Canonical Quantization and Gauge Invariant Anyon Operators in Chern-Simons Scalar Electrodynamics

Banerjee, Rabin; Chatterjee, Ashok; Sreedhar, V. V.

doi:10.1006/aphy.1993.1023

Cited by 27 publications

(41 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, it is necessary to introduce some auxiliary fields for the construction of the corresponding field action and subsequent quantization of the theory. Investigation of the previous problem as well as the search for a possible hidden relation of the theory to the approach involving Chern-Simons U(1) gauge field constructions [15,16] could be helpful for constructing a 'minimal' field action leading to eqs. (4.11) and comprising the minimal number of auxiliary fields.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

See 1 more Smart Citation

Deformed Heisenberg Algebra, Fractional Spin Fields, and Supersymmetry without Fermions

1996

View full text Add to dashboard Cite

Within a group-theoretical approach to the description of (2+1)-dimensional anyons, the minimal covariant set of linear differential equations is constructed for the fractional spin fields with the help of the deformed Heisenberg algebra (DHA), [a − , a + ] = 1 + νK, involving the Klein operator K, {K, a ± } = 0, K 2 = 1. The connection of the minimal set of equations with the earlier proposed 'universal' vector set of anyon equations is established. On the basis of this algebra, a bosonization of supersymmetric quantum mechanics is carried out. The construction comprises the cases of exact and spontaneously broken N = 2 supersymmetry allowing us to realize a Bose-Fermi transformation and spin-1/2 representation of SU(2) group in terms of one bosonic oscillator. The construction admits an extension to the case of OSp(2|2) supersymmetry, and, as a consequence, both applications of the DHA turn out to be related. A possibility of 'superimposing' the two applications of the DHA for constructing a supersymmetric (2+1)-dimensional anyon system is discussed. As a consequential result we point out that osp(2|2) superalgebra is realizable as an operator algebra for a quantum mechanical 2-body (nonsupersymmetric) Calogero model.

show abstract

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

“…Such redefined matter fields are given on the one-dimensional path -unobservable 'string' going to the space infinity and attached to the point in which the initial matter field is given. Therefore in this approach the anyonic field operators are path-dependent and multivalued [16] (see also ref. [13]).…”

Section: Introductionmentioning

confidence: 99%

Deformed Heisenberg Algebra, Fractional Spin Fields, and Supersymmetry without Fermions

1996

View full text Add to dashboard Cite

show abstract

“…This corresponds to a different representation from (32) and so this wavefunctional is not equivalent to (32) in general: Actually, there is a slight difference in the purely gauge field part compared to (32). For two particles sector, for example it becomes…”

Section: Physical Wavefunctional In Schröndinger Picturementioning

confidence: 97%

New Gauge Invariant Formulation of the Chern–simons Gauge Theory: Classical and Quantal Analysis

Park

2009

Int. J. Mod. Phys. A

View full text Add to dashboard Cite

Recently proposed new gauge invariant formulation of the Chern-Simons gauge theory is considered in detail. This formulation is consistent with the gauge fixed formulation. Furthermore it is found that the canonical (Noether) Poincaré generators are not gauge invariant even on the constraints surface and do not satisfy the Poincaré algebra contrast to usual case. It is the improved generators, constructed from the symmetric energy-momentum tensor, which are (manifestly) gauge invariant and obey the quantum as well as classical Poincaré algebra. The physical states are constructed and it is found in the Schrödinger picture that unusual gauge invariant longitudinal mode of the gauge field is crucial for constructing the physical wavefunctional which is genuine to (pure) Chern-Simons theory. In matching to the gauge fixed formulation, we consider three typical gauges, Coulomb, axial and Weyl gauges as explicit examples. Furthermore, recent several confusions about the effect of Dirac's dressing function and the gauge fixings are clarified. The analysis according to old gauge independent formulation a la Dirac is summarized in an appendix.

show abstract

“…sional space-time [25,26,15,1,8,14,17] has been worked out to the extent that the localization structure could be readily constructed from them. Secondly, our analysis is intended to be a step in the construction of a model which resembles as closely as possible a free field for anyons, in the sense of a "second quantization functor" from the single particle theories to field algebras.…”

Section: Introductionmentioning

confidence: 99%

Modular localization of massive particles with “any” spin in d=2+1

Mund

2003

Journal of Mathematical Physics

View full text Add to dashboard Cite

We discuss a concept of particle localization which is motivated from quantum field theory, and has been proposed by Brunetti, Guido and Longo and by Schroer. It endows the single particle Hilbert space with a family of real subspaces indexed by the space-time regions, with certain specific properties reflecting the principles of locality and covariance. We show by construction that such a localization structure exists also in the case of massive anyons in d = 2 + 1, i.e. for particles with positive mass and with arbitrary spin s ∈ R. The construction is completely intrinsic to the corresponding ray representation of the (proper orthochronous) Poincaré group. Our result is of particular interest since there are no free fields for anyons, which would fix a localization structure in a straightforward way. We present explicit formulas for the real subspaces, expected to turn out useful for the construction of a quantum field theory for anyons. In accord with well-known results, only localization in string-like, instead of pointlike or bounded, regions is achieved. We also prove a single-particle PCT theorem, exhibiting a PCT operator which acts geometrically correctly on the family of real subspaces.

show abstract

Canonical Quantization and Gauge Invariant Anyon Operators in Chern-Simons Scalar Electrodynamics

Cited by 27 publications

References 0 publications

Deformed Heisenberg Algebra, Fractional Spin Fields, and Supersymmetry without Fermions

Deformed Heisenberg Algebra, Fractional Spin Fields, and Supersymmetry without Fermions

New Gauge Invariant Formulation of the Chern–simons Gauge Theory: Classical and Quantal Analysis

Modular localization of massive particles with “any” spin in d=2+1

Contact Info

Product

Resources

About