Non-perturbative phenomena in jet modification

The interaction of a jet with the medium created in heavy-ion collisions is not yet fully understood from a QCD perspective. This is mainly due to the non-perturbative nature of this interaction which affects both transverse jet momentum broadening and jet quenching. We discuss how lattice simulations of Electrostatic QCD, can be matched to full, four dimensional QCD, to determine non-perturbative contributions to the momentum broadening kernel. We determine the momentum broadening kernel in impact parameter and momentum space and finally show how these results can be used in phenomenological calculations of in-medium splitting rates.

Uncertainty Relations in the Madelung Picture

Madelung showed how the complex Schrödinger equation can be rewritten in terms of two real equations, one for the phase and one for the amplitude of the complex wave function, where both equations are not independent of each other, but coupled. Although these equations formally look like classical hydrodynamic equations, they contain all the information about the quantum system. Concerning the quantum mechanical uncertainties of position and momentum, however, this is not so obvious at first sight. We show how these uncertainties are related to the phase and amplitude of the wave function in position and momentum space and, particularly, that the contribution from the phase essentially depends on the position–momentum correlations. This will be illustrated explicitly using generalized coherent states as examples.

Relativistic velocity addition from the geometry of momentum space

With the goal of developing didactic tools, we consider the geometrization of the addition of velocities in special relativity by using Minkowski diagrams in momentum space. For the case of collinear velocities, we describe two ruler-and-compass constructions that provide simple graphical solutions working with the mass-shell hyperbola in a 1+1-dimensional energy-momentum plane. In the spirit of dimensional scaffolding, we use those results to build a generalization in 1+2 dimensions for the case of non-collinear velocities, providing in particular a graphical illustration of how the velocity transverse to a boost changes while the momentum remains fixed. We supplement the discussion with a number of interactive applets that implement the diagrammatic constructions and constitute a visual tool that should be useful for students to improve their understanding of the subtleties of special relativity.

Celestial dual superconformal symmetry, MHV amplitudes and differential equations

Celestial and momentum space amplitudes for massless particles are related to each other by a change of basis provided by the Mellin transform. Therefore properties of celestial amplitudes have counterparts in momentum space amplitudes and vice versa. In this paper, we study the celestial avatar of dual superconformal symmetry of $$ \mathcal{N} $$ N = 4 Yang-Mills theory. We also analyze various differential equations known to be satisfied by celestial n-point tree-level MHV amplitudes and identify their momentum space origins.

Momentum-space entanglement in scalar field theory on fuzzy spheres

Quantum field theory defined on a noncommutative space is a useful toy model of quantum gravity and is known to have several intriguing properties, such as nonlocality and UV/IR mixing. They suggest novel types of correlation among the degrees of freedom of different energy scales. In this paper, we investigate such correlations by the use of entanglement entropy in the momentum space. We explicitly evaluate the entanglement entropy of scalar field theory on a fuzzy sphere and find that it exhibits different behaviors from that on the usual continuous sphere. We argue that these differences would originate in different characteristics; non-planar contributions and matrix regularizations. It is also found that the mutual information between the low and the high momentum modes shows different scaling behaviors when the effect of a cutoff becomes important.

Momentum-Space Decoherence of Distinguishable and Identical Particles in the Caldeira–Leggett Formalism

In this work, momentum-space decoherence using minimum and nonminimum-uncertainty-product (stretched) Gaussian wave packets in the framework of Caldeira–Leggett formalism and under the presence of a linear potential is studied. As a dimensionless measure of decoherence, purity, a quantity appearing in the definition of the linear entropy, is studied taking into account the role of the stretching parameter. Special emphasis is on the open dynamics of the well-known cat states and bosons and fermions compared to distinguishable particles. For the cat state, while the stretching parameter speeds up the decoherence, the external linear potential strength does not affect the decoherence time; only the interference pattern is shifted. Furthermore, the interference pattern is not observed for minimum-uncertainty-product-Gaussian wave packets in the momentum space. Concerning bosons and fermions, the question we have addressed is how the symmetry of the wave functions of indistinguishable particles is manifested in the decoherence process, which is understood here as the loss of being indistinguishable due to the gradual emergence of classical statistics with time. We have observed that the initial bunching and anti-bunching character of bosons and fermions, respectively, in the momentum space are not preserved as a function of the environmental parameters, temperature, and damping constant. However, fermionic distributions are slightly broader than the distinguishable ones and these similar to the bosonic distributions. This general behavior could be interpreted as a residual reminder of the symmetry of the wave functions in the momentum space for this open dynamics.