# Quantum Field Theory-Mass spectrum of Lagrangian

• jgarrel
In summary, we are given a Lagrangian density with a complex scalar field and Dirac fields, as well as constants m and g. We are asked to determine the mass and spin of the particles described by this theory. Approaches considered include spontaneous symmetry breaking and the Higgs mechanism, as well as using Feynman rules to calculate propagators.
jgarrel

## Homework Statement

We are given the Lagrangian density:
$$\mathcal{L}=\partial^\mu \phi ^* \partial_\mu \phi - m\phi^* \phi +\sum_{\alpha =1} ^2 ( \overline{\psi}^\alpha (i\gamma^\mu \partial_\mu -m)\psi^\alpha -g\overline{\psi}^\alpha\psi^\alpha \phi^* \phi)$$
, where ##\phi## is a complex scalar field, ##\psi ^1 ## ##\psi ^2 ## are Dirac fields and m,g are constants.

We are asked to find the mass and the spin of the particles that this theory describes.

## The Attempt at a Solution

I thouht about using spontaneous symmetry breaking and the Higgs mechanism, but I don't know how to deal with the kind of coupling presented in this problem.

I also thought about using the Feynman rules to calculate the propagators, but I don't think this is the right approach either. Any help would be appreciated.

## 1. What is Quantum Field Theory?

Quantum Field Theory (QFT) is a theoretical framework that combines the principles of quantum mechanics and special relativity to describe the behavior of particles at a subatomic level.

## 2. What is the Mass Spectrum of Lagrangian in QFT?

The mass spectrum of Lagrangian in QFT refers to the set of possible masses that particles can have according to the equations of the Lagrangian, which describes the dynamics of the quantum fields in the theory.

## 3. How is the Mass Spectrum of Lagrangian determined?

The mass spectrum of Lagrangian is determined through calculations and experiments in QFT. The equations of the Lagrangian are solved to find the possible masses of particles, and these predictions are then tested and refined through experiments.

## 4. What is the significance of the Mass Spectrum of Lagrangian in QFT?

The mass spectrum of Lagrangian is significant because it allows us to understand the properties and behavior of particles at a subatomic level. It also helps us make predictions about the behavior of these particles in different physical situations.

## 5. Can the Mass Spectrum of Lagrangian change?

Yes, the mass spectrum of Lagrangian can change as our understanding of QFT and experimental techniques improve. New particles can be discovered, and the properties of existing particles can be refined, leading to changes in the predicted mass spectrum.

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