$C^*$-fermi systems and detailed balance

• URL: http://arxiv.org/abs/2010.07296v1
• Date: Wed, 14 Oct 2020 15:16:32 GMT
• Title: $C^*$-fermi systems and detailed balance
• Authors: Vitonofrio Crismale, Rocco Duvenhage and Francesco Fidaleo
• Abstract summary: A systematic theory of product and diagonal states is developed for tensor products of $mathbb Z$-graded $*$-algebras. Twisted duals of positive linear maps between von Neumann algebras are then studied, and applied to solve a positivity problem on the infinite Fermi lattice.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A systematic theory of product and diagonal states is developed for tensor products of $\mathbb Z_2$-graded $*$-algebras, as well as $\mathbb Z_2$-graded $C^*$-algebras. As a preliminary step to achieve this goal, we provide the construction of a {\it fermionic $C^*$-tensor product} of $\mathbb Z_2$-graded $C^*$-algebras. Twisted duals of positive linear maps between von Neumann algebras are then studied, and applied to solve a positivity problem on the infinite Fermi lattice. Lastly, these results are used to define fermionic detailed balance (which includes the definition for the usual tensor product as a particular case) in general $C^*$-systems with gradation of type $\mathbb Z_2$, by viewing such a system as part of a compound system and making use of a diagonal state.

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