Nonrelativistic Quantum Electrodynamics Research Articles

QED corrections to the correlated relativistic energy: One-photon processes.

This work is a collection of initial calculations and formal considerations within the Salpeter-Sucher exact equal-time relativistic quantum electrodynamics framework. The calculations are carried out as preparation for the computation of pair, retardation, and radiative corrections to the relativistic energy of correlated two-spin-1/2-fermion systems. In this work, particular attention is paid to the retardation and the "one-loop" self-energy corrections, which are known to be among the largest corrections to the correlated relativistic energy. The theoretical development is supplemented with identifying formal connections to the non-relativistic quantum electrodynamics framework, which is based on a correlated but non-relativistic reference, as well as to the "1/Z approach," which is built on a relativistic but independent-particle zeroth order. The two complementary directions currently provide the theoretical framework for light atomic-molecular precision spectroscopy and heavy-atom phenomena. The present theoretical efforts pave the way for relativistic QED corrections to (explicitly) correlated relativistic computations.

Test for Non-Relativistic QED in decays of positronium atoms

Abstract. Positronium (Ps) is a bound state of electron and positron governed by electromagnetic interactions. Precise measurement of its decay rate is an important observational parameter to test theoretical predictions derived from Non-Relativistic Quantum Electrodynamics (NRQED). In this work, we present a new method for measuring the decay rate of Ps atoms, which has the potential to improve the precision and thus the description of the behavior of particles in bound states and to provide insight into the non-relativistic regime of QED.

Review of physics program at J-PET

The Jagiellonian - Positron Emission Tomograph (J-PET) is a multi purpose detector for tests of discrete symmetries and quantum entanglement of photons originating from the decay of positronium atoms. The research is per formed by measurement of angular correlations between photons from the an nihilations of the lightest leptonic bound system. The J-PET detector is the only device which enables determination of polarisation of photons from positronium annihilation together with estimation of positronium spin axis on the event-by-event basis. The novelty of the system is based on a usage of plastic scintil-lators as active detection material and trigger-less data acquisition system. The aim of two independent detection setups currently in use together with different annihilation chambers is to improve limits on C, CP and CPT symmetries and to search for the entanglement of photons originating from electron-positron annihilation. Additionally a precise measurement of ortho-positronium life time would allow to test of non-relativistic quantum electrodynamics and search for Mirror Matter.

On dilation analyticity and spatial exponential decay of atomic ground states in non-relativistic QED

We consider the ground state and the ground state energy of an atom with spinless electrons in the framework of non-relativistic quantum electrodynamics. We show that the ground state energy as well as the ground state depend analytically on the parameters of the group of dilations, the parameter of a group of spatial dependent phase changes, and on the minimal coupling constant. As a corollary we obtain spatial exponential decay of the ground state as well as of its dilation analytic extension. No infrared regularization is needed for the result. Our result is based on operator theoretic renormalization.

Understanding Polaritonic Chemistry from Ab Initio Quantum Electrodynamics.

In this review, we present the theoretical foundations and first-principles frameworks to describe quantum matter within quantum electrodynamics (QED) in the low-energy regime, with a focus on polaritonic chemistry. By starting from fundamental physical and mathematical principles, we first review in great detail ab initio nonrelativistic QED. The resulting Pauli-Fierz quantum field theory serves as a cornerstone for the development of (in principle exact but in practice) approximate computational methods such as quantum-electrodynamical density functional theory, QED coupled cluster, or cavity Born-Oppenheimer molecular dynamics. These methods treat light and matter on equal footing and, at the same time, have the same level of accuracy and reliability as established methods of computational chemistry and electronic structure theory. After an overview of the key ideas behind those ab initio QED methods, we highlight their benefits for understanding photon-induced changes of chemical properties and reactions. Based on results obtained by ab initio QED methods, we identify open theoretical questions and how a so far missing detailed understanding of polaritonic chemistry can be established. We finally give an outlook on future directions within polaritonic chemistry and first-principles QED.

Symmetries in non-relativistic quantum electrodynamics

We define symmetries in non-relativistic quantum electrodynamics, which have the physical interpretation of rotation, parity, and time reversal symmetry. We collect transformation properties related to these symmetries in Fock space representation as well as in the Schrödinger representation. As an application, we generalize and improve theorems about Kramers’ degeneracy in non-relativistic quantum electrodynamics.

Pre–Born-Oppenheimer Dirac-Coulomb-Breit computations for two-body systems

The sixteen-component, no-pair Dirac--Coulomb--Breit equation, derived from the Bethe--Salpeter equation, is solved in a variational procedure using Gaussian-type basis functions for the example of positronium, muonium, hydrogen atom, and muonic hydrogen. The $\alpha$ fine-structure-constant dependence of the variational energies, through fitting a function of $\alpha^n$ and $\alpha^n\text{ln}\alpha$ terms, shows excellent agreement with the relevant energy expressions of the (perturbative) non-relativistic QED framework, and thereby, establishes a solid reference for the development of a computational relativistic QED approach.

