TOPOLOGICALLY MASSIVE ELECTROMAGNETIC INTERACTION OF COMPOSITE PARTICLES IN A HIGHER-DERIVATIVE NONRELATIVISTIC GAUGE FIELD MODEL

2010 ◽  
Vol 25 (26) ◽  
pp. 4949-4974 ◽  
Author(s):  
EDMUNDO C. MANAVELLA
Keyword(s):  
Electromagnetic Field ◽  
Gauge Field ◽  
Field Model ◽  
Electromagnetic Interaction ◽  
Canonical Quantization ◽  
Landau Gauge ◽  
Composite Particles ◽  
Ultraviolet Divergence ◽  
Higher Derivative ◽  
Derivative Term

A higher-derivative classical nonrelativistic U (1) × U (1) gauge field model that describes the topologically massive electromagnetic interaction of composite particles in 2+1 dimensions is proposed. This is made by adding a suitable higher-derivative term for the electromagnetic field to the Lagrangian of a model previously proposed. The model contains a Chern–Simons U(1) field and the topologically massive electromagnetic U(1) field, and it uses either a composite boson system or a composite fermion one. The second case is explicitly considered. By following the usual Hamiltonian method for singular higher-derivative systems, the canonical quantization is carried out. By extending the Faddeev–Senjanovic formalism, the path integral quantization is developed. Consequently, the Feynman rules are established and the diagrammatic structure is discussed. The use of the higher-derivative term eliminates in the Landau gauge the ultraviolet divergence of the primitively divergent Feynman diagrams where the electromagnetic field propagator is present. The unitarity problem, related to the possible appearance of states with negative norm, is treated. A generalization of the Becchi–Rouet-Stora–Tyutin algorithm is applied to the model.

Quantum field formalism for the higher-derivative nonrelativistic electrodynamics in 1+1 dimensions

2019 ◽  
Vol 34 (09) ◽  
pp. 1950050 ◽  
Author(s):  
E. C. Manavella
Keyword(s):  
Electromagnetic Field ◽  
Brst Quantization ◽  
Canonical Quantization ◽  
Landau Gauge ◽  
Ultraviolet Divergence ◽  
Hamiltonian Method ◽  
Higher Derivative ◽  
Feynman Rules ◽  
Derivative Term ◽  
Field Formalism

Starting from the classical nonrelativistic electrodynamics in 1[Formula: see text]+[Formula: see text]1 dimensions, a higher-derivative version is proposed. This is made by adding a suitable higher-derivative term for the electromagnetic field to the Lagrangian of the original electrodynamics, preserving its gauge invariance. By following the usual Hamiltonian method for singular higher-derivative systems, the canonical quantization for the higher-derivative model is developed. By extending the Faddeev–Senjanovic algorithm, the path integral quantization is carried out. Hence, the Feynman rules are established and the diagrammatic structure is analyzed. The use of the higher-derivative term eliminates in the Landau gauge the ultraviolet divergence of the primitively divergent Feynman diagrams of the original model, where the electromagnetic field propagator is present. A generalization of the BRST quantization is also considered.

NONRELATIVISTIC QUANTUM FORMALISM FOR ELECTROMAGNETIC INTERACTION OF ANYONS IN THE U(1)×U(1) GAUGE MODEL

1996 ◽  
Vol 11 (05) ◽  
pp. 921-940 ◽  
Author(s):  
A. FOUSSATS ◽  
C. REPETTO ◽  
O.P. ZANDRON ◽  
O.S. ZANDRON ◽  
E. MANAVELLA
Keyword(s):  
Electromagnetic Field ◽  
Electromagnetic Interaction ◽  
Canonical Quantization ◽  
Matter Field ◽  
Integral Approach ◽  
Gauge Model ◽  
Nonrelativistic Quantum ◽  
Quantum Formalism ◽  
Feynman Rules ◽  
Dirac Formalism

Starting from the U (1)× U (1) classical gauge model for the nonrelativistic electromagnetic interaction of anyons, the quantum formalism is constructed. This gauge model containing the statistical U(1) field and the electromagnetic field can be coupled to both, a commuting or an anticommuting matter field. We explicitly consider the second case, i.e. a fermionic anyon system in the presence of an electromagnetic field, and we carry out the canonical quantization by following the Dirac formalism. Later on, the path integral approach is developed and the diagrammatic and Feynman rules, in the framework of the perturbation theory, are discussed. Finally, as an alternative method, the BRST formalism for this gauge model is also treated.

Composite particles within the Faddeev–Jackiw framework: Nonequivalence between the Dirac and Faddeev–Jackiw formalisms

2014 ◽  
Vol 29 (15) ◽  
pp. 1450076
Author(s):  
Edmundo C. Manavella
Keyword(s):  
Field Model ◽  
Condensed Matter ◽  
Canonical Quantization ◽  
Constrained Systems ◽  
Composite Particles ◽  
Composite Fermion ◽  
Quantization Formalism ◽  
The One ◽  
Chern Simons ◽  
Dirac Formalism

Some time ago, the Faddeev–Jackiw canonical quantization formalism for constrained systems with Grassmann dynamical variables in the field theory context was reviewed. In the present work, the resulting formalism is applied to a classical nonrelativistic U(1) ×U(1) gauge field model that describes the electromagnetic interaction of composite particles in 2+1 dimensions. The model contains a Chern–Simons U(1) field and the electromagnetic field, and it uses either a composite boson system or a composite fermion one. The obtained results are compared with the ones corresponding to the implementation of the Dirac formalism to this model, concluding that the Faddeev–Jackiw and Dirac methods cannot be considered equivalent. A simplified version of the above model is analyzed in the same way, similar to the one used within the framework of condensed matter. In this case, it is observed that when the results obtained by the Faddeev–Jackiw and Dirac methods coincide, the first method is more economical than the second one. For both models, the composite fermion case is explicitly considered.

scholarly journals ELECTROMAGNETIC INTERACTION OF ANYONS IN NONRELATIVISTIC QUANTUM FIELD THEORY

1994 ◽  
Vol 09 (06) ◽  
pp. 953-967 ◽  
Author(s):  
J. L. CORTÉS ◽  
J. GAMBOA ◽  
L. VELÁZQUEZ
Keyword(s):  
Electromagnetic Field ◽  
Electromagnetic Interaction ◽  
Magnetic Coupling ◽  
Nonrelativistic Limit ◽  
Quantum Field ◽  
Nonrelativistic Quantum ◽  
Statistical Field ◽  
Mechanical Formulation ◽  
Dynamical Spin ◽  
Chern Simons

The nonrelativistic quantum-field-theoretic Lagrangian which describes an anyon system in the presence of an electromagnetic field is identified. A nonminimal magnetic coupling to the Chern–Simons statistical field as well as to the electromagnetic field together with a direct coupling between both fields are the nontrivial ingredients of the Lagrangian obtained from the nonrelativistic limit of the fermionic relativistic formulation. The results, an electromagnetic gyromagnetic ratio 2 for any spin together with a nontrivial dynamical spin-dependent contact interaction between anyons as well as the spin dependence of the electromagnetic effective action, agree with the quantum-mechanical formulation.

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