scholarly journals Canonical Quantization Procedure in a Theory with Absolute Teleparallelism

1985 ◽  
Vol 74 (3) ◽  
pp. 626-629
Author(s):  
R. de A. Campos ◽  
P. S. Letelier ◽  
C. G. de Oliveira
Keyword(s):  
Canonical Quantization ◽  
Quantization Procedure

scholarly journals CANONICAL QUANTIZATION OF THE SELF-DUAL MODEL COUPLED TO FERMIONS

1999 ◽  
Vol 14 (16) ◽  
pp. 2495-2510 ◽  
Author(s):  
H. O. GIROTTI
Keyword(s):  
Canonical Quantization ◽  
High Energy ◽  
The Self ◽  
Simons Theory ◽  
Dual Model ◽  
Dirac Bracket ◽  
Interaction Picture ◽  
Quantization Procedure ◽  
Energy Behavior ◽  
Chern Simons

This paper is devoted to formulating the interaction-picture dynamics of the self-dual field minimally coupled to fermions. As a preliminary, we quantize the free self-dual model by means of the Dirac-bracket quantization procedure. The free self-dual model turns out to be a relativistically invariant quantum field theory whose excitations are identical to the physical (gauge-invariant) excitations of the free Maxwell–Chern–Simons theory. The interacting model is also quantized through the Dirac-bracket quantization procedure. One of the self-dual field components is found not to commute, at equal times, with the fermionic fields. Hence, the formulation of the interaction-picture dynamics demands the elimination of that component. This procedure brings, in turn, two new interactions terms, which are local in space and time while nonrenormalizable by power counting. Relativistic invariance is tested in connection with the elastic fermion–fermion scattering amplitude. We prove that all the noncovariant pieces in the interaction Hamiltonian are equivalent to the covariant minimal interaction of the self-dual field with the fermions. The high-energy behavior of the self-dual field propagator confirms that the coupled theory is nonrenormalizable. The self-dual field minimally coupled to fermions bears no resemblance to the renormalizable model defined by the Maxwell–Chern–Simons field minimally coupled to fermions.

scholarly journals Contextual Quantization and the Principle of Complementarity of Probabilities

2005 ◽  
Vol 12 (03) ◽  
pp. 303-318 ◽  
Author(s):  
Andrei Khrennikov ◽  
Sergei Kozyrev
Keyword(s):  
Canonical Quantization ◽  
General Definition ◽  
Noncommutative Probability ◽  
Quantization Procedure ◽  
Complementarity Principle ◽  
Definition Of ◽  
Principle Of Complementarity

The contextual probabilistic quantization procedure is formulated. This approach to quantization has much broader field of applications, compared with the canonical quantization. The contextual probabilistic quantization procedure is based on the notions of probability context and the principle of complementarity of probabilities. The general definition of probability context is given. The principle of complementarity of probabilities, which combines the ideas of the Bohr complementarity principle and the technique of noncommutative probability, is introduced. The principle of complementarity of probabilities is the criterion of possibility of the contextual quantization.

scholarly journals CANONICAL QUANTIZATION OF THE DEGENERATE WESS–ZUMINO ACTION INCLUDING CHIRAL INTERACTION WITH GAUGE FIELDS

1996 ◽  
Vol 11 (04) ◽  
pp. 747-758 ◽  
Author(s):  
S.A. FROLOV ◽  
A.A. SLAVNOV ◽  
C. SOCHICHIU
Keyword(s):  
Canonical Quantization ◽  
Gauge Fields ◽  
Gauge Model ◽  
Physical Content ◽  
Quantization Procedure ◽  
Chiral Interaction

A consistent quantization procedure for the chiral SU(3) gauge model in the presence of the SO(3)-invariant Wess–Zumino action is constructed. The physical content of the model is analyzed. As a simple example the 2D SU(2) gauge model with the degenerate Wess–Zumino action is also considered.

scholarly journals Using a Toy Model to Improve the Quantization of Gravity and Field Theories

2021 ◽  
Author(s):  
John Klauder
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Positive Result ◽  
Harmonic Oscillator ◽  
Canonical Quantization ◽  
Field Theories ◽  
Quantization Procedure ◽  
Quantization Of Gravity

A half-harmonic oscillator, which gets its name because the coordinate is strictly positive, has been quantized and determined that it was a physically correct quantization. This positive result was found using affine quantization (AQ). The main purpose of this paper is to compare results of this new quantization procedure with those of canonical quantization (CQ). Using Ashtekar-like classical variables and CQ, we quantize the same toy model. While these two quantizations lead to different results, they both would reduce to the same classical Hamiltonian if $\hbar\rightarrow0$. Since these two quantizations have differing results, only one of the quantizations can be physically correct. Two brief sections illustrate how AQ can correctly help quantum gravity and the quantization of most field theory problems.

Vacuum polarization and particle creation in the presence of a potential step

2016 ◽  
Vol 31 (02n03) ◽  
pp. 1641031 ◽  
Author(s):  
S. P. Gavrilov ◽  
D. M. Gitman
Keyword(s):  
Electric Potential ◽  
Canonical Quantization ◽  
Particle Creation ◽  
Pair Creation ◽  
Dirac Field ◽  
Potential Step ◽  
Electron Positron ◽  
Physical Impact ◽  
Particle Interpretation ◽  
Electron Positron Pair

We consider QED with strong external backgrounds that are concentrated in restricted space areas. The latter backgrounds represent a kind of spatial x-electric potential steps for charged particles. They can create particles from the vacuum, the Klein paradox being closely related to this process. We describe a canonical quantization of the Dirac field with x-electric potential step in terms of adequate in- and out-creation and annihilation operators that allow one to have consistent particle interpretation of the physical system under consideration and develop a nonperturbative (in the external field) technics to calculate scattering, reflection, and electron-positron pair creation. We resume the physical impact of this development.

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