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    Wyświetlanie 1-4 z 4
    Tytuł:
    Noether and matrix methods to construct local symmetries of Lagrangians
    Autorzy:
    Lam-Estrada, P.
    Ovando, G.
    López-Bonilla, J.
    López-Vázquez, R.
    Vidal-Beltrán, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/1177899.pdf
    Data publikacji:
    2018
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Gauge identities
    Local symmetries
    Noether theorem
    Singular Lagrangians
    Opis:
    We exhibit an elementary presentation of matrix and Noether techniques to construct infinitesimal point symmetries of Lagrangians. Besides, we employ the Lanczos approach to Noether’s theorem to obtain the first integral associated with each symmetry. We show applications to several singular Lagrangians of interest in classical mechanics.
    Źródło:
    World Scientific News; 2018, 97; 51-68
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Constraints and gauge relations in the Lagrangian formalism
    Autorzy:
    Lam-Estrada, P.
    López-Bonilla, J.
    López-Vázquez, R.
    Vidal-Beltrán, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/1178075.pdf
    Data publikacji:
    2018
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Gauge identities
    Genuine constraints
    Local symmetries
    Noether’s theorem
    Singular Lagrangians
    Opis:
    For several Lagrangians we show that their local symmetries can be obtained from the associated Euler-Lagrange equations, and we exhibit the explicit presence of the genuine constraints into gauge identities. We also employ the Lanczos approach to Noether’s theorem to give connections between the genuine constraints and their time derivatives. Besides, it is evident that the Hamiltonian secondary and tertiary constraints have relationship with the genuine constraints.
    Źródło:
    World Scientific News; 2018, 95; 215-223
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Theoretical Investigations into the Fundamental Understanding of the Nature of Time, Gravity and Dynamics
    Autorzy:
    Kabe, Koustubh
    Powiązania:
    https://bibliotekanauki.pl/articles/1182950.pdf
    Data publikacji:
    2016
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    holonomy
    entropy
    time asymmetry
    gravity
    anderson-higgs mechanism
    gauge field
    vorticity
    dynamics
    spontaneous symmetry breaking
    big bang singularity
    Opis:
    The origins of dynamics, the physical basis of time asymmetry and the nature of gravity are all considered in the model discussed in this paper. The theory takes entropy as not a sheer thermodynamic property but rather considers it as a Quantum Field Theoretic property that emanates from a fundamental field. Also it is quantized, the most fundamental unit being the value of the Boltzmann constant. Ab initio the reason for entropy being a quantum field property is systematically argued. We explicitly show how the fields gain the property of entropy. First and foremost, we get rid of the Penrose-Hawking Big Bang singularity involving all spacetime, by proposing the existence of closed timelike geodesics below the Planck scale since that’s where GR ceases to function. We argue that this corresponds to a breaking of Lorentz covariance symmetry below the Planckian scale. We then explicitly show this symmetry to be broken and then obtain an anomalous current that is non-conserved; we later demonstrate that this is the non-conserved entropy current. This explicitly shows the Planckian nature of the irreversible thermodynamics that yields entropy currents. The static vortex gauge theory that interacts with the entropy endowing K-field actually gives a degree of randomness to the field and endows it with dynamics and gives it the ability to give dynamics to all the other fermionic and bosonic fields including gravity. The acquiring of the property of mass by this field via the Anderson-Higgs mechanism makes the dynamics finite. The positivity of entropy and the mass make the dynamics finite and time asymmetrical. Finally we construct a Hamilton-Volterra system of equations and imposing a special gauge which we call the ”Pauli Gauge”, and then consider the diffusion of curvature mathematically defining it by the Ricci flow, we deliver the pure gravity Einstein field equations. This paper all in all represents a model that gives a new way to think about the origins of dynamics, asymmetry of time, nature of gravity and the finiteness of dynamics.
    Źródło:
    World Scientific News; 2016, 49, 2; 346-380
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Gauge Model for Gravity and considerations on the Asymmetry of Time and the SU (2) Mass Gap
    Autorzy:
    Kabe, Koustubh
    Powiązania:
    https://bibliotekanauki.pl/articles/1178329.pdf
    Data publikacji:
    2017
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Gauge theory
    general relativity
    gravity
    loop quantum gravity
    mass gap
    quantum field theory
    quantum gravity
    string theory
    super gravity (SUGRA)
    super symmetry (SUSY)
    time
    time asymmetry
    Opis:
    A new formulation of the Hamiltonian formalism of general relativity is developed based on the adiabatic variation of the Hamiltonian constraint. This new formulation consists of complex valued anti-Hermitian 1- called the Berry gauge potentials. These are then used to develop the complex Berry-Einstein-Yang-Mills curvature 2- . The Berry-Yang-Mills field equations are then developed and interpreted in a novel manner to incorporate quantum temporal strings in the non-perturbative formalism. This is however just highlighted in this paper and will be pursued in another paper. Since, the holonomy phase construed is that of Lorentz rotation we perceive a new quantum structure of the space-time namely that of causality. The future light cones are soldered internally to the tensor fields naturally so that the Berry-Ehresmann connection defines a quantum gauge field of causality. This field evokes the causal structure attributed to space-time as gauge degrees of freedom of quantum space ― a fluid of future light cones. This symmetry being of the gauge field type has three generators i.e., three gauge bosons― all heavy and therefore attracted by gravity. Thus causality is a local gauge degree of freedom of gravity. Once the theory is developed, the problem of the mass gap is considered for our gauge field. It seems that the problem is solved in this paper.
    Źródło:
    World Scientific News; 2017, 81, 2; 198-220
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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