In the present work we study the Hamiltonian, path integral and BRST formulations of the Chern-Simons-Higgs theory in two-space one-time dimensions, in the so-called broken symmetry phase of the Higgs potential (where...In the present work we study the Hamiltonian, path integral and BRST formulations of the Chern-Simons-Higgs theory in two-space one-time dimensions, in the so-called broken symmetry phase of the Higgs potential (where the phase φ(xμ) of the complex matter field Φ(xμ) carries the charge degree of freedom of the complex matter field and is akin to the Goldstone boson) on the light-front (i.e., on the hyperplanes defined by the fixed light-cone time). The theory is seen to possess a set of first-class constraints and the local vector gauge symmetry. The theory being gauge-invariant is quantized under appropriate gauge-fixing conditions. The explicit Hamiltonian and path integral quantization is achieved under the above light-cone gauges. The Heisenberg equations of motion of the system are derived for the physical degrees of freedom of the system. Finally the BRST quantization of the system is achieved under appropriate BRST gauge-fixing, where the BRST symmetry is maintained even under the BRST light-cone gauge-fixing.展开更多
In this paper,we study the long time asymptotic behaviors for solutions to the Chern-Simons-Higgs equations with a pure power defocusing nonlinearity.We obtain quantitative inverse polynomial time decay for the potent...In this paper,we study the long time asymptotic behaviors for solutions to the Chern-Simons-Higgs equations with a pure power defocusing nonlinearity.We obtain quantitative inverse polynomial time decay for the potential energy for all data with finite conformal energy.Consequently,the solution decays in time in the pointwise sense for all power.We also show that the solution decays as quickly as linear waves for sufficiently large powers.Key ingredients for the proof include the vector field method,conformal compactification,and the geometric bilinear trace theorem for null hypersurfaces developed by Klainerman and Rodnianski(2006).展开更多
文摘In the present work we study the Hamiltonian, path integral and BRST formulations of the Chern-Simons-Higgs theory in two-space one-time dimensions, in the so-called broken symmetry phase of the Higgs potential (where the phase φ(xμ) of the complex matter field Φ(xμ) carries the charge degree of freedom of the complex matter field and is akin to the Goldstone boson) on the light-front (i.e., on the hyperplanes defined by the fixed light-cone time). The theory is seen to possess a set of first-class constraints and the local vector gauge symmetry. The theory being gauge-invariant is quantized under appropriate gauge-fixing conditions. The explicit Hamiltonian and path integral quantization is achieved under the above light-cone gauges. The Heisenberg equations of motion of the system are derived for the physical degrees of freedom of the system. Finally the BRST quantization of the system is achieved under appropriate BRST gauge-fixing, where the BRST symmetry is maintained even under the BRST light-cone gauge-fixing.
基金supported by the National Key R&D Program of China(Grant No.2021YFA1001500)supported by the National Key R&D Program of China(Grant No.2021YFA1001700)National Natural Science Foundation of China(Grant Nos.12171011 and 12141102)。
文摘In this paper,we study the long time asymptotic behaviors for solutions to the Chern-Simons-Higgs equations with a pure power defocusing nonlinearity.We obtain quantitative inverse polynomial time decay for the potential energy for all data with finite conformal energy.Consequently,the solution decays in time in the pointwise sense for all power.We also show that the solution decays as quickly as linear waves for sufficiently large powers.Key ingredients for the proof include the vector field method,conformal compactification,and the geometric bilinear trace theorem for null hypersurfaces developed by Klainerman and Rodnianski(2006).
