New Gauge Invariant Formulation of the Chern-Simons Gauge Theory: Classical and Quantal Analysis

Abstract

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.

arXiv commentNo figures, 44 pages

References in corpus (38)

• High-Energy Tests of Lorentz Invariance
• Radiatively Induced Lorentz and CPT Violation in Electrodynamics
• Constituent Quarks from QCD
• The Fermion-Boson Mapping in Three Dimensional Quantum Field Theory
• On the vacuum wavefunction and string tension of Yang-Mills theories in (2+1) dimensions
• Statistical Entropy of Three-dimensional Kerr-De Sitter Space
• On S-Duality in Abelian Gauge Theory
• A gauge-invariant Hamiltonian analysis for non-Abelian gauge theories in (2+1) dimensions
• Planar Yang-Mills theory: Hamiltonian, regulators and mass gap
• Lorentz and CPT Violating Chern-Simons Term in the Derivative Expansion of QED
• Symmetry Algebras in Chern-Simons Theories with Boundary: Canonical Approach
• On the origin of the mass gap for non-Abelian gauge theories in (2+1) dimensions
• Schrödinger Fields on the Plane with $[U(1){]}^N$ Chern-Simons Interactions and Generalized Self-dual Solitons
• Yang-Mills Fields and Riemannian Geometry
• On the Equivalence of the Maxwell-Chern-Simons Theory and a Self-Dual Model
• Non-Abelian Chern-Simons Particles and their Quantization
• Generalised Hamiltonian embedding of the Proca model
• BRST Quantization of the Proca Model based on the BFT and the BFV Formalism
• BATALIN-FRADKIN-TYUTIN EMBEDDING OF A SELF-DUAL MODEL AND THE MAXWELL-CHERN-SIMONS THEORY
• Hamiltonian Embedding of Self-Dual Model and Equivalence with Maxwell-Chern-Simons Theory
• Perturbative and Non-Perturbative Quarks and Gluons
• Non-Abelian Proca model based on the improved BFT formalism
• Colour Charges and the Anti-Screening Contribution to the Interquark Potential
• On the Physical Propagators of QED
• Gauss's law and gauge-invariant operators and states in QCD
• Gauge Invariant Geometric Variables For Yang-Mills Theory
• Symplectic Reduction and Symmetry Algebra in Boundary Chern-Simons theory
• Quark confinement and color transparency in a gauge-invariant formulation of QCD
• Ground State in Gluodynamics and Quark Confinement
• Non-Yang-Mills Gauge Theories
• Implementing Gauss's law in Yang-Mills theory and QCD
• Gauge Independence in terms of the Functional Integral
• New Gauge Invariant Formulation of the Chern-Simons Gauge Theory
• (1+1)-Dimensional SU(N) Static Sources in E and A Representations
• Comment on Gauge-Independent Analysis of Chern-Simons Theory with Matter Coupling
• Operator Ordering Problem of the Nonrelativistic Chern-Simons Theory
• (2+1)-Dimensional QED, Anomalous Surface-Term Contributions and Superconductivity
• Anyonic physical observables and spin phase transition