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What is the idea behind renormalization group ??

i believe you begin with an action [tex] S[\phi] =\int d^{4}x L(\phi , \partial _{\mu} \phi ) [/tex]

then you expand the fields into its Fourier components upto a propagator..

[tex] \phi (x) =C \int_{ \Lambda}d^{4}x e^{i \vec p \vec x} + c.c [/tex]

but then i do not more, i know that every quantity measured by the QFT theory will have the form:

[tex] m(\Lambda) = alog(\Lambda) + \sum_{n=1}^{\infty} b_{n} \Lambda ^{n} [/tex]

and that from the definition of propagator we should ask for 'conformal invariance' but i do not know how this theory helps to find finite (regularized) value of the quantities.

the idea i am looking for, it is to know if using renormalization group we could find a relation between the bare quantities [tex] m^{(0)} [/tex] and the renormalized ones [tex] m^{(R)} [/tex] via some differential or integral equation.

another mor informal question, if we found a method to obtain finite values for integrals.

[tex] \int_{0}^{T}dx x^{n} [/tex] as T-->oo and for every positive 'n'

would the problem of renormalization be solved ??

i believe you begin with an action [tex] S[\phi] =\int d^{4}x L(\phi , \partial _{\mu} \phi ) [/tex]

then you expand the fields into its Fourier components upto a propagator..

[tex] \phi (x) =C \int_{ \Lambda}d^{4}x e^{i \vec p \vec x} + c.c [/tex]

but then i do not more, i know that every quantity measured by the QFT theory will have the form:

[tex] m(\Lambda) = alog(\Lambda) + \sum_{n=1}^{\infty} b_{n} \Lambda ^{n} [/tex]

and that from the definition of propagator we should ask for 'conformal invariance' but i do not know how this theory helps to find finite (regularized) value of the quantities.

the idea i am looking for, it is to know if using renormalization group we could find a relation between the bare quantities [tex] m^{(0)} [/tex] and the renormalized ones [tex] m^{(R)} [/tex] via some differential or integral equation.

another mor informal question, if we found a method to obtain finite values for integrals.

[tex] \int_{0}^{T}dx x^{n} [/tex] as T-->oo and for every positive 'n'

would the problem of renormalization be solved ??

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