Transformations and BRST-Charges in 2+1 Dimensional Gravitation

Canonical transformations relating the variables of the ADM-, Ashtekar's and Witten's formulations of gravity are computed in 2+1~dimensions. Three different forms of the BRST-charge are given in the 2+1 dimensional Ashtekar formalism, two of them using Ashtekar's form of the constraints and one of them using the forms suggested by Witten. The BRST-charges are of different rank.Comment: 10 page

Gauge fixing, co-BRST and time evolution in QED

We consider BRST-invariant inner product states for quantum electrodynamics constructed from trivial BRST-invariant states and a gauge regulator. The trivial states are products of matter and ghost states and are annihilated by hermitian operators. The co-BRST operator and some further gauge-fixing regulators are found. The relation between gauge fixing and time evolution of both the trivial and the inner product states is discussed.Comment: Latex, 24 pages, included some new references and comment

Relativistic quantum mechanics on the SL(2,R) spacetime

The Schr\"odinger-type formalism of the Klein-Gordon quantum mechanics is adapted for the case of the $SL(2,\R)$ spacetime. The free particle case is solved, the results of a recent work are reproduced while all the other, topologically nontrivial solutions and the antiparticle modes are also found, and a deeper insight into the physical content of the theory is given.Comment: version to appear in J. Math. Phys, 12 pages, LaTe

Probability current in zero-spin relativistic quantum mechanics

We show that the antisymmetric spinor tensor representation of spin-0 relativistic quantum mechanics provides a conserved current with positive definite timelike component, interpretable as probability density. The construction runs in complete analogy to the spin-1/2 case, and provides an analogously natural one-particle Hilbert space description for spin 0. Except for the free particle, the obtained formulation proves to be inequivalent to the one based on the Klein--Gordon equation. The second quantized version may lead to new field theoretical interaction terms for zero-spin particles.Comment: 9 pages, no figures; material presented at the Zim\'anyi School, December 7-11, 2015, Budapest, Hungar

Coherent diffraction radiation of relativistic terahertz pulses from a laser-driven micro-plasma-waveguide

We propose a method to generate isolated relativistic terahertz (THz) pulses using a high-power laser irradiating a mirco-plasma-waveguide (MPW). When the laser pulse enters the MPW, high-charge electron bunches are produced and accelerated to ~ 100 MeV by the transverse magnetic modes. A substantial part of the electron energy is transferred to THz emission through coherent diffraction radiation as the electron bunches exit the MPW. We demonstrate this process with three-dimensional particle-in-cell simulations. The frequency of the radiation is determined by the incident laser duration, and the radiated energy is found to be strongly correlated to the charge of the electron bunches, which can be controlled by the laser intensity and micro-engineering of the MPW target. Our simulations indicate that 100-mJ level relativistic-intense THz pulses with tunable frequency can be generated at existing laser facilities, and the overall efficiency reaches 1%.Comment: 5 pages, 4 figure

Alfv\'enic instabilities driven by runaways in fusion plasmas

Runaway particles can be produced in plasmas with large electric fields. Here we address the possibility that such runaway ions and electrons excite Alfv\'enic instabilities. The magnetic perturbation induced by these modes can enhance the loss of runaways. This may have important implications for the runaway electron beam formation in tokamak disruptions.Comment: 11 pages, 3 figure