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If I have, say three sites in a symbolic operator which is of the form A = a⊗1⊗c and I want it to act on another operator B = a1⊗b⊗1 in order to find the commutator A.B - B.A, the result I expect would be A.B = a.a1⊗b⊗c, but I am unable to achieve such a result using the regular A.B command. A.B gives a⊗c.a1⊗b. I would also like to know how I can expand the dot product to multiple terms if they exist. Any help would be appreciated.

I tried the following:

A = TensorProduct[a, 1, c]

B = TensorProduct[a1, b, 1]

A.B

The output it gives is a⊗c.a1⊗b but the output I expect is a.a1⊗b⊗c

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    – Dunlop
    Commented Sep 17, 2019 at 4:13
  • $\begingroup$ Perhaps you can give some examples of formatted code you have tried ? This makes it much easier for others to try to work on answering your question $\endgroup$
    – Dunlop
    Commented Sep 17, 2019 at 4:14
  • $\begingroup$ @Dunlop Edited as instructed. $\endgroup$
    – Net
    Commented Sep 17, 2019 at 4:36

1 Answer 1

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KroneckerProduct will work with symbolic tensors, although it needs some help from TensorExpand. First, set some assumptions on your tensors:

$Assumptions = (a | a1 | b | c) ∈ Matrices[{n, n}];

Then, your example is:

A = KroneckerProduct[a, IdentityMatrix[n], c];
B = KroneckerProduct[a1, b, IdentityMatrix[n]];

A.B

KroneckerProduct[a, IdentityMatrix[n], c].KroneckerProduct[a1, b, IdentityMatrix[n]]

Using TensorExpand produces your desired result:

TensorExpand[A.B]

KroneckerProduct[a.a1, b, c]

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  • $\begingroup$ Thank you very much! $\endgroup$
    – Net
    Commented Jul 25, 2020 at 3:37

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