The Experts below are selected from a list of 189 Experts worldwide ranked by ideXlab platform

Tsuneo Suzuki - One of the best experts on this subject based on the ideXlab platform.

  • blockspin renormalization group study of color confinement due to violation of the non abelian Bianchi Identity
    Physical Review D, 2018
    Co-Authors: Tsuneo Suzuki
    Abstract:

    Blockspin transformation of topological defects is applied to the violation of the non-Abelian Bianchi Identity (VNABI) on lattice defined as Abelian monopoles. To get rid of lattice artifacts, we introduce (1) smooth gauge fixings such as the maximal center gauge (MCG), (2) blockspin transformations and (3) the tadpole-improved gauge action. The effective action can be determined by adopting the inverse Monte Carlo method. The coupling constants F(i) of the effective action depend on the coupling of the lattice action β and the number of the blocking step n. But it is found that F(i) satisfies a beautiful scaling; that is, they are a function of the product b=na(β) alone for lattice coupling constants 3.0≤β≤3.9 and the steps of blocking 1≤n≤12. The effective action showing the scaling behavior can be regarded as an almost perfect action corresponding to the continuum limit, since a→0 as n→∞ for fixed b. The infrared effective monopole action keeps the global color invariance when smooth gauges such as MCG keeping the invariance are adopted. The almost perfect action showing the scaling is found to be independent of the smooth gauges adopted here as naturally expected from the gauge invariance of the continuum theory. Then we compare the results with those obtained by the analytic blocking method of topological defects from the continuum, assuming local two-point interactions are dominant as the infrared effective action. The action is formulated in the continuum limit while the couplings of these actions can be derived from simple observables calculated numerically on lattices with a finite lattice spacing. When use is made of Berezinskii-Kosterlitz-Thouless (BKT) transformation, the infrared monopole action can be transformed into that of the string model. Since large b=na(β) corresponds to the strong-coupling region in the string model, the physical string tension and the lowest glueball mass can be evaluated analytically with the use of the strong-coupling expansion of the string model. The almost perfect action gives us σ≃1.3σphys for b≥1.0(σphys-1/2), whereas the scalar glueball mass is kept to be near M(0++)∼3.7σphys. In addition, using the effective action composed of 10 simple quadratic interactions alone, we can almost explain analytically the scaling function of the squared monopole density determined numerically for a large b region when b>1.2(σphys-1/2).

Tomi Koivisto - One of the best experts on this subject based on the ideXlab platform.

  • a note on covariant conservation of energy momentum in modified gravities
    Classical and Quantum Gravity, 2006
    Co-Authors: Tomi Koivisto
    Abstract:

    An explicit proof of the vanishing of the covariant divergence of the energy–momentum tensor in modified theories of gravity is presented. The gravitational action is written in arbitrary dimensions and allowed to depend nonlinearly on the curvature scalar and its couplings with a scalar field. Also the case of a function of the curvature scalar multiplying a matter Lagrangian is considered. The proof is given both in the metric and in the first-order formalism, i.e. under the Palatini variational principle. It is found that the covariant conservation of energy–momentum is built in to the field equations. This crucial result, called the generalized Bianchi Identity, can also be deduced directly from the covariance of the extended gravitational action. Furthermore, in all of these cases, the freely falling world lines are determined by the field equations alone and turn out to be the geodesics associated with the metric compatible connection. The independent connection in the Palatini formulation of these generalized theories does not have a similar direct physical interpretation. However, in the conformal Einstein frame a certain bi-metricity emerges into the structure of these theories.

  • a note on covariant conservation of energy momentum in modified gravities
    Classical and Quantum Gravity, 2006
    Co-Authors: Tomi Koivisto
    Abstract:

    An explicit proof of the vanishing of the covariant divergence of the energy–momentum tensor in modified theories of gravity is presented. The gravitational action is written in arbitrary dimensions and allowed to depend nonlinearly on the curvature scalar and its couplings with a scalar field. Also the case of a function of the curvature scalar multiplying a matter Lagrangian is considered. The proof is given both in the metric and in the first-order formalism, i.e. under the Palatini variational principle. It is found that the covariant conservation of energy–momentum is built in to the field equations. This crucial result, called the generalized Bianchi Identity, can also be deduced directly from the covariance of the extended gravitational action. Furthermore, in all of these cases, the freely falling world lines are determined by the field equations alone and turn out to be the geodesics associated with the metric compatible connection. The independent connection in the Palatini formulation of these generalized theories does not have a similar direct physical interpretation. However, in the conformal Einstein frame a certain bi-metricity emerges into the structure of these theories.

