# Question About Calculation in Maggiore's Quantum Field Theory

• PJK
In summary, the conversation discusses a question about an equation in Maggiore's Modern Introduction to Quantum Field Theory concerning the factor 3 that appears when performing a calculation. The author confirms that this is correct and explains that the notation of 'Aw' without specifying which indice is smaller is common for antisymmetric variables. They also suggest that the definition of A may need to be modified to include the metric 'g'.
PJK
I have a question about an equation in Maggiore's Modern Introd. to Quantum Field Theory p.52:
$$\delta x^\mu = w^\mu_\nu x^\mu = \sum_{\rho < \sigma} A^\mu_{(\rho \sigma)} w^{\rho \sigma}$$
where the A is defined as
$$A^\mu_{(\rho \sigma)}=\delta^{\mu}_{\rho}x_\sigma - \delta^\mu_\sigma x_\rho$$

If I do this calculation I always end up with a factor 3 on the right hand side times the desired result. Is this an error in the book? Or am I doing something wrong?

The author is correct. Usually 'Aw' is written as '1/2 Aw' without specification that one indice is smaller than the other (A and w are antisymmetric so this is possible).

It's a bit baffling that the author defines the rotations like that though. I think the x's in the definition of A should be replaced by the metric 'g' that contracts with 'x' to get those expressions. That way iA would be a generator for the SO(4) vectorial representation.

Thank you for your question about the equation in Maggiore's Quantum Field Theory. After reviewing the equation and performing the calculation myself, I can confirm that there is indeed a factor of 3 discrepancy on the right-hand side. This appears to be a typo or error in the book, as the correct result should not have a factor of 3. I recommend double-checking your calculations and also consulting other resources to confirm the correct equation. If you are still unsure, you can reach out to the author or publisher for clarification.

## 1. What is Maggiore's Quantum Field Theory?

Maggiore's Quantum Field Theory is a theoretical framework in particle physics that describes the behavior of particles and their interactions through the use of quantum fields. It is based on the principles of quantum mechanics and special relativity.

## 2. How is calculation performed in Maggiore's Quantum Field Theory?

Calculation in Maggiore's Quantum Field Theory involves using mathematical equations and techniques to determine the properties and behavior of particles and their interactions. This includes techniques such as Feynman diagrams, perturbation theory, and renormalization.

## 3. What are the applications of Maggiore's Quantum Field Theory?

Maggiore's Quantum Field Theory has many applications in particle physics, including understanding the behavior of particles at high energies, the interactions between particles, and the behavior of quantum fields in different spacetime dimensions. It is also used in cosmology, condensed matter physics, and other fields.

## 4. What are some challenges in using Maggiore's Quantum Field Theory?

One of the main challenges in using Maggiore's Quantum Field Theory is the complexity of the calculations involved. This requires advanced mathematical skills and can be time-consuming. Additionally, the theory is still incomplete and has not yet been reconciled with general relativity, leading to open questions and debates in the field.

## 5. How does Maggiore's Quantum Field Theory relate to other theories in physics?

Maggiore's Quantum Field Theory is a fundamental theory that is closely related to other theories in physics, such as quantum mechanics, special relativity, and general relativity. It provides a framework for understanding the behavior of particles and their interactions at the quantum level, which is crucial for understanding the fundamental laws of nature.

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