Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 982-1006 |
| Journal | Foundations of Physics |
| Volume | 48 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - 1 Aug 2018 |
| Externally published | Yes |
Bibliographical note
Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].Funding
We are grateful for financial support from the UK Engineering and Physical Sciences Research Council, the John Templeton Foundation, the Foundational Questions Institute, EU Collaborative Project TherMiQ (Grant Agreement 618074), the London Institute for Mathematical Sciences and Wolfson College, University of Oxford.
Research Keywords
- Energy
- Generalized probabilistic theories
- Hamiltonian
- Time evolution
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