Contact geometry and quantum mechanics
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental “phase-spacetime”. We show that this covariant starting point makes quantization into a purely geometric flatness condition. This make...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2018-06-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269318302922 |
| _version_ | 1819298434673278976 |
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| author | Gabriel Herczeg Andrew Waldron |
| author_facet | Gabriel Herczeg Andrew Waldron |
| author_sort | Gabriel Herczeg |
| collection | DOAJ |
| description | We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental “phase-spacetime”. We show that this covariant starting point makes quantization into a purely geometric flatness condition. This makes quantum mechanics purely geometric, and possibly even topological. Our approach is especially useful for time-dependent problems and systems subject to ambiguities in choices of clock or observer. As a byproduct, we give a derivation and generalization of the Wigner functions of standard quantum mechanics. |
| first_indexed | 2024-12-24T05:29:51Z |
| format | Article |
| id | doaj.art-9d8db2de610a407e823fbfe8b2dec91d |
| institution | Directory Open Access Journal |
| issn | 0370-2693 |
| language | English |
| last_indexed | 2024-12-24T05:29:51Z |
| publishDate | 2018-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj.art-9d8db2de610a407e823fbfe8b2dec91d2022-12-21T17:13:12ZengElsevierPhysics Letters B0370-26932018-06-01781312315Contact geometry and quantum mechanicsGabriel Herczeg0Andrew Waldron1Department of Physics, University of California, Davis, CA 95616, USACenter for Quantum Mathematics and Physics (QMAP), Department of Mathematics, University of California, Davis, CA 95616, USA; Corresponding author.We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental “phase-spacetime”. We show that this covariant starting point makes quantization into a purely geometric flatness condition. This makes quantum mechanics purely geometric, and possibly even topological. Our approach is especially useful for time-dependent problems and systems subject to ambiguities in choices of clock or observer. As a byproduct, we give a derivation and generalization of the Wigner functions of standard quantum mechanics.http://www.sciencedirect.com/science/article/pii/S0370269318302922 |
| spellingShingle | Gabriel Herczeg Andrew Waldron Contact geometry and quantum mechanics Physics Letters B |
| title | Contact geometry and quantum mechanics |
| title_full | Contact geometry and quantum mechanics |
| title_fullStr | Contact geometry and quantum mechanics |
| title_full_unstemmed | Contact geometry and quantum mechanics |
| title_short | Contact geometry and quantum mechanics |
| title_sort | contact geometry and quantum mechanics |
| url | http://www.sciencedirect.com/science/article/pii/S0370269318302922 |
| work_keys_str_mv | AT gabrielherczeg contactgeometryandquantummechanics AT andrewwaldron contactgeometryandquantummechanics |