# Σ Model, from not obvious to obvious?

• PhyAmateur

#### PhyAmateur

Georgi in his book, for reference: http://www.people.fas.harvard.edu/~hgeorgi/weak.pdf he says that it is not obvious that the form of $$\Sigma = \sigma + i\tau_a\pi_a$$ is preserved under (2.6.6) $$\delta \Sigma = i \epsilon_L^aT_a \Sigma - i \Sigma \epsilon_R^aT_a$$

But then he said, "But it is true, and you can work out by explicit calculation the transformations of the $\sigma$ and $\pi _a$ fields":

$$\delta \sigma = \epsilon_5^a \pi_a$$
$$\delta \pi_a = - \epsilon_{abc}\epsilon^b\pi_c - \epsilon_5^a \sigma$$

But I have no idea how after what he wrote it became obvious? It is still not obvious to me how it is preserved though he saying it must be.

I don't think he wants to say that it becomes obvious but simply that if you actually do the calculation with the change of the ##\sigma## and ##\pi_a## fields that you listed before you'll find that it is actually invariant. By ''obvious'' he probably means that can be seen by eye, without doing the explicit calculation.

## 1. What is the Σ Model and how does it work?

The Σ Model is a scientific model that is used to analyze and interpret data. It works by taking a set of data and using mathematical equations to create a simplified representation of the data. This allows scientists to make predictions and draw conclusions about the data.

## 2. What are the advantages of using the Σ Model?

One of the main advantages of using the Σ Model is that it can help to simplify complex data and make it easier to analyze. It also allows for predictions to be made based on the data, which can help guide future research and experiments. Additionally, the Σ Model can help to identify patterns and relationships within the data that may not be immediately obvious.

## 3. How is the Σ Model different from other scientific models?

The Σ Model is a mathematical model that uses equations to represent data, while other models may use diagrams, simulations, or other methods. Additionally, the Σ Model is often used to analyze and interpret data, rather than to represent a physical system or process.

## 4. Can the Σ Model be used for all types of data?

The Σ Model is suitable for a wide range of data, including numerical, categorical, and time series data. However, it may not be appropriate for all types of data, such as non-linear or highly complex data.

## 5. How can I apply the Σ Model in my own research?

The Σ Model can be applied in a variety of scientific fields, such as biology, physics, economics, and psychology. To use the Σ Model, you will need to have a good understanding of mathematics and statistics, as well as the specific data you are working with. It is also important to carefully consider the assumptions and limitations of the model before applying it to your research.