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I recently watch drphysics video on deriving dirac equation and he use two waves moving in opposite directions to derive it, without touching clifford algebra. If this possible, what is the intuition behind it?

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- Thread starter TimeRip496
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In summary, it is not necessary to have knowledge of Clifford algebra in order to derive the Dirac equation. Some sources, such as the video by drphysics, use two waves moving in opposite directions to derive the equation without touching Clifford algebra. However, most introductory books do use Clifford algebra in the process of deriving the equation, as it is a natural representation of the proper orthochronous Lorentz group. The famous Handbook "Enzykloädie der mathematischen Wissenschaften" and the book "Atombau und Spektrallinien" also use alternative methods, such as quaternions, to derive the Dirac equation. Ultimately, all methods lead to the same result.

- #1

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I recently watch drphysics video on deriving dirac equation and he use two waves moving in opposite directions to derive it, without touching clifford algebra. If this possible, what is the intuition behind it?

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Do you have any sources that will allow me to derive the dirac equation without clifford algebra? Cause I have been searching on the Internet and all of it involves clifford algebra. Besides the one by drphysics he didnt really derive it fully such as the dirac matrix.ChrisVer said:

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However, I don't understand this "clifford algebra" thing. In every introductory book, they never used the Clifford algebra to derive the Dirac equation.

Most of them are starting by a linear Hamiltonian operator, which they act to reproduce the result of the relativistic energy-momentum-mass relation [itex]E^2 = m^2 +p^2 [/itex]. By doing so, you see that the objects that you used in your operator were not just complex numbers, but they should satisfy certain relations, one of them is the Clifford Algebra. You don't "use" it, you "result" in it...

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The Dirac equation is a relativistic quantum mechanical wave equation that describes the behavior of fermions, such as electrons, in a relativistic quantum system. It was developed by physicist Paul Dirac in 1928.

Clifford algebra, also known as geometric algebra, is a mathematical structure that extends the concepts of complex numbers and vectors to higher dimensions. It is based on the work of mathematician William Kingdon Clifford and is used in a variety of fields, including physics, computer graphics, and robotics.

Clifford algebra is used to represent the mathematical objects, known as spinors, that are necessary for the formulation of the Dirac equation. The properties of clifford algebra, such as its ability to handle rotations and reflections, make it a useful tool in understanding the behavior of particles described by the Dirac equation.

The Dirac equation and clifford algebra have a wide range of applications in various fields of physics, including quantum mechanics, particle physics, and cosmology. They are also used in engineering, particularly in the fields of computer graphics and robotics.

While the Dirac equation and clifford algebra have been successful in describing the behavior of particles at the quantum level, they are not able to fully explain all phenomena, such as gravity. Additionally, the mathematics involved in clifford algebra can be complex and difficult to work with, making it challenging to apply in some situations.

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