What Does quantization Mean
The notion of quantization refers to the process that is carried out to, starting from a description of classical physics , develop the construction of a quantum model . In this way, it is considered a classical theory and transformed into quantum theory .
Classical and quantum physics
To understand what quantization is, therefore, you must first know how to differentiate between classical physics and quantum physics . In classical physics, states are values of observables (detectable properties through physical actions) that can be measured . The measurement of the observables does not alter the states.
A quantum theory from a classical one
In quantum physics, on the other hand, states appear as abstract objects that house, in a hidden way, the data of the values of the observables. The coding of the observables is developed in operators (mathematical objects).
Returning to the idea of quantization, it is about finding the states and the corresponding observables, finding their representation as operators and taking classical theory as a starting point.
Classification
It should be noted that there are different quantization methods , following various mathematical forms. This leads us to an inevitable division into two groups, to facilitate both its study and its application in the corresponding fields.
Thus, it is possible to distinguish between first quantization procedures and second quantization procedures . In the first case, models of a particle are built , while in the second, systems of multiple equal particles are analyzed.
The canonical quantization , the algebraic quantization , the geometric quantization , the quantization of Weyl and covariant quantization are some procedures that can run quantization. It is important to bear in mind that the theories that result from the quantization of the same classical theory have to be equivalent and consistent, regardless of the method used.
First quantization
The procedures that fall into this first group are methods thanks to which it is possible to build models of a particle in the field of quantum mechanics starting from the classical description of phasic space (also known as phase diagram or phase space ). of a particle.
This is where the aforementioned canonical quantization is located . It is an informal procedure by which an operator is assigned to a physical quantity: the first must be obtained by substituting hermitic operators for the canonical variables directly, and the result must satisfy a defined series of relationships between the variables .
Weyl quantization , a procedure for the construction of a hermitic operator in the L 2 space for a system that has a classical phase space with a R 2n topology, also falls into this group . The first description of this technique took place in 1927 and was in charge of the German mathematician Hermann Weyl .
Second quantization
In this group we find a series of methods that pursue the construction of field theories starting from a classical theory. Note that the physical discipline known as quantum field theory is used to apply the principles of quantum mechanics to classical systems of continuous fields.
The canonical quantization of the second group contemplates more than one particle
Here we also speak of canonical quantization , although it differs from the procedure described in the first group in that it is applied to a group of particles, and not to just one. On the other hand we are using path integral , which is based on building a space of Hilbert of a bounded measure based on the functional action.
La segunda cuantización es importante porque permite: el estudio de los campos físicos desde una perspectiva cuántica; incluir los aspectos combinatorios que se desprenden de la estadística del tipo de partículas usado; simplifica la extensión de la mecánica cuántica no relativista a aquellos sistemas en los que la cantidad de partículas no se entiende como una constante del movimiento.