Schwinger's Picture of Quantum Mechanics IV: Composition and independence

Abstract

The groupoids description of Schwinger's picture of quantum mechanics is continued by discussing the closely related notions of composition of systems, subsystems, and their independence. Physical subsystems have a neat algebraic description as subgroupoids of the Schwinger's groupoid of the system. The groupoids picture offers two natural notions of composition of systems: Direct and free products of groupoids, that will be analyzed in depth as well as their universal character. Finally, the notion of independence of subsystems will be reviewed, finding that the usual notion of independence, as well as the notion of free independence, find a natural realm in the groupoids formalism. The ideas described in this paper will be illustrated by using the EPRB experiment. It will be observed that, in addition to the notion of the non-separability provided by the entangled state of the system, there is an intrinsic `non-separability' associated to the impossibility of identifying the entangled particles as subsystems of the total system.

32 pages. Comments are welcome!

Cited by in corpus (8)

• From the Jordan product to Riemannian geometries on classical and quantum states
• Quantum States, Groups and Monotone Metric Tensors
• Differential geometric aspects of parametric estimation theory for states on finite-dimensional C*-algebras
• Schrödinger's problem with cats: measurements and states in the Groupoid Picture of Quantum Mechanics
• Feynman's Propagator in Schwinger's picture of Quantum Mechanics
• Covariant Variational Evolution and Jacobi Brackets: Fields
• Covariant Variational Evolution and Jacobi Brackets: Particles
• Covariant reduction of classical Hamiltonian Field Theories: From D'Alembert to Klein-Gordon and Schrödinger