# Where does energy come from in QFT?

• lindl
In summary, energy in quantum field theory (QFT) is a fundamental concept that arises from the principles of quantum mechanics. It is quantized due to the wave-particle duality and is closely related to mass according to Einstein's famous equation, E=mc². This differs from classical physics where energy is continuous and conserved on its own. In QFT, energy is constantly transforming and exchanging between different forms, as explained by the Big Bang theory.
lindl
Homework Statement
The origin of energy in the creation of elementary particles
Relevant Equations
QFT
When we say energy is applied to that field to create an excitation which is a particle, where does that energy come from and how is it applied? For example on beta decay where a new electron is formed, where does the energy come from the create an excitement in the electron field?

From the W boson that it's annihilated.

## 1. Where does the concept of energy come from in QFT?

In quantum field theory (QFT), energy is a fundamental quantity that arises from the mathematical framework of the theory. It is a conserved quantity that describes the ability of a system to do work or cause change. In QFT, energy is associated with the fields that make up the universe, and it can be transferred between particles through interactions.

## 2. How is energy defined in QFT?

In QFT, energy is defined as the generator of time translations. This means that energy is the quantity that determines how a system evolves over time. It is also defined as the eigenvalue of the Hamiltonian operator, which represents the total energy of a system.

## 3. Can energy be created or destroyed in QFT?

In QFT, energy is a conserved quantity, which means it cannot be created or destroyed. It can only be transferred or converted into different forms. This is known as the law of conservation of energy, which is a fundamental principle in physics.

## 4. How does the concept of energy in QFT differ from classical mechanics?

In classical mechanics, energy is a continuous quantity that can take on any value. However, in QFT, energy is quantized, meaning it can only take on certain discrete values. This is due to the probabilistic nature of quantum mechanics, where energy levels are determined by the wave function of a particle.

## 5. What is the relationship between energy and mass in QFT?

In QFT, energy and mass are two sides of the same coin, known as mass-energy equivalence. This is described by Einstein's famous equation, E=mc^2, where energy (E) and mass (m) are interchangeable. In QFT, particles can also gain or lose energy through interactions, which can affect their mass.

• Introductory Physics Homework Help
Replies
12
Views
413
• High Energy, Nuclear, Particle Physics
Replies
3
Views
2K
Replies
4
Views
874
• High Energy, Nuclear, Particle Physics
Replies
32
Views
2K
• High Energy, Nuclear, Particle Physics
Replies
21
Views
1K
Replies
1
Views
1K
Replies
14
Views
1K
Replies
1
Views
989
• High Energy, Nuclear, Particle Physics
Replies
8
Views
1K