Dirac Equation

When the Dirac equation was not introduced, it was very difficult to explain the behaviour of the particles as the particles with higher velocities were not studied. The Dirac equation introduced four new components of the waves, further, those four components are divided into two energy states: positive and negative. Both the energy states will spin half up and down. With the help of the Dirac equation, new spin properties and magnetic moments were assigned.

The magnetic moment is given as - \[\mu_{D} = \frac{qS}{m}\]

Where,

• S is the spin vector.

• q is the charge.

• m is the mass.

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What is Dirac Equation?

Dirac’s equation is a relativistic wave equation that explains that for all the half-spin electrons and quarks parity inversion (sign inversion of spatial coordinates) is symmetrical. The Dirac equation was first explained by P. A. M. Dirac in the year 1928. This equation of Dirac was used to predict the existence of antiparticles and it also supports a solution for free moving electrons. According to the Wiktionary, the Dirac equation meaning - It is a relativistic wave equation that describes the electron and similar kind of particle, It is also used to predict the existence of antiparticles.

Dirac Equation Formula (Dirac Formula)

\[(\beta mc^{2} + c \int_{n=1}^{3} \alpha_{n} p_{n}) \psi (x, t) = i h \frac{\partial \psi(x, t)}{\partial t}\]

Where,

• 𝜓 = 𝜓(x, t) is the electron wave function

• M is the electron mass at rest

• X, t is the spacetime coordinates

• p₁, p₂, p₃ are the momentum components

• c is the speed of light

• ℏ is the Planck constant

All these physical constants stated above in the Dirac formula equation are the reflection of special relativity and quantum mechanics. The main purpose behind the formulation of this equation was to study the relative motion of the electron and to treat the atom as consistent with relativity. This equation can be formulated in a number of ways, for more details you can find the Dirac equation PDF on the internet.

Dirac Theory

Dirac’s relativistic theory is the quantum theory of the electron. In particular, we can say that experimental data that we have already talked about contradicts Dirac’s prediction that certain hydrogen electrons that really are of the stationary states have degenerated. And it has the same energy as certain other states, which are as well as Dirac’s prediction that are for the value of the magnetic moment of the electron.

The physicist named Schwinger built quantum electrodynamical calculation, which made use of the notions that are related to mass and charge renormalization. which we can say that brought agreement between the experiment and the theory data. This was one of the crucial breakthroughs which initiated a new era in the quantum field theory. The physicist Richard Feynman and Tomonaga Shin’ichirō were said to be independent in 1965 had carried out similar calculations and the three of them shared the Nobel Prize as well.

Applications of Dirac Equation

• In quantum mechanics, to resolve paradoxical features.

• The study of Dirac see was done, with the help of “hole theory”, which states that there are many negatively charged electrons occupied in the vacuum, and they are at eigenstate.

Other Formulations of the Equation

• In the polar form with the help of Lorentz transformation, Dirac spinor can be represented using two degrees of freedom, that are the derivatives of scalar and pseudoscalar bi-linear quantities.

• As a differential equation: The spinor function of the Dirac equation for three out of four components can be represented as a partial differential equation for one component.

• It is used in the formulation of curved space-time to represent the equation in curved space-time.

Did You Know?

What is the Dirac field? Dirac field is an example of the fermion field In which the canonical time equal communication relations are replaced with the canonical time equal anti-communication relations.