A particular representation of gamma matrices

In summary, the conversation discusses the existence of a representation of gamma matrices that is unitarily equivalent to the standard representation and results in Dirac Spinors with positive energy and generic momentum having only the first two components different from zero. The concept of unitary equivalence and the potential use of the Foldy Wouthuysen transformation are also mentioned.
  • #1
array89
2
0
I was wondering if there is a representation of gamma matrices unitarily equivalent to the standard representation for which Dirac Spinors with positiv energy and generic momentum have only the first two component different prom zero. Anyone can help me?
 
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  • #2
array89 said:
I was wondering if there is a representation of gamma matrices unitarily equivalent to the standard representation...

yeah, presumably there are lots of representations which are unitarily equivalent to the standard representation... I'm not sure what you are asking? As far as I know unitary equivalence means a matrix A is related to another matrix B via A=UBU^\dagger where U is unitary. So take any unitary matrix U and apply U\gamma_\mu U^\dagger for each mu to generate an equivalent rep.
 
  • #3
yes I know it. I was wondering what's the representation for which any spinor of positive energy and momentum p have only the first two component different from zero
 
  • #4
Isn't that the definition of the Foldy Wouthuysen transformation?
 

1. What are gamma matrices?

Gamma matrices are a set of mathematical objects used in quantum field theory to represent the spin of particles. They are used to describe the behavior of fermions, which are particles with half-integer spin.

2. How are gamma matrices represented?

There are several ways to represent gamma matrices, but the most common is the Dirac representation, which uses 4x4 matrices that satisfy the Clifford algebra. Another representation is the Weyl representation, which uses 2x2 matrices.

3. What is the significance of gamma matrices?

Gamma matrices are significant because they allow us to study and understand the behavior of particles with spin. They are also essential in the development of quantum field theories, such as the Standard Model.

4. Can gamma matrices be used to describe all particles?

No, gamma matrices are only applicable to fermions. Bosons, which have integer spin, are described using different mathematical objects, such as gauge fields.

5. How are gamma matrices related to the Lorentz group?

Gamma matrices are closely related to the Lorentz group, which describes the symmetries of special relativity. In fact, the Dirac and Weyl representations of gamma matrices are representations of the Lorentz group. This allows us to use gamma matrices to study the behavior of particles in relativistic systems.

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