Journal
FOUNDATIONS OF PHYSICS
Volume 48, Issue 8, Pages 982-1006Publisher
SPRINGER
DOI: 10.1007/s10701-018-0205-9
Keywords
Hamiltonian; Generalized probabilistic theories; Energy; Time evolution
Categories
Funding
- UK Engineering and Physical Sciences Research Council
- John Templeton Foundation
- Foundational Questions Institute
- EU Collaborative Project TherMiQ [618074]
- London Institute for Mathematical Sciences
- Wolfson College, University of Oxford
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Energy is a crucial concept within classical and quantum physics. An essential tool to quantify energy is the Hamiltonian. Here, we consider how to define a Hamiltonian in general probabilistic theories-a framework in which quantum theory is a special case. We list desiderata which the definition should meet. For 3-dimensional systems, we provide a fully-defined recipe which satisfies these desiderata. We discuss the higher dimensional case where some freedom of choice is left remaining. We apply the definition to example toy theories, and discuss how the quantum notion of time evolution as a phase between energy eigenstates generalises to other theories.
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