Dirac Equation

What is Dirac equation?

Dirac’s equation is a relativistic wave equation explaining that parity inversion (sign inversion of spatial coordinates) is symmetrical for all half-spin electrons and quarks. The equation was first explained in 1928 by P. A. M. Dirac. The equation is used to predict the existence of antiparticles. The equation also supports a solution for free moving electrons.

Dirac Equation Formula

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

All these physical constants are the reflection of special relativity and quantum mechanics. The purpose of formulating this equation was to study the relative motion of the electron and to treat the atom as consistent with relativity.

Applications of Dirac Equation

• In quantum mechanics, to resolve paradoxical features, the Dirac field is used.
• The Dirac sea was studied with the help of “hole theory” according to which there are many negative charged electrons occupied in the vacuum, and they are at eigenstate.

Other Formulations of the Equation

• Polar form: With the help of Lorentz transformation, Dirac spinors can be represented using two degrees of freedom ie; as the derivatives of scalar and pseudo scalar bi-linear quantities.
• As a differential equation: Spinor function of the Dirac equation for three out of four components can be represented as a partial differential equation for one component.
• Curved space-time: The equation can also be represented in curved space-time.

What is 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.