Gauge theory of Gravity based on the correspondence between the 1st and the 2nd order formalisms

by David Benisty

at Particles and Fields Seminar

Mon, 03 Dec 2018, 14:00
Physics building (#54) room 207

Abstract

A way to obtain a correspondence between the first order and second order formalism is studied By introducing a Lagrange multiplier coupled to the covariant derivative of the metric a metricity constraint is implemented The new contribution which comes from the variation of the Lagrange multiplier transforms the field equations from the first order to the second order formalism yet the action is formulated in the first order In this way all the higher derivatives terms in the second order formalism appear as derivatives of the Lagrange multiplier A covariant canonical gauge theory of gravity free from torsion is based on this formalism Using a metric conjugate momentum and a connection conjugate momentum which takes the form of the Riemann tensor a gauge theory of gravity is formulated with form invariant Hamiltonian Through the introduction of the metric conjugate momenta a correspondence between the Affine Palatini formalism and the metric formalism is established For when the dynamical gravitational Hamiltonian H Dyn does not depend on the metric conjugate momenta a metric compatibility is obtained from the equation of motions and the energy momentum is covariant conserved When the gravitational Hamiltonian H Dyn depends on the metric conjugate momentum an extension to the metric compatibility comes from the equation of motion and the energy momentum covariant conservation is violated For a sample of the H Dyn which consists of a quadratic term of the connection conjugate momentum the effective Lagrangian has the Einstein Hilbert term with a quadratic Riemann term in the second order formalism

Created on 26-11-2018 by Bar Lev, Yevgeny (ybarlev)
Updaded on 26-11-2018 by Bar Lev, Yevgeny (ybarlev)