Schwinger’s picture of quantum mechanics
F. M. Ciaglia, F. Di Cosmo, A. Ibort, G. Marmo
Abstract
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.
Topics & Concepts
AxiomObservableInterpretation (philosophy)Interpretations of quantum mechanicsTheoretical physicsAlgebraic structureQuantumMathematical structureRelational quantum mechanicsAlgebraic numberCategorical quantum mechanicsQuantum probabilityQuantum processMinority interpretations of quantum mechanicsPhysicsAlgebra over a fieldMathematicsStochastic interpretationQuantum statistical mechanicsConsistent historiesQuantum mechanicsComputer sciencePhysical systemStatistical physicsQuantum dynamicsOpen quantum systemSIC-POVMClassical mechanicsMathematical formulation of quantum mechanicsComposition (language)Calculus (dental)Statistical mechanicsQuantum field theoryAlgebraic propertiesQuantum Mechanics and ApplicationsQuantum and Classical ElectrodynamicsAlgebraic and Geometric Analysis