Relation between tensor decomposition and helicity amplitude

In summary, the conversation discusses the common practice of writing the photon two point function in terms of manifest transverse and longitudinal form factors, with the Lorentz structure factored out. The individual form factors, T_T and T_L, are then related to helicity amplitudes, which are typically given in terms of ++, --, or 00 for different degrees of freedom. It is also mentioned that for two transverse photons, g^{++} is used, but its meaning is unclear. The question posed is how to relate the helicity summed expressions to the individual helicity components.
  • #1
CAF123
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It is common to write e.g photon two point function in terms of manifest transverse and longitudinal form factors with lorentz structure factored out, e.g $$\Pi^{\mu \nu} = (g^{\mu \nu} - q^{\mu} q^{\nu}/q^2)T_T + q^{\mu} q^{\nu}T_L,$$ where mu and nu are polarisation indices.

How do I relate such expressions to helicity amplitudes which are usually given in terms of e.g ++, -- for transverse degrees of freedom or 00 for longitudinal?

If I take two transverse photons, then mu and nu are both +, but then what is ##g^{++}##? Looks like light cone components but I am not sure if this is the correct notation.
 
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  • #2
Perhaps put another way, how to go from helicity summed expressions to the individual helicity components?
 

1. What is tensor decomposition?

Tensor decomposition is a mathematical technique used to break down a multidimensional array, or tensor, into a combination of smaller, simpler tensors. It can be thought of as the equivalent of factoring a number into its prime factors.

2. How is tensor decomposition related to helicity amplitude?

Helicity amplitude is a physical quantity that describes the polarization of particles in a quantum field theory. Tensor decomposition is used to analyze and simplify the mathematical equations used to calculate helicity amplitude in particle physics.

3. What are the benefits of using tensor decomposition in studying helicity amplitude?

Tensor decomposition allows for a more efficient and accurate analysis of the complex equations involved in calculating helicity amplitude. It also helps to identify patterns and relationships between different components of the tensor, making it easier to interpret the physical meaning of the results.

4. Are there different methods of tensor decomposition used in studying helicity amplitude?

Yes, there are various methods of tensor decomposition, such as singular value decomposition, parallel factor analysis, and Tucker decomposition. Each method has its own advantages and may be more suitable for certain types of data or research questions.

5. How does tensor decomposition contribute to our understanding of particle physics?

Tensor decomposition plays a crucial role in analyzing and interpreting the complex equations and data involved in particle physics. It allows for a deeper understanding of the underlying patterns and relationships between different physical quantities, leading to new insights and discoveries in the field.

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