<i>p</i>-mechanics as a physical theory: an introduction

Kisil, Vladimir V.

doi:10.1088/0305-4470/37/1/013

Cited by 27 publications

(56 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As such, CQG-theory is endowed with a number of key features, since: A) it preserves the background metric tensor g(r) which is identified with a classical field tensor; B) it satisfies the quantum unitarity principle, i.e., the quantum probability is conserved; C) it is constraint-free, in the sense that the quantum Lagrangian variables g ≡ g(r, s) are identified with independent tensor fields; D) it is non-perturbative so that the quantum fluctuations δg(r, s) and δπ(r, s) need not be regarded as asymptotically "small" in some appropriate sense with respect to the background metric tensor g(r). Its foundations (for a detailed discussion see [9]) lie on the preliminary establishment of a variational formulation of GR achieved in the context of a covariant DeDonder-Weyl-type approach to continuum field-Hamiltonian dynamics [12][13][14][15][16][17][18][19] in which the background space-time Q 4 , g is considered prescribed [7,8].…”

Section: Introductionmentioning

confidence: 99%

Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory

Tessarotto

Cremaschini

2018

Entropy

104

View full text Add to dashboard Cite

A trajectory-based representation for the quantum theory of the gravitational field is formulated. This is achieved in terms of a covariant Generalized Lagrangian-Path (GLP) approach which relies on a suitable statistical representation of Bohmian Lagrangian trajectories, referred to here as GLP-representation. The result is established in the framework of the manifestly-covariant quantum gravity theory (CQG-theory) proposed recently and the related CQG-wave equation advancing in proper-time the quantum state associated with massive gravitons. Generally non-stationary analytical solutions for the CQG-wave equation with non-vanishing cosmological constant are determined in such a framework, which exhibit Gaussian-like probability densities that are non-dispersive in proper-time. As a remarkable outcome of the theory achieved by implementing these analytical solutions, the existence of an emergent gravity phenomenon is proven to hold. Accordingly, it is shown that a mean-field background space-time metric tensor can be expressed in terms of a suitable statistical average of stochastic fluctuations of the quantum gravitational field whose quantum-wave dynamics is described by GLP trajectories.

show abstract

Section: Introductionmentioning

confidence: 99%

Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory

Tessarotto

Cremaschini

2018

Entropy

104

View full text Add to dashboard Cite

show abstract

“…Nevertheless, the mathematical framework to be adopted for the construction of manifestly-covariant classical Lagrangian and Hamiltonian theories is well-established both for particle dynamics [16][17][18][19][20] as well in continuum field theory, where it is known as the DeDonder-Weyl formalism [21][22][23][24][25][26][27][28][29]. This type of formulation has been developed and applied consistently to the case of the gravitational field described by SF-GR only recently in Refs.…”

Section: Introductionmentioning

confidence: 99%

Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity

Cremaschini

Tessarotto

2017

Entropy

View full text Add to dashboard Cite

Key aspects of the manifestly-covariant theory of quantum gravity Tessarotto 2015-2017) are investigated. These refer, first, to the establishment of the four-scalar, manifestly-covariant evolution quantum wave equation, denoted as covariant quantum gravity (CQG) wave equation, which advances the quantum state ψ associated with a prescribed background space-time. In this paper, the CQG-wave equation is proved to follow at once by means of a Hamilton-Jacobi quantization of the classical variational tensor field g ≡ g µν and its conjugate momentum, referred to as (canonical) g-quantization. The same equation is also shown to be variational and to follow from a synchronous variational principle identified here with the quantum Hamilton variational principle. The corresponding quantum hydrodynamic equations are then obtained upon introducing the Madelung representation for ψ, which provides an equivalent statistical interpretation of the CQG-wave equation. Finally, the quantum state ψ is proven to fulfill generalized Heisenberg inequalities, relating the statistical measurement errors of quantum observables. These are shown to be represented in terms of the standard deviations of the metric tensor g ≡ g µν and its quantum conjugate momentum operator.

show abstract

“…Corresponding to the Euler-Lagrange equations of field theory, the canonical field equations then take on a symmetric form with respect to the four independent variables of space-time. This approach is commonly referred to as "multisymplectic" or "polysymplectic field theory", thereby labeling the covariant extension of the symplectic geometry of the conventional Hamiltonian theory [Kanatchikov (1998); Gotay et al (2004); Kastrup (1983); Paufler (2001) ;Forger et al (2003); Echeverría-Enríquez et al (1996); Sardanashvily (1995); Kisil (2004)]. Mathematically, the phase space of multisymplectic Hamiltonian field theory is defined within modern differential geometry in the language of "jet bundles" [Saunders (1989); Günther (1987)].…”

Section: Introductionmentioning

confidence: 99%

Covariant Hamiltonian Field Theory

Struckmeier

Redelbach²

2008

Int. J. Mod. Phys. E

View full text Add to dashboard Cite

A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. Whereas the covariant canonical field equations are equivalent to the EulerLagrange field equations, the covariant canonical transformation theory offers more general means for defining mappings that preserve the form of the field equations than the usual Lagrangian description. It is proved that Poisson brackets, Lagrange brackets, and canonical 2-forms exist that are invariant under canonical transformations of the fields. The technique to derive transformation rules for the fields from generating functions is demonstrated by means of various examples. In particular, it is shown that the infinitesimal canonical transformation furnishes the most general form of Noether's theorem. We furthermore specify the generating function of an infinitesimal space-time step that conforms to the field equations.

show abstract

p-mechanics as a physical theory: an introduction

Cited by 27 publications

References 35 publications

Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory

Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory

Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity

Covariant Hamiltonian Field Theory

Contact Info

Product

Resources

About