Counterterms for Linear Divergences in Real-Time Classical Gauge Theories at High Temperature

Real-time classical SU($N$) gauge theories at non-zero temperature contain linear divergences. We introduce counterterms for these divergences in the equations of motion in the continuum and on the lattice. These counterterms can be given in terms of auxiliary fields that satisfy local equations of motion. We present a lattice model with 6+1D auxiliary fields that for IR-sensitive quantities yields cut-off independent results to leading order in the coupling. Also an approximation with 5+1D auxiliary fields is discussed.Comment: 10 pages, major change

A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions

We define and discuss classical and quantum gravity in 2+1 dimensions in the Galilean limit. Although there are no Newtonian forces between massive objects in (2+1)-dimensional gravity, the Galilean limit is not trivial. Depending on the topology of spacetime there are typically finitely many topological degrees of freedom as well as topological interactions of Aharonov-Bohm type between massive objects. In order to capture these topological aspects we consider a two-fold central extension of the Galilei group whose Lie algebra possesses an invariant and non-degenerate inner product. Using this inner product we define Galilean gravity as a Chern-Simons theory of the doubly-extended Galilei group. The particular extension of the Galilei group we consider is the classical double of a much studied group, the extended homogeneous Galilei group, which is also often called Nappi-Witten group. We exhibit the Poisson-Lie structure of the doubly extended Galilei group, and quantise the Chern-Simons theory using a Hamiltonian approach. Many aspects of the quantum theory are determined by the quantum double of the extended homogenous Galilei group, or Galilei double for short. We study the representation theory of the Galilei double, explain how associated braid group representations account for the topological interactions in the theory, and briefly comment on an associated non-commutative Galilean spacetime.Comment: 38 pages, 1 figure, references update

Covariant derivative expansion of fermionic effective action at high temperatures

We derive the fermionic contribution to the 1-loop effective action for A_4 and A_i fields at high temperatures, assuming that gluon fields are slowly varying but allowing for an arbitrary amplitude of A_4.Comment: RevTex 4, 11 pages, 3 figures. Version 2: Typos corrected; magnetic fields restricted to parallel sector. Version accepted for publication in PR

Quantum Blobs

Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries. Quantum blobs are in a bijective correspondence with the squeezed coherent states from standard quantum mechanics, of which they are a phase space picture. This allows us to propose a substitute for phase space in quantum mechanics. We study the relationship between quantum blobs with a certain class of level sets defined by Fermi for the purpose of representing geometrically quantum states.Comment: Prepublication. Dedicated to Basil Hile

Covariant derivative expansion of Yang-Mills effective action at high temperatures

Integrating out fast varying quantum fluctuations about Yang--Mills fields A_i and A_4, we arrive at the effective action for those fields at high temperatures. Assuming that the fields A_i and A_4 are slowly varying but that the amplitude of A_4 is arbitrary, we find a non-trivial effective gauge invariant action both in the electric and magnetic sectors. Our results can be used for studying correlation functions at high temperatures beyond the dimensional reduction approximation, as well as for estimating quantum weights of classical static configurations such as dyons.Comment: Minor changes. References added. Paper accepted for publication in Phys.Rev.

Effective Classical Theory for Real-Time SU(N) Gauge Theories at High Temperature

We derive an effective classical theory for real-time SU($N$) gauge theories at high temperature. By separating off and integrating out quantum fluctuations we obtain a 3D classical path integral over the initial fields and conjugate momenta. The leading hard mode contribution is incorporated in the equations of motion for the classical fields. This yields the gauge invariant hard thermal loop (HTL) effective equation of motion. No gauge-variant terms are generated as in treatments with an intermediate momentum cut-off. Quantum corrections to classical correlation functions can be calculated perturbatively. The 4D renormalizability of the theory ensures that the 4D counterterms are sufficient to render the theory finite. The HTL contributions of the quantum fluctuations provide the counterterms for the linear divergences in the classical theory.Comment: 13 pages, 1 figure, title changed, discussion on the classical approximation include

Bounds and optimisation of orbital angular momentum bandwidths within parametric down-conversion systems

The measurement of high-dimensional entangled states of orbital angular momentum prepared by spontaneous parametric down-conversion can be considered in two separate stages: a generation stage and a detection stage. Given a certain number of generated modes, the number of measured modes is determined by the measurement apparatus. We derive a simple relationship between the generation and detection parameters and the number of measured entangled modes.Comment: 6 pages, 4 figure

Interaction of N solitons in the massive Thirring model and optical gap system: the Complex Toda Chain Model

Using the Karpman-Solov''ev quasiparticle approach for soliton-soliton interaction I show that the train propagation of N well separated solitons of the massive Thirring model is described by the complex Toda chain with N nodes. For the optical gap system a generalised (non-integrable) complex Toda chain is derived for description of the train propagation of well separated gap solitons. These results are in favor of the recently proposed conjecture of universality of the complex Toda chain.Comment: RevTex, 23 pages, no figures. Submitted to Physical Review

High-energy physics with particles carrying non-zero orbital angular momentum

Thanks to progress in optics in the past two decades, it is possible to create photons carrying well-defined non-zero orbital angular momentum (OAM). Boosting these photons into high-energy range preserving their OAM seems feasible. Intermediate energy electrons with OAM have also been produced recently. One can, therefore, view OAM as a new degree of freedom in high-energy collisions and ask what novel insights into particles' structure and interactions it can bring. Here we discuss generic features of scattering processes involving particles with OAM in the initial state. We show that they make it possible to perform a Fourier analysis of a plane wave cross section with respect to the azimuthal angles of the initial particles, and to probe the autocorrelation function of the amplitude, a quantity inaccessible in plane wave collisions.Comment: 7 pages, 1 figure, talk given at the workshop "30 years of strong interactions", Spa, Belgium, 6-8 April 201