About non-maximality of the action functional
In this work first we review some cases where the action exhibits a minimal or a saddle-point criticality for velocity-independent potentials (V(x, t)) and maximum when the potential is velocity-dependent (V(x,ẋ,t)). In the following we will use the functional (“directional”) derivative of second o...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIP Publishing LLC
2012-09-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/1.4747508 |
| _version_ | 1811321531717910528 |
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| author | W. Freire J. P. N. Lima |
| author_facet | W. Freire J. P. N. Lima |
| author_sort | W. Freire |
| collection | DOAJ |
| description | In this work first we review some cases where the action exhibits a minimal or a saddle-point criticality for velocity-independent potentials (V(x, t)) and maximum when the potential is velocity-dependent (V(x,ẋ,t)). In the following we will use the functional (“directional”) derivative of second order to present a mathematically rigorous proof of the non-maximality of the classical functional action for potentials V(x, t) velocity-independent. |
| first_indexed | 2024-04-13T13:19:42Z |
| format | Article |
| id | doaj.art-4f2e0c1fa95d4bfeb99ce5a5e1a08437 |
| institution | Directory Open Access Journal |
| issn | 2158-3226 |
| language | English |
| last_indexed | 2024-04-13T13:19:42Z |
| publishDate | 2012-09-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj.art-4f2e0c1fa95d4bfeb99ce5a5e1a084372022-12-22T02:45:22ZengAIP Publishing LLCAIP Advances2158-32262012-09-0123032141032141-510.1063/1.4747508041203ADVAbout non-maximality of the action functionalW. Freire0J. P. N. Lima1Departamento de Física, Universidade Regional do Cariri - Campus Crajubar, Rua Leão Sampaio, 107 - Triângulo 63.040-000 - Juazeiro do Norte, Ceará, BrazilDepartamento de Física, Universidade Regional do Cariri - Campus Crajubar, Rua Leão Sampaio, 107 - Triângulo 63.040-000 - Juazeiro do Norte, Ceará, BrazilIn this work first we review some cases where the action exhibits a minimal or a saddle-point criticality for velocity-independent potentials (V(x, t)) and maximum when the potential is velocity-dependent (V(x,ẋ,t)). In the following we will use the functional (“directional”) derivative of second order to present a mathematically rigorous proof of the non-maximality of the classical functional action for potentials V(x, t) velocity-independent.http://dx.doi.org/10.1063/1.4747508 |
| spellingShingle | W. Freire J. P. N. Lima About non-maximality of the action functional AIP Advances |
| title | About non-maximality of the action functional |
| title_full | About non-maximality of the action functional |
| title_fullStr | About non-maximality of the action functional |
| title_full_unstemmed | About non-maximality of the action functional |
| title_short | About non-maximality of the action functional |
| title_sort | about non maximality of the action functional |
| url | http://dx.doi.org/10.1063/1.4747508 |
| work_keys_str_mv | AT wfreire aboutnonmaximalityoftheactionfunctional AT jpnlima aboutnonmaximalityoftheactionfunctional |