Chiral Bosons in Noncommutative Spacetime

Abstract

Underlying a general noncommutative algebra with both noncommutative coordinates and noncommutative momenta in a (1+1)-dimensional spacetime, a chiral boson Lagrangian with manifest Lorentz covariance is proposed by linearly imposing a generalized self-duality condition on a noncommutative generalization of massless real scalar fields. A significant property uncovered for noncommutative chiral bosons is that the left- and right-moving chiral scalars cannot be distinguished from each other, which originates from the noncommutativity of coordinates and momenta. An interesting result is that Dirac's method can be consistently applied to the constrained system whose Lagrangian explicitly contains space and time. The self-duality of the noncommutative chiral boson action does not exist.

22 pages, 1 eps figure. Note and references are added, the final version will appear in JHEP

References in corpus (5)

• Exact PT-Symmetry Is Equivalent to Hermiticity
• The Kepler problem and non commutativity
• Exact Solution of Noncommutative Field Theory in Background Magnetic Fields
• Constant magnetic field and 2d non-commutative inverted oscillator
• Parent Actions, Dualities and New Weyl-invariant Actions of Bosonic p-branes

Cited by in corpus (11)

• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces
• Duality in Noncommutative Topologically Massive Gauge Field Theory Revisited
• Nonlinear Non-Hermitian Landau-Zener-Stückelberg-Majorana interferometry
• Chiral bosonization for non-commutative fields
• Test of Quantum Effects of Spatial Noncommutativity using Modified Electron Momentum Spectroscopy
• Spontaneous breaking of permutation symmetry in pseudo-Hermitian quantum mechanics
• A possible method for non-Hermitian and non-$PT$-symmetric Hamiltonian systems
• Deformed "Commutative" Chern - Simons System
• From Noncommutative Sphere to Nonrelativistic Spin
• Modified gauge unfixing formalism and gauge symmetries in the non-commutative chiral bosons theory
• The coordinate coherent states approach revisited