Understanding Fields in Quantum Mechanics: Electrons, Waves, & Particles

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In summary, a field in quantum mechanics is a mathematical concept used to describe the behavior of particles. It involves the quantization of a classical field, which is then translated into operators for each momentum, similar to the creation and annihilation operators in the harmonic oscillator. Each fundamental particle requires its own field, though some theories aim to find one unified field. Resources for further reading include books on quantum field theory by Ryder, Weinberg, and Srednicki.
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gk007
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What is a field in quantum mechanics (not the classical version)? And when it is said that an electron is an "excitation state of a field", does that mean that electrons are created by wave or disturbances in a field? Also, is there a different type of field for each fundamental particle, or can it be simplified to one big field?
 
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gk007 said:
What is a field in quantum mechanics
You have to study quantum field theory.

What one does is (roughly speaking) the following. One takes the Dirac field (mathematically it is a classical field), takes it's Fourier transform and translates the Fourier components b(p), b*(p) and d(p) d*(p) into operators. This step is called quantization. For each three-momentum p there are these operators which are related to the creation and annihilation operators in case of the harmonic oscillator. That means a plane wave with a certain momentum p is "created" in the Hilbert space using a creation operator. Attention: there is not only one pair, but two pairs for each p.

gk007 said:
Also, is there a different type of field for each fundamental particle, or can it be simplified to one big field?
One needs a field for each particle, e.g. one field for the photon (4-potential), one for the electron and the positron, one for the quarks (the different colors are treated via indices, so the field becomes a 4-spinor with an additional color-index i=1..3), one for the gluon (4-potential now with a color index a=1..8) etc.

Finding one big field is the dream of theoretical physicists in the context of a "theory of everything". String theory (a much debated, partial controversial issue) comes rather close to this dream, as there is only one string.
 
  • #3
OK, thanks for clearing everything up :)
 
  • #4
really, everything?
 
  • #5
Do you have any papers or references to someone performing those operations? Id be interested to see...
 
  • #6
Every book on quantum field theory will do.

I recommend
- Ryder
- Weinberg
- Srednicki (draft: http://www.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf; ; chapter 3 Canonical Quantization of Scalar Fields)
 
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1. What are fields in quantum mechanics?

Fields in quantum mechanics are physical quantities that exist in space and time and can interact with particles to exert forces or produce energy. In the context of electrons, waves, and particles, fields are used to describe the behavior and interactions of these entities.

2. How do fields interact with particles in quantum mechanics?

In quantum mechanics, fields interact with particles through the exchange of energy and momentum. This interaction can be described by mathematical equations such as quantum field theory, which allows for the prediction of particle behavior and the creation of new particles through the manipulation of fields.

3. What is the relationship between fields and waves in quantum mechanics?

Fields and waves are closely related in quantum mechanics. Particles, such as electrons, can be described as both particles and waves, and their behavior is influenced by the surrounding fields. The wave-like nature of particles can also be observed in phenomena such as diffraction and interference.

4. How do electrons behave in fields in quantum mechanics?

Electrons behave differently depending on the type of field they are interacting with. In the presence of an electric field, electrons can be accelerated or decelerated, while in a magnetic field, they can experience a force that changes their direction of motion. In quantum mechanics, the behavior of electrons in fields is described by the Schrödinger equation.

5. What is the significance of understanding fields in quantum mechanics?

Understanding fields in quantum mechanics is crucial for understanding and predicting the behavior of particles and their interactions. This knowledge has led to advancements in technology, such as the development of transistors and lasers, and has also helped us gain a deeper understanding of the fundamental laws of nature.

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