scholarly journals Hamiltonian formalism and constraint analysis of three-form matter models coupled with general relativity

2018 ◽  
Vol 97 (12) ◽  
Author(s):  
David Brizuela ◽  
Iñaki Garay
Keyword(s):  
General Relativity ◽  
Hamiltonian Formalism ◽  
Constraint Analysis

scholarly journals SYMPLECTIC STRUCTURE OF ISOSPIN PARTICLES IN YANG-MILLS FIELDS

1992 ◽  
Vol 07 (21) ◽  
pp. 1923-1930 ◽  
Author(s):  
PHILLIAL OH
Keyword(s):  
Symplectic Structure ◽  
Magnetic Monopole ◽  
Magnetic Charge ◽  
Geometric Quantization ◽  
Hamiltonian Formalism ◽  
Quantization Condition ◽  
Energy Term ◽  
Yang Mills ◽  
Constraint Analysis ◽  
Potential Energy Term

Using Dirac’s constraint analysis, we explore the Hamiltonian formalism of isospin particles in external Yang-Mills fields without kinetic and potential energy term. We consider an example of isospin particle in ’t Hooft-Polyakov magnetic monopole field and discuss possible quantization condition of magnetic charge in terms of geometric quantization.

scholarly journals Classification of primary constraints for new general relativity in the premetric approach

2021 ◽  
pp. 2140003
Author(s):  
María-José Guzmán ◽  
Shymaa Khaled Ibraheem
Keyword(s):  
General Relativity ◽  
Hessian Matrix ◽  
Hamiltonian Formalism ◽  
Temporal Part ◽  
Tetrad Field ◽  
Mathematical Properties ◽  
Constitutive Tensor ◽  
Hamiltonian Analysis

We introduce a novel procedure for studying the Hamiltonian formalism of new general relativity (NGR) based on the mathematical properties encoded in the constitutive tensor defined by the premetric approach. We derive the canonical momenta conjugate to the tetrad field and study the eigenvalues of the Hessian tensor, which is mapped to a Hessian matrix with the help of indexation formulas. The properties of the Hessian matrix heavily rely on the possible values of the free coefficients [Formula: see text] appearing in the NGR Lagrangian. We find four null eigenvalues associated with trivial primary constraints in the temporal part of the momenta. The remaining eigenvalues are grouped in four sets, which have multiplicity 3, 1, 5 and 3, and can be set to zero depending on different choices of the coefficients [Formula: see text]. There are nine possible different cases when one, two, or three sets of eigenvalues are imposed to vanish simultaneously. All cases lead to a different number of primary constraints, which are consistent with previous work on the Hamiltonian analysis of NGR by Blixt et al. (2018).

Hamiltonian formalism for perfect fluids in general relativity

1980 ◽  
Vol 21 (10) ◽  
pp. 2785-2793 ◽  
Author(s):  
Jacques Demaret ◽  
Vincent Moncrief
Keyword(s):  
General Relativity ◽  
Hamiltonian Formalism ◽  
Perfect Fluids

scholarly journals HAMILTONIAN ANALYSIS OF GENERAL RELATIVITY WITH THE IMMIRZI PARAMETER

2001 ◽  
Vol 10 (03) ◽  
pp. 261-272 ◽  
Author(s):  
NUNO BARROS E SÁ
Keyword(s):  
General Relativity ◽  
Gauge Symmetries ◽  
Constraint Analysis ◽  
Hamiltonian Analysis

Starting from a Lagrangian we perform the full constraint analysis of the Hamiltonian for General relativity in the tetrad-connection formulation for an arbitrary value of the Immirzi parameter and solve the second class constraints, presenting the theory with a Hamiltonian composed of first class constraints which are the generators of the gauge symmetries of the action. In the time gauge we then recover Barbero's formulation of gravity.

scholarly journals Spinning bodies in general relativity

2016 ◽  
Vol 13 (08) ◽  
pp. 1640002 ◽  
Author(s):  
J. W. van Holten
Keyword(s):  
General Relativity ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Hamiltonian Formalism ◽  
Momentum Tensor ◽  
Curved Space ◽  
Constants Of Motion ◽  
Spinning Bodies ◽  
Compact Spinning ◽  
Independent Derivation

A covariant Hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of Hamiltonians accounting for specific properties and interactions of spinning bodies. The dynamics for a minimal and a specific non-minimal Hamiltonian is discussed. An independent derivation of the equations of motion from an appropriate energy–momentum tensor is provided. It is shown how to derive constants of motion, both background-independent and background-dependent ones.

scholarly journals On the nonperturbative graviton propagator

2018 ◽  
Vol 33 (36) ◽  
pp. 1850220 ◽  
Author(s):  
V. M. Khatsymovsky
Keyword(s):  
General Relativity ◽  
Functional Integration ◽  
Hamiltonian Formalism ◽  
Planck Scale ◽  
Functional Integral ◽  
Perturbative Expansion ◽  
Length Scale ◽  
Leading Order ◽  
Starting Point ◽  
Graviton Propagator

To reduce general relativity to the canonical Hamiltonian formalism and construct the path (functional) integral in a simpler and, especially in the discrete case, less singular way, one extends the configuration superspace, as in the connection representation. Then we perform functional integration over connection. The module of the result of this integration arises in the leading order of the expansion over a scale of the discrete lapse-shift functions and has maxima at finite (Planck scale) areas/lengths and rapidly decreases at large areas/lengths, as we have mainly considered previously; the phase arises in the leading order (Regge action) of the stationary phase expansion. Now we consider the possibility of confining ourselves to these leading terms in a certain region of the parameters of the theory; consider background edge lengths as an optimal starting point for the perturbative expansion of the theory; estimate the background length scale and consider the form of the graviton propagator. In parallel with the general simplicial structure, we consider the simplest periodic simplicial structure with a part of the variables frozen (“hypercubic”), for which also the propagator in the leading approximation over metric variations can be written in a closed form.

scholarly journals Spectrum of area in the Faddeev formulation of gravity

2016 ◽  
Vol 31 (19) ◽  
pp. 1650114 ◽  
Author(s):  
V. M. Khatsymovsky
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Hamiltonian Formalism ◽  
Black Hole Entropy ◽  
Field Equations ◽  
Piecewise Constant ◽  
First Order ◽  
Connection Matrices ◽  
Order Representation ◽  
Connection Type

Faddeev formulation of general relativity (GR) is considered where the metric is composed of ten vector fields or a ten-dimensional tetrad. Upon partial use of the field equations, this theory results in the usual general relativity (GR). Earlier, we have proposed first-order representation of the minisuperspace model for the Faddeev formulation where the tetrad fields are piecewise constant on the polytopes like four-simplices or, say, cuboids into which [Formula: see text] can be decomposed, an analogue of the Cartan–Weyl connection-type form of the Hilbert–Einstein action in the usual continuum GR. In the Hamiltonian formalism, the tetrad bilinears are canonically conjugate to the orthogonal connection matrices. We evaluate the spectrum of the elementary areas, functions of the tetrad bilinears. The spectrum is discrete and proportional to the Faddeev analog [Formula: see text] of the Barbero–Immirzi parameter [Formula: see text]. The possibility of the tetrad and metric discontinuities in the Faddeev gravity allows to consider any surface as consisting of a set of virtually independent elementary areas and its spectrum being the sum of the elementary spectra. Requiring consistency of the black hole entropy calculations known in the literature we are able to estimate [Formula: see text].

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