dorsal/arxiv
View Schema(j,0)+(0,j) Covariant spinors and causal propagators based on Weinberg formalism
| Authors | D. V. Ahluwalia, D. J. Ernst |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9905047 |
| URL | https://arxiv.org/abs/nucl-th/9905047 |
| DOI | 10.1142/S0218301393000145 |
| Journal | Int.J.Mod.Phys.E2:397-422,1993 |
Abstract
A pragmatic approach to constructing a covariant phenomenology of the interactions of composite, high-spin hadrons is proposed. Because there are no known wave equations without significant problems, we propose to construct the phenomenology without explicit reference to a wave equation. This is done by constructing the individual pieces of a perturbation theory and then utilizing the perturbation theory as the definition of the phenomenology. The covariant spinors for a particle of spin $j$ are constructed directly from Lorentz invariance and the basic precepts of quantum mechanics following the logic put forth originally by Wigner and developed by Weinberg. Explicit expressions for the spinors are derived for j=1, 3/2 and 2. Field operators are constructed from the spinors and the free-particle propagator is derived from the vacuum expectation value of the time-order product of the field operators. A few simple examples of model interactions are given. This provides all the necessary ingredients to treat at a phenomenological level and in a covariant manner particles of arbitrary spin.
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"abstract": "A pragmatic approach to constructing a covariant phenomenology of the\ninteractions of composite, high-spin hadrons is proposed. Because there are no\nknown wave equations without significant problems, we propose to construct the\nphenomenology without explicit reference to a wave equation. This is done by\nconstructing the individual pieces of a perturbation theory and then utilizing\nthe perturbation theory as the definition of the phenomenology. The covariant\nspinors for a particle of spin $j$ are constructed directly from Lorentz\ninvariance and the basic precepts of quantum mechanics following the logic put\nforth originally by Wigner and developed by Weinberg. Explicit expressions for\nthe spinors are derived for j=1, 3/2 and 2. Field operators are constructed\nfrom the spinors and the free-particle propagator is derived from the vacuum\nexpectation value of the time-order product of the field operators. A few\nsimple examples of model interactions are given. This provides all the\nnecessary ingredients to treat at a phenomenological level and in a covariant\nmanner particles of arbitrary spin.",
"arxiv_id": "nucl-th/9905047",
"authors": [
"D. V. Ahluwalia",
"D. J. Ernst"
],
"categories": [
"nucl-th",
"hep-ph"
],
"doi": "10.1142/S0218301393000145",
"journal_ref": "Int.J.Mod.Phys.E2:397-422,1993",
"title": "(j,0)+(0,j) Covariant spinors and causal propagators based on Weinberg formalism",
"url": "https://arxiv.org/abs/nucl-th/9905047"
},
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