The -order Foldy–Wouthuysen Hamiltonian and relativistic corrections to Coulomb systems

The order nonrelativistic Hamiltonians of scalar, spinor and vector particles in the electromagnetic field are studied by applying the Douglas–Kroll–Hess approach. The result of the spin-1/2 spinor agrees with the Hamiltonian of the nonrelativistic quantum electrodynamics (Zhou et al 2019 Phys. Rev. A 100 012513). Additionally, the -order relativistic correction to few-electron Coulomb systems and the -order relativistic correction to two-electron Coulomb systems are derived. The singularities of Hamiltonians of Coulomb systems are separated out and cancelled. The regularized Hamiltonians up to -order for scalar and electron in the Coulomb field are obtained. Their numerical results agree with the relativistic theory. The regularized Hamiltonian, up to for few-electrons in the Coulomb field, is also derived.

About Non-relativistic Quantum Mechanics and Electromagnetism

We describe here the coherent formulation of electromagnetism in the non-relativistic quantum-mechanical many-body theory of interacting charged particles. We use the mathematical frame of the field theory and its quantization in the spirit of the quantum electrodynamics (QED). This is necessary because a manifold of misinterpretations emerged especially regarding the magnetic field and gauge invariance. The situation was determined by the historical development of quantum mechanics, starting from the Schrödinger equation of a single particle in the presence of given electromagnetic fields, followed by the many-body theories of many charged identical particles having just Coulomb interactions. Our approach to the non-relativistic QED emphasizes the role of the gauge-invariance and of the external fields. We develop further the approximation of this theory allowing a closed description of the interacting charged particles without photons. The resulting Hamiltonian coincides with the quantized version of the Darwin Hamiltonian containing besides the Coulomb also a current-current diamagnetic interaction. We show on some examples the importance of this extension of the many-body theory.

On the analogy between stochastic electrodynamics and nonrelativistic quantum electrodynamics

I expose nonrelativistic quantum electrodynamics in the Weyl–Wigner representation. Hence, I prove that an approximation to first order in Planck constant has a formal analogy with stochastic electrodynamics (SED), that is classical electrodynamics of charged particles immersed in a random radiation filling space. The analogy elucidates why SED agrees with quantum theory for particle Hamiltonians quadratic in coordinates and momenta, but fails otherwise.

The Electromagnetic Vacuum Field as an Essential Hidden Ingredient of the Quantum-Mechanical Ontology.

This paper provides elements in support of the random zero-point radiation field (zpf) as an essential ontological ingredient needed to explain distinctive properties of quantum-mechanical systems. We show that when an otherwise classical particle is connected to the zpf, a drastic, qualitative change in the dynamics takes place, leading eventually to the quantum dynamics. In particular, we demonstrate that in parallel with the evolution of the canonical variables of the particle into quantum operators satisfying the basic commutator x^,p^=iℏ, also the field canonical variables are transformed, giving rise to the corresponding creation and annihilation operators a^†,a^, satisfying a^,a^†=1. This allows for an explanation of quantum features such as quantum fluctuations, stationary states and transitions, and establishes a natural contact with (nonrelativistic) quantum electrodynamics.

Implications of gauge freedom for nonrelativistic quantum electrodynamics

Gauge freedom in quantum electrodynamics (QED) outside of textbook regimes is reviewed. It is emphasized that QED subsystems are defined relative to a choice of gauge. Each definition uses different gauge-invariant observables. This relativity is eliminated only if a sufficient number of Markovian and weak-coupling approximations are employed. All physical predictions are gauge invariant, including subsystem properties such as photon number and entanglement. However, subsystem properties naturally differ for different physical subsystems. Gauge ambiguities arise not because it is unclear how to obtain gauge-invariant predictions, but because it is not always clear which physical observables are the most operationally relevant. The gauge invariance of a prediction is necessary but not sufficient to ensure its operational relevance. It is shown that, in controlling which gauge invariant observables are used to define a material system, the choice of gauge affects the balance between the material system's localization and its electromagnetic dressing. Various implications of subsystem gauge relativity for deriving effective models, for describing time-dependent interactions, for photodetection theory, and for describing matter within a cavity are reviewed.

Transition from Lorentz to Fano Spectral Line Shapes in Nonrelativistic Quantum Electrodynamics

Transition from Lorentz to Fano Spectral Line Shapes in Nonrelativistic Quantum Electrodynamics

On Lieb–Robinson Bounds for the Bose–Hubbard Model

We consider the dynamics of the Bose-Hubbard model on general lattices and prove a Lieb-Robinson bound for observables whose supports are separated by an initially almost particle-free region. We further obtain a maximal velocity bound for particle transport through an initially empty region which also applies to long-range hopping. Our techniques originate in the proofs of maximal velocity bounds for Schr\"odinger operators and scattering theory in non-relativistic QED.

