Geometric Event-Based Relativistic Quantum Mechanics

Abstract

We propose a special relativistic framework for quantum mechanics. It is based on introducing a Hilbert space for events. Events are taken as primitive notions (as customary in relativity), whereas quantum systems (e.g. fields and particles) are emergent in the form of joint probability amplitudes for position and time of events. Textbook relativistic quantum mechanics and quantum field theory can be recovered by dividing the event Hilbert spaces into space and time (a foliation) and then conditioning the event states onto the time part. Our theory satisfies the full Poincare' symmetry as a `geometric' unitary transformation, and possesses observables for space (location of an event) and time (position in time of an event).

Years of hard work

References in corpus (4)

• Reference frames, superselection rules, and quantum information
• Conditional probabilities with Dirac observables and the problem of time in quantum gravity
• Equivalence of approaches to relational quantum dynamics in relativistic settings
• History state formalism for scalar particles

Cited by in corpus (12)

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• Parallel-in-time quantum simulation via Page and Wootters quantum time
• A Stochastic Origin of Spacetime Non-Commutativity
• Quantum Time and the Time-Dilation induced Interaction Transfer mechanism
• A statistical model for quantum spin and photon number states
• Spacetime quantum mechanics for bosonic and fermionic systems
• Dirac Theory as a Relativistic Flow
• Quantum Theory, Gravity and Second Order Geometry