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Is the one-loop corrected vacuum expectation value of a field renormalization scheme independent?

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- Thread starter Kfir Dolev
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In summary, renormalization scheme dependence refers to the fact that the values of vacuum expectation values (vevs) in a quantum field theory can change depending on the specific renormalization scheme used to calculate them. This occurs because the values of vevs are affected by the choice of renormalization scale and conditions, leading to difficulties in comparing results and the need for careful consideration when making predictions. Scientists deal with this by choosing appropriate schemes and considering the effects of scheme dependence on results, but it cannot be completely eliminated.

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Is the one-loop corrected vacuum expectation value of a field renormalization scheme independent?

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No. since you need to choose parameters. The choices cancel only in the fully summed answer.Kfir Dolev said:Is the one-loop corrected vacuum expectation value of a field renormalization scheme independent?

Renormalization scheme dependence refers to the fact that the values of vacuum expectation values (vevs) in a quantum field theory can change depending on the specific renormalization scheme used to calculate them. This means that different schemes can give slightly different results for the same vev.

Renormalization scheme dependence occurs because the values of vevs are affected by the choice of renormalization scale and the specific renormalization conditions used. This can lead to differences in the vevs calculated in different schemes, even though they are all valid and consistent methods of renormalization.

The consequences of renormalization scheme dependence can include difficulties in comparing results from different schemes and the need for careful consideration when making predictions based on vevs. It also highlights the fact that there is no unique or "correct" way to renormalize a theory, and different schemes can be used depending on the needs of the calculation.

To deal with renormalization scheme dependence, scientists often choose a specific renormalization scheme that is most suitable for their particular calculations. They may also use techniques such as renormalization group equations to relate results obtained in different schemes. In addition, it is important for scientists to carefully consider the implications of renormalization scheme dependence when interpreting their results.

No, renormalization scheme dependence cannot be completely eliminated. However, it can be minimized by choosing appropriate renormalization schemes and carefully considering the effects of scheme dependence on results. In some cases, certain schemes may also be chosen specifically because they are less affected by scheme dependence.

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