What is the first and second quantization?

• Gabriel Maia
In summary, first quantization treats time as a parameter and replaces position with an operator, while second quantization treats time and position as parameters and everything is considered a field. This allows for the treatment of particles and fields in the same way and respects the principles of relativity. It is called second quantization because it is a different way of writing the same equations used in first quantization.
Gabriel Maia
I believe the title says it all.

What is the first and second quantization? What is the difference?

Thank you.

Tspirit
First quantiization replaces position by an operator and time is a parameter. However relativity requires time and position to be treated on the same footing. Second quatiziation, aka, Quantum Field Theory, treats time and position as parameters, ie everything is a field. This way not only is relativity respected, but particles like electrons are treated in exactly the same way as EM fields that are quantisized. It was called second quantisation because originally the wavefunction was thought of as a field and was quantisized like EM fields were, but nowadays is viewed a bit differently.

Thanks
Bill

1 person
Let' say you have a system of many identical particles and you write Schroedinger's equation for them (ie. first quantization). Second quantization is simply a different way of writing the same equations, so that the symmetrization or anti-symmetrization of the wave function for identical particles is taken care of by the commutation properties of operators.

1 person
You may also find the following of value:
http://www-physique.u-strasbg.fr/cours/l3/divers/meca_q_hervieux/Articles/Nine_form.pdf

See interpretation F: Second quantization.

Thanks
Bill

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Gabriel Maia

What is the first quantization?

The first quantization is a mathematical framework used in quantum mechanics to describe the behavior of particles at a microscopic level. It involves assigning wave functions to particles and using mathematical operators to represent physical quantities such as position and momentum.

What is the second quantization?

The second quantization is an extension of the first quantization framework that takes into account the existence of multiple identical particles. It involves representing particles as creation and annihilation operators that act on a quantum state, allowing for the description of systems with varying numbers of particles.

How does first quantization differ from classical mechanics?

In classical mechanics, particles are described using classical equations of motion and are treated as distinct, localized objects. In first quantization, particles are described as waves and their behavior is governed by probabilities rather than definite values. Additionally, classical mechanics does not take into account the effects of quantum entanglement, which is a key aspect of first quantization.

What are some practical applications of first and second quantization?

First and second quantization have numerous applications in physics, chemistry, and engineering. They are used to understand and predict the behavior of subatomic particles, atoms, and molecules. They are also essential in the development of technologies such as transistors, lasers, and nuclear reactors.

What are the limitations of first and second quantization?

First and second quantization are powerful tools for describing the behavior of particles, but they are not without limitations. They are unable to fully explain certain phenomena such as gravitation and the behavior of particles at extremely high energies. Additionally, the mathematical formalism of second quantization can be complex and difficult to apply in certain situations.

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