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Bobhawke
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Some papers I am looking over at the moment mention both additive and multiplicative renormalisations. What is the difference between them?
...so it seems we are still stuck with a divergent expression for the total amplitude of any genuinely quantum process...from a strict matehmatical viewpoint we have got officially "nowhere in the sense that all our expressions are still "mathematically meaningless"...yet good physicsts will not give up so easily...and they were right not to do so...whatever philosophical position is taken...renormalization is an essential feature..of modern QFT...very few theories pass the test of renormalizability and only those that do pass have a chance of being regarded as acceptable for physics...
Bobhawke said:"The quark mass has both multiplicative and additive renormalisations due to the explicit breaking of chiral symmetry by the wilson term"
The main difference between additive and multiplicative renormalisations lies in the way they account for the divergences in a physical theory. Additive renormalisation involves adding a constant term to the original equation, while multiplicative renormalisation involves multiplying the original equation by a factor.
Additive renormalisation does not alter the overall structure of the physical theory, but it does affect the numerical values of the parameters. On the other hand, multiplicative renormalisation can change the entire form of the theory, leading to a different physical interpretation.
Multiplicative renormalisation is more commonly used in theoretical physics, as it allows for a more systematic and elegant treatment of divergences. It is also more effective in eliminating divergences in quantum field theories.
Yes, it is possible to combine additive and multiplicative renormalisations to obtain a more comprehensive renormalisation scheme. This is known as the "minimal subtraction" scheme, which is often used in quantum field theory calculations.
The use of additive or multiplicative renormalisations can lead to non-physical results if they are not applied carefully. In some cases, a combination of both types of renormalisation may be necessary to obtain meaningful results. Additionally, renormalisation is not a universal solution and may not work for all types of divergences in a physical theory.