Tensor product of fields

Okay, imagine you have two toy boxes, one with red toys and another with blue toys. If you want to combine these two toy boxes, you can line them up next to each other and make a bigger toy box with both red and blue toys inside. This is kind of like the tensor product of two fields.

Fields are like toy boxes that hold numbers instead of toys. Let's say you have two fields, one with numbers that are only even and another with numbers that are only odd. If you want to combine these two fields, you can use the tensor product to make a bigger field that has both even and odd numbers inside.

The way the tensor product works is that it takes all possible combinations of pairs of numbers from each field and multiplies them together. For example, if the first field has 2 and 4 in it and the second field has 1 and 3 in it, then the tensor product field will have 2*1, 2*3, 4*1, and 4*3 in it.

So basically, the tensor product is a way to combine two fields so that you get a new field with all possible combinations of pairs of numbers from the original fields. It's kind of like making a bigger toy box by combining two smaller ones.