How do I use tensors in Mathematica 7?

• Mathematica
• Dox
In summary, the conversation discusses the use of the R_\xi gauge fixing for calculating the propagator of a gauge field. The propagator has a matricial structure and the speaker wants to check it using the fact that the propagator can be written in a specific form. They use a command line to write the needed expression and then want to compute the residues of any component without losing the matricial structure. The suggested method for computing the residues is to use the function Residue[expr, var].
Dox
Hi there!

I'm tring to check some calculations of the propagator of a gauge field using the $R_\xi$ gauge fixing.

Since the propagator has a matricial structure,

$\Delta_{\mu\nu}=\frac{1}{(p^0)^2+E_p^2}\left[\delta_{\mu\nu}-\frac{1-\xi}{(p^0)^2+E_p^2}p_\mu p_\nu\right],$​

I'd like to check it using that fact. Using the command line

Array[(KroneckerDelta[#1,#2]-(1- xi) p[#1] p[#2]/(p[0]^2+ep^2))/(p[0]^2+ep^2) & , {4,4}, {0,0}]

I was able to write the needed expression, but then I'd like to compute the residues of ANY component... without losing the matricial structure. Is this possible?

All my guesses are fraud.For example... if I try to give a name to the array

M=Array[(...)]

it does not recognize the matrix structure.Whatever help is useful. Thanks.

Last edited:
The best way to compute the residues of any component is to use the function Residue[expr, var]. For example, to compute the residue of the (1, 2) element of the matrix M, you can useResidue[M[[1,2]], p[0]]

Hi there,

Thank you for your question. To use tensors in Mathematica 7, you can use the built-in tensor functions such as TensorProduct, TensorTranspose, and TensorContract. These functions allow you to manipulate tensors and perform operations such as multiplication, transposition, and contraction.

In your specific case, you can use the TensorProduct function to create a tensor with the desired structure. For example, you can create a tensor with components \Delta_{\mu\nu} as follows:

TensorProduct[KroneckerDelta[\[Mu], \[Nu]], (1/(p[0]^2 + Ep^2)) - (1 - xi)/(p[0]^2 + Ep^2)^2 p[\[Mu]] p[\[Nu]]]

To compute the residues of any component, you can use the TensorContract function with the appropriate indices. For example, to compute the residue of the first component, you can use:

TensorContract[%, {\[Mu], \[Nu]}]

As for giving a name to the array, you can use the Set function to assign a name to the tensor. For example:

M = TensorProduct[KroneckerDelta[\[Mu], \[Nu]], (1/(p[0]^2 + Ep^2)) - (1 - xi)/(p[0]^2 + Ep^2)^2 p[\[Mu]] p[\[Nu]]]

I hope this helps. Let me know if you have any further questions. Good luck with your calculations!

1. What is a tensor in Mathematica 7?

A tensor in Mathematica 7 is a multidimensional array or data structure that can hold numerical or symbolic data. It is commonly used in mathematics and physics for representing and manipulating vectors, matrices, and higher-order arrays.

2. How do I create a tensor in Mathematica 7?

To create a tensor in Mathematica 7, you can use the "TensorProduct" function or the "Array" function. The "TensorProduct" function allows you to create a tensor by specifying the dimensions and filling it with a specific value. The "Array" function allows you to create a tensor by specifying the dimensions and providing a function to generate the values for each element.

3. How do I perform operations on tensors in Mathematica 7?

You can perform various operations on tensors in Mathematica 7 using built-in functions such as "Dot", "Transpose", and "TensorReduce". These functions allow you to perform operations like matrix multiplication, transposition, and simplification on tensors.

4. Can I import and export tensors in Mathematica 7?

Yes, you can import and export tensors in Mathematica 7 using the "Import" and "Export" functions. You can import tensors from external files in various formats such as CSV, JSON, and MATLAB, and export tensors to these formats as well.

5. Are there any special functions for working with tensors in Mathematica 7?

Yes, there are several special functions specifically designed for working with tensors in Mathematica 7. These include "TensorContract", "TensorTranspose", and "TensorExpand", which allow you to manipulate tensors in specific ways, such as contracting or transposing indices.

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