Where is sum of divergent series used in physics?

In summary, the conversation discusses the use of summing divergent series and determining the value of divergent integrals in physics. The mathematician is interested in the application of these concepts in physics and is looking for examples to challenge their method. It is mentioned that divergent integrals appear in quantum field theory, but the discussion of personal theories and the use of vixra is deemed as a bad idea."
  • #1
Sinisa
2
0
Hello everyone!

My question is:

Where is sum of divergent series and divergent integrals used in physics? What it all means? Where can I find examples of divergent integrals? Is there a book of problems for physicists?

I am mathematician. I developed a method for summing divergent series and determines the value of divergent integrals. I am fascinated by the time they have the application in physics. What is the point of it all? How to interpret all physicists? Also looking for examples of divergent integrals to challenge that method. So far I've found three examples that I have tested in the work.

Thanx.
 
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  • #2
Divergent integrals appear frequently in quantum field theory.

Note that the discussion of personal theories is against the forum rules. And vixra is a very bad idea if you want to be taken seriously.
 
  • #3
Ok. Thanx. My questions still stand.
 
Last edited:

1. What is a divergent series in physics?

A divergent series is a mathematical series in which the terms increase without bound, meaning that the sum of the series also increases without bound. In physics, this can occur when calculating certain physical quantities in theoretical models that do not converge to a finite value.

2. Why is it important to understand divergent series in physics?

Understanding divergent series in physics is important because it helps us identify and address potential problems in theoretical models. It also allows us to better understand the limitations of our current understanding of physical phenomena and to develop more accurate and reliable models.

3. How is the sum of divergent series used in physics?

The sum of divergent series is often used in physics to calculate certain physical quantities, such as the energy of a system or the value of a physical constant. It is also used in theoretical models to analyze the behavior of physical systems and make predictions about their behavior.

4. Can the sum of a divergent series ever be a useful result in physics?

Yes, in some cases, the sum of a divergent series can be a useful result in physics. For example, in renormalization techniques, divergent series are used to cancel out infinities and obtain meaningful results for physical quantities. However, these results must always be interpreted with caution and may require further refinement.

5. How do physicists deal with the challenges posed by divergent series?

Physicists use a variety of techniques to deal with the challenges posed by divergent series. These may include renormalization, regularization, and other mathematical tools to obtain meaningful results from divergent series. Additionally, experimental data can help guide and validate theoretical models that involve divergent series.

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