How to check theoretical point of view

[Saturnine]

I'm reading Frederic's Paugam "Towards the Mathematics
of Quantum Field Theory."
I'm also interested in higher structures in mathematics which could have applications in physics.
How to check theese theories with the experimental data ?
For example the data in LHC. Where can I find experimental results to check QFT from theoretical point of view ?

 

[mfb]

Where can I find experimental results to check QFT from theoretical point of view ?

You can find experimental results in the publications of the collaborations of the experiments. Usually those results include comparisons to theoretical predictions.

The interesting raw datasets are available to members of the collaborations only, but some older data is made public sometimes.

 

[Demystifier]

I'm reading Frederic's Paugam "Towards the Mathematics
of Quantum Field Theory."
I'm also interested in higher structures in mathematics which could have applications in physics.
How to check theese theories with the experimental data ?
For example the data in LHC. Where can I find experimental results to check QFT from theoretical point of view ?

When "higher" structures in mathematics (such as categories) are applied to physics, usually such results cannot be compared with experimental data. As a rule, the experimental data are associated with "lower" mathematical structures. If you want a book on QFT containing many comparisons with experimental data, one good choice is Donoghue Golowich Holstein:
https://www.amazon.com/dp/0521476526/?tag=pfamazon01-20
But this book is 20 years old, so if you prefer something very recent, see Nagashima
https://www.amazon.com/dp/3527409629/?tag=pfamazon01-20
https://www.amazon.com/dp/3527409661/?tag=pfamazon01-20

 

[Saturnine]

But what are then foundations to use for example category theory and modern math ?
Whre can I get the data of LHC or some other particle accelerator ?

 

[Demystifier]

But what are then foundations to use for example category theory and modern math ?

Pure mathematicians study these things for the sake of mathematics itself. Those who try to apply this stuff to physics hope to gain deeper understanding of physics, but deeper understanding is not the same as comparison with experiments.

Eventually, deeper understanding by higher abstract mathematics may result in new numbers which can be compared with experiments, but that is usually not the primary motivation for studying abstract mathematical formulation of physics.

 

[Saturnine]

Eventually, deeper understanding by higher abstract mathematics may result in new numbers which can be compared with experiments, but that is usually not the primary motivation for studying abstract mathematical formulation of physics.

Isn't the goal to have some application of higher mathematics in sciences ?
What is primary motivation ?

 

[Demystifier]

Isn't the goal to have some application of higher mathematics in sciences ?
What is primary motivation ?

It's all individual. Different people have different motivations and goals.

There is no such thing as a "goal of science". There are only particular goals by particular scientists.

 

[Saturnine]

How to work in theoretical field but also do some experiments with your work ?

 

[mfb]

In particle physics?
Typical theory positions won't give you hands-on work. You might come in contact with the mess of data-analysis if you work together with collaborations. If you count that as "do some experiments", ...
Experimental positions can span the whole range from "I solder together stuff in the lab" to "I improve a mathematical method used in data analysis" or "I use this theory model to calculate the cross-section in this region of phase-space".

 

[Saturnine]

In particle physics?
Typical theory positions won't give you hands-on work. You might come in contact with the mess of data-analysis if you work together with collaborations. If you count that as "do some experiments", ...
Experimental positions can span the whole range from "I solder together stuff in the lab" to "I improve a mathematical method used in data analysis" or "I use this theory model to calculate the cross-section in this region of phase-space".

Can you give me some books or tutorial for data analysis which is used in collaborations.

For example, in the "Towards the Mathematics of Quantum Field Theory" I would like to test everything what I can. Can I test it in crystals and lasers for example. So, the data I can collect, how to use it in higher mathematics.
Thx

 

[mfb]

Google "data analysis high energy physics" -> Data Analysis in High Energy Physics: A Practical Guide to Statistical Methods
I didn't read it, but it looks good.
Individual analyses might use more specialized publications, but it is impossible to read all of them.

Can I test it in crystals and lasers for example.

Test what, why, how?

So, the data I can collect, how to use it in higher mathematics.

How do you want to use experimental data in mathematics? Mathematics does not care about measurement results.

 

[DEvens]

I'm reading Frederic's Paugam "Towards the Mathematics
of Quantum Field Theory."
I'm also interested in higher structures in mathematics which could have applications in physics.
How to check theese theories with the experimental data ?
For example the data in LHC. Where can I find experimental results to check QFT from theoretical point of view ?

It is unlikely you will make any useful progress comparing to LHC data, even supposing you could get it. This is a drastically specialist area. You would need to have a detailed understanding of a huge amount of context and detail of the specifics of he lab and the detector you had data for. This would involve, probably, many months of intense effort just to get the background. And unless you are in a graduate program actually working on the project, you are going to have trouble getting anybody to help you to the extent you would need. The people working in these labs are very busy.

You will likely do better by looking at some of the "standard" experiments that form the foundation of quantum mechanics. For example, you could start with such old-time enjoyments as black body radiation, the double slit experiment, the Hydrogen atom spectrum, and Rutherford scattering. If you get to the point where those seem too easy, you could move on to things like the Lamb shift and Compton scattering. These are all such standard things that you will find them in many standard textbooks.

Reading the jacket text on the book you mention, it says he gives examples from experiments. What experiments does he refer to?