On Sunday, May 10, 2020 at 7:20:16 AM UTC-5, Bruno Marchal wrote: > > > On 10 May 2020, at 13:45, Philip Thrift <[email protected] <javascript:>> > wrote: > > > > > cf. > https://www.researchgate.net/publication/325907723_A_gentle_introduction_to_Schwinger's_formulation_of_quantum_mechanics_The_groupoid_picture > > > > > *Schwinger’s picture of Quantum Mechanics* > https://arxiv.org/pdf/2002.09326.pdf > > > > > Those are good papers. > > (I am not entirely sure why you refer to them, but Swinger is very good on > this). When I teach quantum mechanics, I use an informal version of this, > based on a textbook by Thomson (but I failed to find it right now). This > helps to understand than both complex numbers and three dimension marry > well together to make the quantum weirdness hard to avoid. It provides > short path to the violation of Bell’s inequality. > > Bruno > > > > *In this paper we will present the main features of what can be called > Schwinger's foundational approach to Quantum Mechanics. The basic > ingredients of this formulation are the selective measurements, whose > algebraic composition rules define a mathematical structure called > groupoid, which is associated with any physical system. After the > introduction of the basic axioms of a groupoid, the concepts of observables > and states, statistical interpretation and evolution are derived. An > example is finally introduced to support the theoretical description of > this approach.* > > Finally, we will introduce *a quantum measure* associated with the state > ρ > > First, we realize that the state ρ on C∗(G) defines a decoherence > functional D on the σ-algebra Σ of events of the groupoid G > > We define a quantum measure µ on Σ > > ... > > > > @philipthrift > Click > > > > @philipthrift > > > A measure theory on *the appropriate measure space* underlies both probability theory and what has been called quantum-probability theory.
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