CHRONOLOGICAL PRODUCTS, ENERGY-MOMENTUM TENSORS OF SCALAR FIELDS FOR PARTICLE GENERATIONS, AND INDEFINITE METRICS
The solutions of generalized Klein-Gordon equations are considered. The generalizations of the Klein-Gordon equation allow one to derive convergent integrals for the Green functions of these equations. The generalized equations are presented as products of the operators for the Klein-Gordon equation...
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| Format: | Article |
| Language: | English |
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V.N. Karazin Kharkiv National University Publishing
2018-06-01
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| Series: | East European Journal of Physics |
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| Online Access: | https://periodicals.karazin.ua/eejp/article/view/10751 |
| _version_ | 1818509401936363520 |
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| author | Yu. V. Kulish |
| author_facet | Yu. V. Kulish |
| author_sort | Yu. V. Kulish |
| collection | DOAJ |
| description | The solutions of generalized Klein-Gordon equations are considered. The generalizations of the Klein-Gordon equation allow one to derive convergent integrals for the Green functions of these equations. The generalized equations are presented as products of the operators for the Klein-Gordon equation with different masses. The solutions of derived homogeneous equations (total fields) are sums of fields corresponding to particles with the same values of the spin, the electric charge, the parities, but with different masses. Such particles are grouped into the kinds (families, dynasties) with members which are the generations. The chronological products of the scalar fields for kinds of particles are obtained at arbitrary quantity of the generations. These chronological products are the causal Green functions of generalized Klein-Gordon equations. The Lagrangians for the generalized Klein-Gordon equations of arbitrary order are derived. These Lagrangians are used to obtain the energy-momentum tensors for the particle kinds at arbitrary quantity of generations. It is shown that the generalized Hamiltonians (for total fields) have got positive eigenvalues for all the generations. These results are derived with the use of the indefinite metrics. |
| first_indexed | 2024-12-10T22:45:02Z |
| format | Article |
| id | doaj.art-37045301e65c49a994d27426b2998e73 |
| institution | Directory Open Access Journal |
| issn | 2312-4334 2312-4539 |
| language | English |
| last_indexed | 2024-12-10T22:45:02Z |
| publishDate | 2018-06-01 |
| publisher | V.N. Karazin Kharkiv National University Publishing |
| record_format | Article |
| series | East European Journal of Physics |
| spelling | doaj.art-37045301e65c49a994d27426b2998e732022-12-22T01:30:36ZengV.N. Karazin Kharkiv National University PublishingEast European Journal of Physics2312-43342312-45392018-06-015241510.26565/2312-4334-2018-2-0110751CHRONOLOGICAL PRODUCTS, ENERGY-MOMENTUM TENSORS OF SCALAR FIELDS FOR PARTICLE GENERATIONS, AND INDEFINITE METRICSYu. V. Kulish0Ukrainian State University of Railway Transport Sq. Feuerbach 7, Kharkiv region, 61050, UkraineThe solutions of generalized Klein-Gordon equations are considered. The generalizations of the Klein-Gordon equation allow one to derive convergent integrals for the Green functions of these equations. The generalized equations are presented as products of the operators for the Klein-Gordon equation with different masses. The solutions of derived homogeneous equations (total fields) are sums of fields corresponding to particles with the same values of the spin, the electric charge, the parities, but with different masses. Such particles are grouped into the kinds (families, dynasties) with members which are the generations. The chronological products of the scalar fields for kinds of particles are obtained at arbitrary quantity of the generations. These chronological products are the causal Green functions of generalized Klein-Gordon equations. The Lagrangians for the generalized Klein-Gordon equations of arbitrary order are derived. These Lagrangians are used to obtain the energy-momentum tensors for the particle kinds at arbitrary quantity of generations. It is shown that the generalized Hamiltonians (for total fields) have got positive eigenvalues for all the generations. These results are derived with the use of the indefinite metrics.https://periodicals.karazin.ua/eejp/article/view/10751generalized Klein-Gordon equations, generations of particles, chronological products of fields, Green functions, Lagrangians, particle energies, particle moments, indefinite metrics. |
| spellingShingle | Yu. V. Kulish CHRONOLOGICAL PRODUCTS, ENERGY-MOMENTUM TENSORS OF SCALAR FIELDS FOR PARTICLE GENERATIONS, AND INDEFINITE METRICS East European Journal of Physics generalized Klein-Gordon equations, generations of particles, chronological products of fields, Green functions, Lagrangians, particle energies, particle moments, indefinite metrics. |
| title | CHRONOLOGICAL PRODUCTS, ENERGY-MOMENTUM TENSORS OF SCALAR FIELDS FOR PARTICLE GENERATIONS, AND INDEFINITE METRICS |
| title_full | CHRONOLOGICAL PRODUCTS, ENERGY-MOMENTUM TENSORS OF SCALAR FIELDS FOR PARTICLE GENERATIONS, AND INDEFINITE METRICS |
| title_fullStr | CHRONOLOGICAL PRODUCTS, ENERGY-MOMENTUM TENSORS OF SCALAR FIELDS FOR PARTICLE GENERATIONS, AND INDEFINITE METRICS |
| title_full_unstemmed | CHRONOLOGICAL PRODUCTS, ENERGY-MOMENTUM TENSORS OF SCALAR FIELDS FOR PARTICLE GENERATIONS, AND INDEFINITE METRICS |
| title_short | CHRONOLOGICAL PRODUCTS, ENERGY-MOMENTUM TENSORS OF SCALAR FIELDS FOR PARTICLE GENERATIONS, AND INDEFINITE METRICS |
| title_sort | chronological products energy momentum tensors of scalar fields for particle generations and indefinite metrics |
| topic | generalized Klein-Gordon equations, generations of particles, chronological products of fields, Green functions, Lagrangians, particle energies, particle moments, indefinite metrics. |
| url | https://periodicals.karazin.ua/eejp/article/view/10751 |
| work_keys_str_mv | AT yuvkulish chronologicalproductsenergymomentumtensorsofscalarfieldsforparticlegenerationsandindefinitemetrics |