We study a general tensor product for two collections of related physical operations or observations. This is a free product, subject only to the condition that the operations in the first collection fail to have any influence on the statistics of operations in the second collection and vice versa. In the finite-dimensional case, it is shown that the vector space generated by the probability weights on the general tensor product is the algebraic tensor product of the vector spaces generated by the probability weights on the components. The relationship between the general tensor product and the tensor product of Hilbert spaces is examined in the light of this result.
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Kläy, M., Randall, C. & Foulis, D. Tensor products and probability weights. Int J Theor Phys 26, 199–219 (1987). https://doi.org/10.1007/BF00668911
- Hilbert Space
- Field Theory
- Vector Space
- Elementary Particle
- Quantum Field Theory