What is an effective field theory?

[StarsRuler]

What is an effective field theory??

Yeah, there is many information on Internet, but it is a complicated level, they speak about cut-off, top-down, series development without justify limit the coefficients of ignored terms in the development.
Aren´t there a simple (but rigurous) explanation about this question? A explanation here or a link, it is indifferent for me. The Wikipedia page don´t explain nothing, only names examples about with what interactions it is used, and the "introductions" write downs are for a level very over graduate level.

Thanks

 

[AndyW]

for your question about effective field theories. I understand that the concept can seem overwhelming and confusing, but I will do my best to provide a clear and concise explanation.

An effective field theory (EFT) is a theoretical framework used to describe physical phenomena at a specific energy scale or range. It is based on the idea that at different energy scales, different degrees of freedom become relevant in the description of the system. For example, at low energies, we can use Newton's laws of motion to describe the behavior of objects, but at very high energies, we need to use the theory of relativity.

In EFT, we start with a more fundamental theory, such as quantum field theory, and then we systematically integrate out the high-energy degrees of freedom to create a simplified theory that is applicable at a specific energy scale. This simplified theory is known as the effective field theory.

One of the key aspects of EFT is the use of a cut-off, which is a maximum energy scale at which the theory is valid. This is necessary because the effective theory is only valid within a certain energy range and breaks down at higher energies. The cut-off allows us to determine which terms in the theory are important and which can be ignored, leading to a more manageable and accurate description of the system.

EFTs are used in many areas of physics, such as particle physics, condensed matter physics, and cosmology. They allow us to make predictions and calculations without needing to know all of the details of the underlying fundamental theory. This makes them a powerful tool for understanding and predicting physical phenomena.

I hope this explanation helps to clarify the concept of effective field theories. If you would like to learn more, here are some resources that may be helpful:

1. "Effective Field Theories" by John F. Donoghue, Eugene Golowich, and Barry R. Holstein
2. "Effective Field Theories in Particle Physics" by Aneesh V. Manohar and Mark B. Wise
3. "Introduction to Effective Field Theory" by C. P. Burgess
4. "Effective Field Theory: A Primer" by David B. Kaplan
5. "Effective Field Theory and Quantum Gravity" by Don N. Page

I wish you the best in your studies and understanding of this important concept in physics.