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.

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.

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.

scholarly journals HIGHER-DERIVATIVE TWO-DIMENSIONAL MASSIVE FERMION THEORIES

2000 ◽  
Vol 15 (15) ◽  
pp. 2237-2254 ◽  
Author(s):  
L. V. BELVEDERE ◽  
R. L. P. G. AMARAL ◽  
N. A. LEMOS ◽  
C. G. CARVALHAES
Keyword(s):  
Lorentz Invariance ◽  
Canonical Quantization ◽  
Mass Term ◽  
Two Dimensional ◽  
Massive Fermion ◽  
Higher Derivative ◽  
Odd Order ◽  
Boson Theory ◽  
Current Interaction ◽  
Hilbert Subspace

We consider the canonical quantization of a generalized two-dimensional massive fermion theory containing higher odd-order derivatives. The requirements of Lorentz invariance, hermiticity of the Hamiltonian and absence of tachyon excitations suffice to fix the mass term, which contains a derivative coupling. We show that the basic quantum excitations of a higher-derivative theory of order 2N+1 consist of a physical usual massive fermion, quantized with positive metric, plus 2N unphysical massless fermions, quantized with opposite metrics. The positive-metric Hilbert subspace, which is isomorphic to the space of states of a massive free fermion theory, is selected by a subsidiary-like condition. Employing the standard bosonization scheme, the equivalent boson theory is derived. The results obtained are used as a guideline to discuss the solution of a theory including a current–current interaction.

Quantum vacuum torque on a bi-anisotropic absorbing magneto-dielectric cylindrical shell co-axis with a perfectly conductor cylindrical shell

2019 ◽  
Vol 34 (26) ◽  
pp. 1950149
Author(s):  
Marzieh Hossein Zadeh ◽  
Majid Amooshahi
Keyword(s):  
Cylindrical Shell ◽  
Electromagnetic Field ◽  
Angular Momentum ◽  
Thermal State ◽  
Canonical Quantization ◽  
Vacuum State ◽  
Quantum Vacuum ◽  
Ladder Operators ◽  
Quantized Electromagnetic Field ◽  
Series Technique

A fully canonical quantization of electromagnetic field in the presence of a bi-anisotropic absorbing magneto-dielectric cylindrical shell is provided. The mode expansions of the dynamical quantum fields, contained in the theory, is achieved and the ladder operators of the system are introduced. Using the Frobenius’s series technique, the Maxwell’s equations in the presence of the bi-anisotropic absorbing magneto-dielectric cylindrical shell are solved and the space–time dependence of the quantized electromagnetic field is obtained. Applying the conservation principle of the angular momentum, the net quantum vacuum torque exerted on the bi-anisotropic absorbing magneto-dielectric cylindrical shell is calculated. The net quantum vacuum torque exerted on the cylindrical shell is calculated in the vacuum state and the thermal state of the system. The quantum vacuum torque on the cylindrical shell identically vanishes when the bi-anisotropic absorbing magneto-dielectric cylindrical shell is converted to an isotropic one.

The interaction of molecular multipoles with the electromagnetic field in the canonical formulation of non-covariant quantum electrodynamics

1970 ◽  
Vol 319 (1539) ◽  
pp. 549-563 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Physical Interpretation ◽  
Quantum Electrodynamics ◽  
Unitary Transformation ◽  
Canonical Quantization ◽  
Multipole Moments ◽  
Gauge Invariant ◽  
Covariant Quantum ◽  
Canonical Formulation ◽  
Gauge Conditions

The procedure devised by Dirac for the canonical quantization of systems described by degenerate lagrangians is used to construct the hamiltonian for molecules interacting with the electromagnetic field. The hamiltonian obtained is expressed in terms of the gauge invariant field strengths and the electric and magnetic multipole moments of the molecules. The Coulomb gauge is introduced but other gauge conditions could be used. Finally, a physical interpretation of the unitary transformation that may be used to generate the multipole hamiltonian is given.

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