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quantum_field_theory [2017/05/09 05:32]
jakobadmin [Problems and Their Solutions]
quantum_field_theory [2017/12/06 09:33] (current)
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 The probability is calculated using a perturbation series in the coupling constant, where each term in the series can be visualized with Feynman diagrams. The two problems are: The probability is calculated using a perturbation series in the coupling constant, where each term in the series can be visualized with Feynman diagrams. The two problems are:
  
-  - It is well known that the [[quantum_field_theorys:​radius_of_convergence]] of the perturbation series in QFT is zero. This means simply, that there is no value of the coupling constant, except for $0$, such that the overall value when consider all terms in the perturbation series is not zero. Formulated differently:​ when we add the contributions from all loop-orders,​ we always get infinity as value. (Take note that this problem is really separate from the second problem! Even when all terms are renormalized and thus finite, the sum of all terms is infinite.)+  - It is well known that the [[quantum_field_theory:​radius_of_convergence]] of the perturbation series in QFT is zero. This means simply, that there is no value of the coupling constant, except for $0$, such that the overall value when consider all terms in the perturbation series is not zero. Formulated differently:​ when we add the contributions from all loop-orders,​ we always get infinity as value. (Take note that this problem is really separate from the second problem! Even when all terms are renormalized and thus finite, the sum of all terms is infinite.)
   - As if this weren'​t bad enough, the individual terms in the perturbation series yield infinity if we do not treat them "​carefully"​. Usually, carefully means that we somehow hide the infinity by absorbing it into some constants. ​   - As if this weren'​t bad enough, the individual terms in the perturbation series yield infinity if we do not treat them "​carefully"​. Usually, carefully means that we somehow hide the infinity by absorbing it into some constants. ​
  
quantum_field_theory.txt · Last modified: 2017/12/06 09:33 (external edit)