Mechanical form factors and densities of non-relativistic fermions

Abstract

The hadron physics community has been actively debating the interpretation of so-called mechanical properties of hadrons. Non-relativistic quantum-mechanical systems like the hydrogen atom have been appealed to in these debates as analogies. Since such appeals are likely to continue, it is important to have Galilei-covariant expressions for matrix elements of the energy-momentum tensor. In this work, I obtain Galilei-covariant breakdowns of such matrix elements into mechanical form factors, with a special focus on spin-half states. I additionally study the spatial densities associated with these form factors, using the pilot wave interpretation to guide their breakdown into contributions from internal structure and from quantum-mechanical effects such as wave packet dispersion. For completeness, I also obtain non-relativistic Breit frame densities.

26 pages, version accepted for publication

References in corpus (31)

• Defining the Proton Radius: a Unified Treatment
• Gluon gravitational structure of hadrons of different spin
• Gravitational form factors of the proton from lattice QCD
• Revisiting the proton mass decomposition
• Forces within hadrons on the light front
• Ambiguities in the definition of local spatial densities in light hadrons
• Forces inside the nucleon on the light front from 3D Breit frame force distributions: Abel tomography case
• The energy-momentum tensor of spin-1 hadrons: formalism
• Unified formalism for electromagnetic and gravitational probes: densities
• Effects of long-range forces on the D-term and the energy-momentum structure
• Momentum-Current Gravitational Multipoles of Hadrons
• The gravitational form factor D(t) of the electron
• 2D energy-momentum tensor distributions of nucleon in a large-$N_c$ quark model from ultra-relativistic to non-relativistic limit
• Gravitational form factors and mechanical properties of a quark at one loop in light-front Hamiltonian QCD
• Pressure inside hadrons: criticism, conjectures, and all that
• Spinors in Polar Form
• The gravitational form factors of the electron in quantum electrodynamics
• Forces inside a strongly-coupled scalar nucleon
• Galilei invariant theories. I. Constructions of indecomposable finite-dimensional representations of the homogeneous Galilei group: directly and via contractions
• Minkowski's lost legacy and hadron electromagnetism
• Dirac Theory in Hydrodynamic Form
• Spatial densities of the photon on the light front
• de Broglie-Bohm formulation of Dirac fields
• Quantum stresses in the hydrogen atom
• Gravitational form factor $D$ of charmonium from shear stress
• Relativistic energy-momentum tensor distributions in a polarized nucleon
• The de Sitter group and its representations: a window on the notion of de Sitterian elementary systems
• Energy momentum tensor on and off the light cone: exposition with scalar Yukawa theory
• One-loop electron mass and QED trace anomaly
• An 8-dimensional realization of the Clifford algebra in the 5-dimensional Galilean space-time
• Visualization of internal forces inside the proton in a classical relativistic model

Cited by in corpus (3)

• Quantum stress and torsion distributions in the deuteron
• Energy-momentum tensor form factor D(t) of proton and neutron
• Transverse energy-momentum tensor distributions in polarized nucleons