Hubbard Stratonovich transformation

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    Hubbard Transformation
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SUMMARY

The discussion centers on the Hubbard Stratonovich transformation, specifically addressing the normalization constant and its role in achieving unity within the functional measure. Participants clarify that the normalization constant, which includes factors like ##\det V##, is absorbed into the definition of the functional measure. This absorption ensures that overall rescalings do not affect the calculations of observables, confirming the transformation's validity in quantum field theory contexts.

PREREQUISITES
  • Understanding of quantum field theory concepts
  • Familiarity with functional measures in physics
  • Knowledge of determinants, specifically ##\det V##
  • Basic grasp of the Hubbard Stratonovich transformation
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  • Study the derivation and applications of the Hubbard Stratonovich transformation
  • Explore the role of normalization constants in functional integrals
  • Learn about determinants in the context of quantum mechanics
  • Investigate the implications of rescaling in quantum field theory calculations
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Physicists, particularly those specializing in quantum field theory, researchers working with functional integrals, and students seeking to deepen their understanding of the Hubbard Stratonovich transformation.

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Introducing the Hubbard Stratonovich transformation my book uses an expression for completeness that I don't understand (the one indicated on the picture). Can anyone explain why this is indeed unity?
 

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The normalization constant that they refer to being absorbed into the definition of the functional measure is presumably the appropriate power of ##\det V## and other factors that makes that unity. Overall rescalings of the functional measure should drop out of calculations of observables.
 

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