Covariant canonical quantization of fields and Bohmian mechanics
@article{Nikoli2004CovariantCQ, title={Covariant canonical quantization of fields and Bohmian mechanics}, author={Hrvoje Nikoli{\'c}}, journal={The European Physical Journal C - Particles and Fields}, year={2004}, volume={42}, pages={365-374} }
Abstract.We propose a manifestly covariant canonical method of field quantization based on the classical De Donder-Weyl covariant canonical formulation of field theory. Owing to covariance, the space and time arguments of fields are treated on an equal footing. To achieve both covariance and consistency with standard non-covariant canonical quantization of fields in Minkowski spacetime, it is necessary to adopt a covariant Bohmian formulation of quantum field theory. A preferred foliation of…
16 Citations
Covariant canonical quantization
- Physics
- 2005
We present a manifestly covariant quantization procedure based on the de Donder–Weyl Hamiltonian formulation of classical field theory. This procedure agrees with conventional canonical quantization…
Strings, world-sheet covariant quantization and Bohmian mechanics
- Physics
- 2006
The covariant canonical method of quantization based on the De Donder–Weyl covariant canonical formalism is used to formulate a world-sheet covariant quantization of bosonic strings. To provide the…
Boson-Fermion Unification, Superstrings, and Bohmian Mechanics
- Physics
- 2009
Bosonic and fermionic particle currents can be introduced in a more unified way, with the cost of introducing a preferred spacetime foliation. Such a unified treatment of bosons and fermions…
Bohmian mechanics in relativistic quantum mechanics, quantum field theory and string theory
- Physics
- 2006
I present a short overview of my recent achievements on the Bohmian interpretation of relativistic quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant…
QUANTUM DETERMINISM FROM QUANTUM GENERAL COVARIANCE
- Physics
- 2006
The requirement of general covariance of quantum field theory (QFT) naturally leads to quantization based on the manifestly covariant De Donder–Weyl formalism. To recover the standard noncovariant…
Covariant Guiding Laws for Fields
- Physics, Mathematics
- 2021
After reviewing what is known about the passage from the classical Hamilton–Jacobi formulation of non-relativistic point-particle dynamics to the non-relativistic quantum dynamics of point particles…
Noncommutative conformally coupled scalar field cosmology and its commutative counterpart
- Physics
- 2005
We study the implications of a noncommutative geometry of the minisuperspace variables for the Friedmann-Robertson-Walker universe with a conformally coupled scalar field. The investigation is…
PROBABILITY IN RELATIVISTIC QUANTUM MECHANICS AND FOLIATION OF SPACE–TIME
- Mathematics
- 2007
The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be nonnegative and the integral of them over an entire hypersurface should…
Precanonical quantization and the Schr\"odinger wave functional revisited
- Mathematics
- 2011
We address the issue of the relation between the canonical functional Schr\"odinger representation in quantum field theory and the approach of precanonical field quantization proposed by the author,…
On the Covariant Hamilton-Jacobi Equation for the Teleparallel Equivalent of General Relativity
- Physics
- 2022
The covariant Hamilton-Jacobi equation for the Teleparallel Equivalent of General Relativity is derived based on the analysis of constraints within the De Donder-Weyl covariant Hamiltonian theory…
References
SHOWING 1-10 OF 82 REFERENCES
A relativistically covariant version of Bohm's quantum field theory for the scalar field
- Physics
- 2004
We give a relativistically covariant, wave-functional formulation of Bohm's quantum field theory for the scalar field based on a general foliation of spacetime by space-like hypersurfaces. The wave…
Precanonical Quantum Gravity: Quantization Without the Space–Time Decomposition
- Physics
- 2000
A nonpertubative approach to quantum gravity using precanonical field quantization originating from the covariant De Donder–Weyl Hamiltonian formulation, which treats space and time variables on an…
Space-time covariant form of Ashtekar’s constraints
- Physics
- 1995
SummaryThe Lagrangian formulation of classical field theories and, in particular, general relativity leads to a coordinate-free, fully covariant analysis of these constrained systems. This paper…
On a covariant Hamilton-Jacobi framework for the Einstein-Maxwell theory
- Mathematics
- 1991
The author extends the previously developed covariant Hamilton-Jacobi description of pure gravity in any dimension greater than two, to coupled electromagnetic and gravitational fields. In the case…
Constraint algebra and equations of motion in the Bohmian interpretation of quantum gravity
- Physics
- 2004
It is shown that introducing quantum effects using de Broglie–Bohm theory in the canonical formulation of gravity changes the constraint algebra. The new algebra is a clear projection of general…
Loop Quantum Gravity and the Meaning of Diffeomorphism Invariance
- Physics
- 1999
This series of lectures gives an introduction to the non-perturbative and background-independent formulation for a quantum theory of gravitation which is called loop quantum gravity. The Hilbert…
Symplectic geometry of the convariant phase space
- Physics
- 1988
Develops a formalism for a covariant treatment of the phase space of field theories. Within that formalism, an expression for the symplectic form of a general Lagrangian field theory is presented. As…