The Dirac equation solved in Weyl representation is a mathematical equation that describes the behavior of spin-1/2 particles such as electrons. It combines principles from special relativity and quantum mechanics to accurately predict the behavior of fundamental particles.
In the standard Dirac representation, the Dirac equation is represented by a 4x4 matrix. In the Weyl representation, the same equation is represented by two 2x2 matrices, one for left-handed particles and one for right-handed particles. This representation is more useful for studying particles with definite chirality.
The Weyl representation simplifies the Dirac equation and makes it easier to study particles with specific properties, such as chirality. It also allows for a more direct connection to certain physical phenomena, such as the quantum Hall effect.
The Dirac equation was first solved in Weyl representation by physicists Tsutomu Yanagida and Tetsuo Yanagida in 1970. They derived two 2x2 matrices that satisfied the Dirac equation and were equivalent to the 4x4 matrix in the standard representation. Later, other physicists refined this solution and developed various techniques for solving the Dirac equation in Weyl representation.
The Weyl representation of the Dirac equation has been used in various fields of physics, including particle physics, condensed matter physics, and cosmology. It has helped to explain phenomena such as the behavior of particles in magnetic fields, the quantum Hall effect, and the properties of topological insulators. It also plays a crucial role in the Standard Model of particle physics.