Covariant canonical quantization of the relativistic free particle top

1991 ◽  
Vol 43 (6) ◽  
pp. 1914-1918 ◽  
Author(s):  
R. P. Malik
Keyword(s):  
Free Particle ◽  
Canonical Quantization

Quantization of a Free Particle in a Dissipative Medium: Interaction of Charged Particles With Matter

2005 ◽  
Author(s):  
Eqab M. Rabei ◽  
Abdul-Wali Ajlouni ◽  
Humam B. Ghassib
Keyword(s):  
Wave Function ◽  
Energy Loss ◽  
Free Particle ◽  
Canonical Quantization ◽  
Charged Particles ◽  
Dissipative Medium ◽  
Nonconservative Systems ◽  
Damping Effect ◽  
Free Particles ◽  
Set Up

Following our work on the quantization of nonconservative systems using fractional calculus, the canonical quantization of a system of free particles in a dissipative medium is carried out according to the Dirac method. A suitable Schro¨dinger equation is set up and solved for the Lagrangian representing this system. The wave function is plotted and the damping effect manifests itself very clearly. This formalism is then applied to the problem of energy loss of charged particles when passing through matter. The results are plotted and the relation between the energy loss and the range agrees qualitatively with experimental results.

scholarly journals Group Theoretical Derivation of Consistent Free Particle Theories

2020 ◽  
Vol 50 (9) ◽  
pp. 977-1007
Author(s):  
Giuseppe Nisticò
Keyword(s):  
Particle Physics ◽  
Free Particle ◽  
Canonical Quantization ◽  
Present Approach ◽  
Theoretical Derivation ◽  
Spin Particle ◽  
Elementary Particle Physics ◽  
Massive Spin ◽  
Klein Gordon

AbstractThe difficulties of relativistic particle theories formulated by means of canonical quantization, such as those of Klein–Gordon and Dirac, ultimately led theoretical physicists to turn to quantum field theory to model elementary particle physics. In order to overcome these difficulties, the theories of the present approach are developed deductively from the physical principles that specify the system, without making use of canonical quantization. For a free particle these starting assumptions are invariance of the theory and covariance of position with respect to Poincaré transformations. In pursuing the approach, the effectiveness of group theoretical methods is exploited. The coherent development of our program has shown that robust classes of representations of the Poincaré group, discarded by the known particle theories, can in fact be taken as bases for perfectly consistent theories. For massive spin zero particles, six inequivalent theories have been determined, two of which do not correspond to any of the current ones; all of these theories overcome the difficulties of Klein–Gordon one. The present lack of the explicit transformation properties of position with respect to boosts prevents the complete determination of non zero spin particle theories. In the past a particular form of these transformation properties was adopted by Jordan and Mukunda. We check its consistency within the present approach and find that for spin $$\frac{1}{2}$$ 1 2 particles there is only one consistent theory, which is unitarily related to Dirac’s; yet, once again, it requires classes of irreducible representations previously discarded.

CANONICAL QUANTIZATION AND MASS SPECTRUM OF RELATIVISTIC PARTICLE ANALOGUE OF RELATIVISTIC STRING WITH RIGIDITY

1988 ◽  
Vol 03 (13) ◽  
pp. 1299-1308 ◽  
Author(s):  
M.S. PLYUSHCHAY
Keyword(s):  
Mass Spectrum ◽  
Mass Shell ◽  
Relativistic Particle ◽  
Free Particle ◽  
Canonical Quantization ◽  
Additional Term ◽  
Relativistic String ◽  
Generalized Model ◽  
Relativistic Rotator

The generalized model of relativistic particle is studied. Its action contains the term for a free particle of mass m together with an additional term proportional to the curvature of its world trajectory. From the full set of Hamiltonian constraints, the mass shell condition is singled out and canonical quantization of the model is performed. The quantized system is shown to be equivalent to relativistic rotator with the mass spectrum coinciding with the spectrum of squared Majorana equation: [Formula: see text], where M is rotator’s mass, s is its spin and α−1 is a constant in additional term in action.

scholarly journals Colourful Poincaré symmetry, gravity and particle actions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Joaquim Gomis ◽  
Euihun Joung ◽  
Axel Kleinschmidt ◽  
Karapet Mkrtchyan
Keyword(s):  
Field Theory ◽  
Free Particle ◽  
Three Dimensional ◽  
Background Field ◽  
Quantum Field ◽  
Symmetry Factor ◽  
Starting Point ◽  
Poincaré Algebra ◽  
Poincaré Symmetry ◽  
Three Space

Abstract We construct a generalisation of the three-dimensional Poincaré algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincaré gravity in three space-time dimensions as well as to study generalisations of massive and massless free particle models. We present various such generalised particle models that differ in which orbits of the coloured Poincaré symmetry are described. Our approach can be seen as a stepping stone towards the description of particles interacting with a non-abelian background field or as a starting point for a worldline formulation of an associated quantum field theory.

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.

Free Particle Motion in Three Dimensions

2010 ◽  
pp. 138-157
Author(s):  
Siegmund Brandt ◽  
Hans Dieter Dahmen ◽  
Tilo Stroh
Keyword(s):  
Particle Motion ◽  
Free Particle ◽  
Three Dimensions
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