Nonrelativistic Approximation in the Theory of a Spin-2 Particle with Anomalous Magnetic Moment
We start with the 50-component relativistic matrix equation for a hypothetical spin-2 particle in the presence of external electromagnetic fields. This equation is hypothesized to describe a particle with an anomalous magnetic moment. The complete wave function consists of a two-rank symmetric tenso...
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2025-01-01
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| author | Alina Ivashkevich Viktor Red’kov Artur Ishkhanyan |
| author_facet | Alina Ivashkevich Viktor Red’kov Artur Ishkhanyan |
| author_sort | Alina Ivashkevich |
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| description | We start with the 50-component relativistic matrix equation for a hypothetical spin-2 particle in the presence of external electromagnetic fields. This equation is hypothesized to describe a particle with an anomalous magnetic moment. The complete wave function consists of a two-rank symmetric tensor and a three-rank tensor that is symmetric in two indices. We apply the general method for performing the nonrelativistic approximation, which is based on the structure of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>50</mn><mo>×</mo><mn>50</mn></mrow></semantics></math></inline-formula> matrix <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mo>Γ</mo><mn>0</mn></msup></semantics></math></inline-formula> of the main equation. Using the 7th-order minimal equation for the matrix <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mo>Γ</mo><mn>0</mn></msup></semantics></math></inline-formula>, we introduce three projective operators. These operators permit us to decompose the complete wave function into the sum of three parts: one large part and two smaller parts in the nonrelativistic approximation. We have found five independent large variables and 45 small ones. To simplify the task, by eliminating the variables related to the 3-rank tensor, we have derived a relativistic system of second-order equations for the 10 components related to the symmetric tensor. We then take into account the decomposition of these 10 variables into linear combinations of large and small ones. In accordance with the general method, we separate the rest energy in the wave function and specify the orders of smallness for different terms in the arising equations. Further, after performing the necessary calculations, we derive a system of five linked equations for the five large variables. This system is presented in matrix form, which has a nonrelativistic structure, where the term representing additional interaction with the external magnetic field through three spin projections is included. The multiplier before this interaction contains the basic magnetic moment and an additional term due to the anomalous magnetic moment. The latter characteristic is treated as a free parameter within the hypothesis. |
| format | Article |
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| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-01-01 |
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| spelling | doaj-art-10383e6836fa483682f4166be2564f892025-01-24T13:22:13ZengMDPI AGAxioms2075-16802025-01-011413510.3390/axioms14010035Nonrelativistic Approximation in the Theory of a Spin-2 Particle with Anomalous Magnetic MomentAlina Ivashkevich0Viktor Red’kov1Artur Ishkhanyan2B.I. Stepanov Institute of Physics of NAS of Belarus, 220072 Minsk, BelarusB.I. Stepanov Institute of Physics of NAS of Belarus, 220072 Minsk, BelarusInstitute for Physical Research of NAS of Armenia, Ashtarak 0204, ArmeniaWe start with the 50-component relativistic matrix equation for a hypothetical spin-2 particle in the presence of external electromagnetic fields. This equation is hypothesized to describe a particle with an anomalous magnetic moment. The complete wave function consists of a two-rank symmetric tensor and a three-rank tensor that is symmetric in two indices. We apply the general method for performing the nonrelativistic approximation, which is based on the structure of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>50</mn><mo>×</mo><mn>50</mn></mrow></semantics></math></inline-formula> matrix <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mo>Γ</mo><mn>0</mn></msup></semantics></math></inline-formula> of the main equation. Using the 7th-order minimal equation for the matrix <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mo>Γ</mo><mn>0</mn></msup></semantics></math></inline-formula>, we introduce three projective operators. These operators permit us to decompose the complete wave function into the sum of three parts: one large part and two smaller parts in the nonrelativistic approximation. We have found five independent large variables and 45 small ones. To simplify the task, by eliminating the variables related to the 3-rank tensor, we have derived a relativistic system of second-order equations for the 10 components related to the symmetric tensor. We then take into account the decomposition of these 10 variables into linear combinations of large and small ones. In accordance with the general method, we separate the rest energy in the wave function and specify the orders of smallness for different terms in the arising equations. Further, after performing the necessary calculations, we derive a system of five linked equations for the five large variables. This system is presented in matrix form, which has a nonrelativistic structure, where the term representing additional interaction with the external magnetic field through three spin projections is included. The multiplier before this interaction contains the basic magnetic moment and an additional term due to the anomalous magnetic moment. The latter characteristic is treated as a free parameter within the hypothesis.https://www.mdpi.com/2075-1680/14/1/35spin-2 particleinteraction with electromagnetic fieldnonrelativistic approximationprojective operatorsfive-dimensional Pauli-like equationanomalous magnetic moment |
| spellingShingle | Alina Ivashkevich Viktor Red’kov Artur Ishkhanyan Nonrelativistic Approximation in the Theory of a Spin-2 Particle with Anomalous Magnetic Moment Axioms spin-2 particle interaction with electromagnetic field nonrelativistic approximation projective operators five-dimensional Pauli-like equation anomalous magnetic moment |
| title | Nonrelativistic Approximation in the Theory of a Spin-2 Particle with Anomalous Magnetic Moment |
| title_full | Nonrelativistic Approximation in the Theory of a Spin-2 Particle with Anomalous Magnetic Moment |
| title_fullStr | Nonrelativistic Approximation in the Theory of a Spin-2 Particle with Anomalous Magnetic Moment |
| title_full_unstemmed | Nonrelativistic Approximation in the Theory of a Spin-2 Particle with Anomalous Magnetic Moment |
| title_short | Nonrelativistic Approximation in the Theory of a Spin-2 Particle with Anomalous Magnetic Moment |
| title_sort | nonrelativistic approximation in the theory of a spin 2 particle with anomalous magnetic moment |
| topic | spin-2 particle interaction with electromagnetic field nonrelativistic approximation projective operators five-dimensional Pauli-like equation anomalous magnetic moment |
| url | https://www.mdpi.com/2075-1680/14/1/35 |
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