Abstract:We discuss the coupling of the electromagnetic field with a curved and torsioned Lyra manifold using the Duffin-Kemmer-Petiau theory. We will show how to obtain the equations of motion and energy-momentum and spin density tensors by means of the Schwinger Variational Principle.
“…The second class of models that we are specially concerned with in this work is the scalar-tensor theories [24][25][26][27]. In these theories, part of the gravitational interaction is described by a scalar field.…”
The equivalence between theories depending on the derivatives of R, i.e. f (R, ∇R, ..., ∇ n R), and scalar-multi-tensorial theories is verified. The analysis is done in both metric and Palatini formalisms. It is shown that f (R, ∇R, ..., ∇ n R) theories are equivalent to scalar-multi-tensorial ones resembling Brans-Dicke theories with kinetic terms ω0 = 0 and ω0 = − 3 2 for metric and Palatini formalisms respectively. This result is analogous to what happens for f (R) theories. It is worthy emphasizing that the scalar-multi-tensorial theories obtained here differ from Brans-Dicke ones due to the presence of multiple tensorial fields absent in the last. Furthermore, sufficient conditions are established for f (R, ∇R, ..., ∇ n R) theories to be written as scalar-multi-tensorial theories. Finally, some examples are studied and the comparison of f (R, ∇R, ..., ∇ n R) theories to f (R, R, ... n R) theories is performed.
“…The second class of models that we are specially concerned with in this work is the scalar-tensor theories [24][25][26][27]. In these theories, part of the gravitational interaction is described by a scalar field.…”
The equivalence between theories depending on the derivatives of R, i.e. f (R, ∇R, ..., ∇ n R), and scalar-multi-tensorial theories is verified. The analysis is done in both metric and Palatini formalisms. It is shown that f (R, ∇R, ..., ∇ n R) theories are equivalent to scalar-multi-tensorial ones resembling Brans-Dicke theories with kinetic terms ω0 = 0 and ω0 = − 3 2 for metric and Palatini formalisms respectively. This result is analogous to what happens for f (R) theories. It is worthy emphasizing that the scalar-multi-tensorial theories obtained here differ from Brans-Dicke ones due to the presence of multiple tensorial fields absent in the last. Furthermore, sufficient conditions are established for f (R, ∇R, ..., ∇ n R) theories to be written as scalar-multi-tensorial theories. Finally, some examples are studied and the comparison of f (R, ∇R, ..., ∇ n R) theories to f (R, R, ... n R) theories is performed.
“…Desde a sua concepção, o princípio de ação quântica de Schwinger tem sido utilizado tanto na obtenção de resultados formais sobre a estrutura da teoria quântica quanto em aplicações específicas [13] que demonstram o seu poder de cálculo. Ele foi empregado para se investigar as relações entre spin e estatística que governam as partículas elementares [14], no estudo do acoplamento entre campos em espaços curvos ou torcidos [15][16][17], na investigação do problema de fixação de calibre para quantização de campos [18], na formulação de teorias de gauge de ordem superior [19] e até mesmo na construção de uma versão quaterniônica da mecânica quântica [20]. Uma das primeiras introduções didáticas à formulação de Schwinger para a mecânica quântica foi apresentada em [21].…”
O princípio de ação quântica de Schwinger é uma caracterização dinâmica das funções de transformação e está fundamentado na estrutura algébrica derivada da análise cinemática dos procesos de medida em nível quântico. Como tal, este princípio variacional permite derivar as relações de comutação canônicas numa forma totalmente consistente. Além disso, propociona as descrições dinâmicas de Schrödinger, Heisenberg e uma equação de Hamilton-Jacobi em nível quântico. Implementaremos este formalismo na resolução de sistemas simples como a partícula livre, o oscilador harmônico quântico e o oscilador harmônico quântico forçado.
“…The Schwinger action principle was introduced in the context of Quantum Field Theory (Schwinger 1951(Schwinger , 1953a(Schwinger , 1953b(Schwinger , 1953c(Schwinger , 1954a(Schwinger , 1954b and recently has been used to study classical and quantum fields in spacetimes with curvature and torsion (Casana et al 2005(Casana et al , 2006(Casana et al , 2007 or even to investigate the gauge fixing in quantized electromagnetic field . It is worth to emphasize that the choice (2) constitutes a phenomenological model valid within a limited interval of energy (set by the values of the coupling constant β); it does not hold during all the cosmological history (as we shall see) but only for a certain period.…”
We construct a phenomenological theory of gravitation based on a second order
gauge formulation for the Lorentz group. The model presents a long-range
modification for the gravitational field leading to a cosmological model
provided with an accelerated expansion at recent times. We estimate the model
parameters using observational data and verify that our estimative for the age
of the Universe is of the same magnitude than the one predicted by the standard
model. The transition from the decelerated expansion regime to the accelerated
one occurs recently (at $\sim9.3\;Gyr$).Comment: RevTex4 15 pages, 1 figure. Accepted for publication in Astrophysics
& Space Scienc
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