dorsal/arxiv
View SchemaFibre bundle formulation of relativistic quantum mechanics
| Authors | Bozhidar Z. Iliev |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0201085 |
| URL | https://arxiv.org/abs/quant-ph/0201085 |
Abstract
We propose a fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in different directions. In the bundle description the wavefunctions are replaced with (state) sections (covariant approach) or liftings of paths (equivalently: sections along paths) (time-dependent approach) of a suitably chosen vector bundle over space-time whose (standard) fibre is the space of the wavefunctions. Now the quantum evolution is described as a linear transportation of the state sections/liftings in the (total) bundle space. The equations of these transportations turn to be the bundle versions of the corresponding relativistic wave equations. Connections between the (retarded) Green functions of these equations and the evolution operators and transports are found. Especially the Dirac and Klein-Gordon equations are considered.
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"abstract": "We propose a fibre bundle formulation of the mathematical base of\nrelativistic quantum mechanics. At the present stage the bundle form of the\ntheory is equivalent to its conventional one, but it admits new types of\ngeneralizations in different directions. In the bundle description the\nwavefunctions are replaced with (state) sections (covariant approach) or\nliftings of paths (equivalently: sections along paths) (time-dependent\napproach) of a suitably chosen vector bundle over space-time whose (standard)\nfibre is the space of the wavefunctions. Now the quantum evolution is described\nas a linear transportation of the state sections/liftings in the (total) bundle\nspace. The equations of these transportations turn to be the bundle versions of\nthe corresponding relativistic wave equations. Connections between the\n(retarded) Green functions of these equations and the evolution operators and\ntransports are found. Especially the Dirac and Klein-Gordon equations are\nconsidered.",
"arxiv_id": "quant-ph/0201085",
"authors": [
"Bozhidar Z. Iliev"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"title": "Fibre bundle formulation of relativistic quantum mechanics",
"url": "https://arxiv.org/abs/quant-ph/0201085"
},
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