  • covariant conservation of energy momentum in modified gravities
    arXiv: General Relativity and Quantum Cosmology, 2005
    Co-Authors: Tomi Koivisto
    Abstract:

    An explicit proof of the vanishing of the covariant divergence of the energy-momentum tensor in modified theories of gravity is presented. The gravitational action is written in arbitrary dimensions and allowed to depend nonlinearly on the curvature scalar and its couplings with a scalar field. Also the case of a function of the curvature scalar multiplying a matter Lagrangian is considered. The proof is given both in the metric and in the first-order formalism, i.e. under the Palatini variational principle. It is found that the covariant conservation of energy-momentum is built-in to the field equations. This crucial result, called the generalized Bianchi Identity, can also be deduced directly from the covariance of the extended gravitational action. Furthermore, we demonstrate that in all of these cases, the freely falling world lines are determined by the field equations alone and turn out to be the geodesics associated with the metric compatible connection. The independent connection in the Palatini formulation of these generalized theories does not have a similar direct physical interpretation. However, in the conformal Einstein frame a certain bi-metricity emerges into the structure of these theories. In the light of our interpretation of the independent connection as an auxiliary variable we can also reconsider some criticisms of the Palatini formulation originally raised by Buchdahl.

Geoff Kagel - One of the best experts on this subject based on the ideXlab platform.

  • exact Bianchi Identity in regge gravity
    Classical and Quantum Gravity, 2004
    Co-Authors: Herbert W Hamber, Geoff Kagel
    Abstract:

    In the continuum the Bianchi Identity implies a relationship between different components of the curvature tensor, thus ensuring the internal consistency of the gravitational field equations. In this paper the exact form for the Bianchi Identity in Regge's discrete formulation of gravity is derived, by considering appropriate products of rotation matrices constructed around null-homotopic paths. The discrete Bianchi Identity implies an algebraic relationship between deficit angles belonging to neighbouring hinges. As in the continuum, the derived Identity is valid for arbitrarily curved manifolds without a restriction to the weak field small curvature limit, but is in general not linear in the curvatures.

  • exact Bianchi Identity in regge gravity
    arXiv: General Relativity and Quantum Cosmology, 2001
    Co-Authors: Herbert W Hamber, Geoff Kagel
    Abstract:

    In the continuum the Bianchi Identity implies a relationship between different components of the curvature tensor, thus ensuring the internal consistency of the gravitational field equations. In this paper an exact form for the Bianchi Identity in Regge's discrete formulation of gravity is derived, by considering appropriate products of rotation matrices constructed around null-homotopic paths. It implies an algebraic relationship between deficit angles belonging to neighboring hinges. As in the continuum, the derived Identity is valid for arbitrarily curved manifolds, without a restriction to the weak field, small curvature limit, but is in general not linear in the curvatures.

Abolfazl Mirjalili - One of the best experts on this subject based on the ideXlab platform.

  • the riemann tensor and the Bianchi Identity in 5d space time
    Comptes Rendus Physique, 2017
    Co-Authors: Mehran Taki, Abolfazl Mirjalili
    Abstract:

    Abstract The initial assumption of theories with extra dimension is based on the efforts to yield a geometrical interpretation of the gravitation field. In this paper, using an infinitesimal parallel transportation of a vector, we generalize the obtained results in four dimensions to five-dimensional space–time. For this purpose, we first consider the effect of the geometrical structure of 4D space–time on a vector in a round trip of a closed path, which is basically quoted from chapter three of Ref. [5] . If the vector field is a gravitational field, then the required round trip will lead us to an equation which is dynamically governed by the Riemann tensor. We extend this idea to five-dimensional space–time and derive an improved version of Bianchi's Identity. By doing tensor contraction on this Identity, we obtain field equations in 5D space–time that are compatible with Einstein's field equations in 4D space–time. As an interesting result, we find that when one generalizes the results to 5D space–time, the new field equations imply a constraint on Ricci scalar equations, which might be containing a new physical insight.

Herbert W Hamber - One of the best experts on this subject based on the ideXlab platform.

  • exact Bianchi Identity in regge gravity
    Classical and Quantum Gravity, 2004
    Co-Authors: Herbert W Hamber, Geoff Kagel
    Abstract:

    In the continuum the Bianchi Identity implies a relationship between different components of the curvature tensor, thus ensuring the internal consistency of the gravitational field equations. In this paper the exact form for the Bianchi Identity in Regge's discrete formulation of gravity is derived, by considering appropriate products of rotation matrices constructed around null-homotopic paths. The discrete Bianchi Identity implies an algebraic relationship between deficit angles belonging to neighbouring hinges. As in the continuum, the derived Identity is valid for arbitrarily curved manifolds without a restriction to the weak field small curvature limit, but is in general not linear in the curvatures.

  • exact Bianchi Identity in regge gravity
    arXiv: General Relativity and Quantum Cosmology, 2001
    Co-Authors: Herbert W Hamber, Geoff Kagel
    Abstract:

    In the continuum the Bianchi Identity implies a relationship between different components of the curvature tensor, thus ensuring the internal consistency of the gravitational field equations. In this paper an exact form for the Bianchi Identity in Regge's discrete formulation of gravity is derived, by considering appropriate products of rotation matrices constructed around null-homotopic paths. It implies an algebraic relationship between deficit angles belonging to neighboring hinges. As in the continuum, the derived Identity is valid for arbitrarily curved manifolds, without a restriction to the weak field, small curvature limit, but is in general not linear in the curvatures.