate its usefulness with the help of various concrete examples. In particular, the strong-coupling limit of the Gaussian effective potential is analyzed.
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Supported by Deutsche Forschungsgemeinschaft (DFG) under contract IIC4-Ri-549/1; Present address: Fachbereich Physik, Universität GH Essen, W-4300 Essen 1, FRG
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Ritschel, U. Variance method in quantum field theory and exact strong-coupling limit of the Gaussian effective potential. Z. Phys. C - Particles and Fields 54, 297–306 (1992). https://doi.org/10.1007/BF01566659
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DOI: https://doi.org/10.1007/BF01566659