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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2406.00089 |
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| _version_ | 1866914819010985984 |
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| author | Gitman, D. M. Shelepin, A. L. |
| author_facet | Gitman, D. M. Shelepin, A. L. |
| contents | In our previous works, we have proposed a quantum description of relativistic orientable objects by a scalar field on the Poincaré group. This description is, in a sense, a generalization of ideas used by Wigner, Casimir and Eckart back in the 1930's in constructing a non-relativistic theory of a rigid rotator. The present work is a continuation and development of the above mentioned our works. The position of the relativistic orientable object in Minkowski space is completely determined by the position of a body-fixed reference frame with respect to the space-fixed reference frame, and can be specified by elements $q$ of the motion group of the Minkowski space - the Poincaré group $M(3,1)$. Quantum states of relativistic orientable objects are described by scalar wave functions $f(q)$ where the arguments $q=(x,z)$ consist of Minkowski space-time points $x$, and of orientation variables $z$ given by elements of the matrix $Z\in SL(2,C)$. Technically, we introduce and study the so-called double-sided representation $\boldsymbol{T}(\boldsymbol{g})f(q)=f(g_l^{-1}qg_r)$, $\boldsymbol{g}=(g_l,g_r)\in \boldsymbol{M}$, of the group $\boldsymbol{M}$, in the space of the scalar functions $f(q)$. Here the left multiplication by $g_l^{-1}$ corresponds to a change of space-fixed reference frame, whereas the right multiplication by $g_r$ corresponds to a change of body-fixed reference frame. On this basis, we develop a classification of the orientable objects and draw the attention to a possibility of connecting these results with the particle phenomenology. In particular, we demonstrate how one may identify fields described by linear and quadratic functions of $z$ with known elementary particles of spins $0$,$\frac{1}{2}$, and $1$. The developed classification does not contradict the phenomenology of elementary particles and, moreover, in some cases give its group-theoretic explanation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00089 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Group-theoretical classification of orientable objects and particle phenomenology Gitman, D. M. Shelepin, A. L. General Physics High Energy Physics - Theory In our previous works, we have proposed a quantum description of relativistic orientable objects by a scalar field on the Poincaré group. This description is, in a sense, a generalization of ideas used by Wigner, Casimir and Eckart back in the 1930's in constructing a non-relativistic theory of a rigid rotator. The present work is a continuation and development of the above mentioned our works. The position of the relativistic orientable object in Minkowski space is completely determined by the position of a body-fixed reference frame with respect to the space-fixed reference frame, and can be specified by elements $q$ of the motion group of the Minkowski space - the Poincaré group $M(3,1)$. Quantum states of relativistic orientable objects are described by scalar wave functions $f(q)$ where the arguments $q=(x,z)$ consist of Minkowski space-time points $x$, and of orientation variables $z$ given by elements of the matrix $Z\in SL(2,C)$. Technically, we introduce and study the so-called double-sided representation $\boldsymbol{T}(\boldsymbol{g})f(q)=f(g_l^{-1}qg_r)$, $\boldsymbol{g}=(g_l,g_r)\in \boldsymbol{M}$, of the group $\boldsymbol{M}$, in the space of the scalar functions $f(q)$. Here the left multiplication by $g_l^{-1}$ corresponds to a change of space-fixed reference frame, whereas the right multiplication by $g_r$ corresponds to a change of body-fixed reference frame. On this basis, we develop a classification of the orientable objects and draw the attention to a possibility of connecting these results with the particle phenomenology. In particular, we demonstrate how one may identify fields described by linear and quadratic functions of $z$ with known elementary particles of spins $0$,$\frac{1}{2}$, and $1$. The developed classification does not contradict the phenomenology of elementary particles and, moreover, in some cases give its group-theoretic explanation. |
| title | Group-theoretical classification of orientable objects and particle phenomenology |
| topic | General Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2406.00089 |