Thermal Fluctuations and Electromagnetic Noise Spectra in Quantum Statistical Mechanics

We derive the thermal noise spectrum of the longitudinal and transverse electric field operator of a given wave vector starting from the quantum-statistical definitions and relate it to the frequency and wave vector dependent complex conductivity in a homogeneous, isotropic system of electromagnetic interacting charged particles in the frame of the non-relativistic QED. No additional assumptions except the validity of linear response are used in the proof. The Nyquist formula for vanishing frequency, as well as the noise spectral density of Callen-Welton follow as byproduct. Furthermore we discuss also the noise of the photon occupation numbers.

Effective Hamiltonians in Nonrelativistic Quantum Electrodynamics

In this paper, we consider some second-order effective Hamiltonians describing the interaction of the quantum electromagnetic field with atoms or molecules in the nonrelativistic limit. Our procedure is valid only for off-energy-shell processes, specifically virtual processes such as those relevant for ground-state energy shifts and dispersion van der Waals and Casimir-Polder interactions, while on-energy-shell processes are excluded. These effective Hamiltonians allow for a considerable simplification of the calculation of radiative energy shifts, dispersion, and Casimir-Polder interactions, including in the presence of boundary conditions. They can also provide clear physical insights into the processes involved. We clarify that the form of the effective Hamiltonian depends on the field states considered, and consequently different expressions can be obtained, each of them with a well-defined range of validity and possible applications. We also apply our results to some specific cases, mainly the Lamb shift, the Casimir-Polder atom-surface interaction, and the dispersion interactions between atoms, molecules, or, in general, polarizable bodies.

Two-photon-exchange corrections to the g factor of Li-like ions

We report calculations of QED corrections to the $g$ factor of Li-like ions induced by the exchange of two virtual photons between the electrons. The calculations are performed within QED theory to all orders in the nuclear binding strength parameter $Z\alpha$, where $Z$ is the nuclear charge number and $\alpha$ is the fine-structure constant. In the region of low nuclear charges we compare results from three different methods: QED, relativistic many-body perturbation theory, and nonrelativistic QED. All three methods are shown to yield consistent results. With our calculations we improve the accuracy of the theoretical predictions of the $g$ factor of the ground state of Li-like carbon and oxygen by about an order of magnitude. Our theoretical results agree with those from previous calculations but differ by 3-4 standard deviations from the experimental results available for silicon and calcium.

Quantum Optical Aspects of High-Harmonic Generation

The interaction of electrons with strong laser fields is usually treated with semiclassical theory, where the laser is represented by an external field. There are analytic solutions for the free electron wave functions, which incorporate the interaction with the laser field exactly, but the joint effect of the atomic binding potential presents an obstacle for the analysis. Moreover, the radiation is a dynamical system, the number of photons changes during the interactions. Thus, it is legitimate to ask how can one treat the high order processes nonperturbatively, in such a way that the electron-atom interaction and the quantized nature of radiation be simultaneously taken into account? An analytic method is proposed to answer this question in the framework of nonrelativistic quantum electrodynamics. As an application, a quantum optical generalization of the strong-field Kramers-Heisenberg formula is derived for describing high-harmonic generation. Our formalism is suitable to analyse, among various quantal effects, the possible role of arbitrary photon statistics of the incoming field. The present paper is dedicated to the memory of Prof. Dr. Fritz Ehlotzky, who had significantly contributed to the theory of strong-field phenomena over many decades.

The Non-Relativistic Many-Body Quantum-Mechanical Hamiltonian with Diamagnetic Current-Current Interaction

We extend the standard solid-state quantum mechanical Hamiltonian containing only Coulomb interactions between the charged particles by inclusion of the (transverse) current-current diamagnetic interaction starting from the non-relativistic QED restricted to the states without photons and neglecting the retardation in the photon propagator. This derivation is supplemented with a derivation of an analogous result along the non-rigorous old classical Darwin-Landau-Lifshitz argumentation within the physical Coulomb gauge.

Gapped Goldstones at the cut-off scale: a non-relativistic EFT

At finite density, the spontaneous breakdown of an internal non-Abelian symmetry dictates, along with gapless modes, modes whose gap is fixed by the algebra and proportional to the chemical potential: the gapped Goldstones. Generically the gap of these states is comparable to that of other non-universal excitations or to the energy scale where the dynamics is strongly coupled. This makes it non-straightforward to derive a universal effective field theory (EFT) description realizing all the symmetries. Focusing on the illustrative example of a fully broken SU(2) group, we demonstrate that such an EFT can be constructed by carving out around the Goldstones, gapless and gapped, at small 3-momentum. The rules governing the EFT, where the gapless Goldstones are soft while the gapped ones are slow, are those of standard nonrelativistic EFTs, like for instance nonrelativistic QED. In particular, the EFT Lagrangian formally preserves gapped Goldstone number, and processes where such number is not conserved are described inclusively by allowing for imaginary parts in the Wilson coefficients. Thus, while the symmetry is manifestly realized in the EFT, unitarity is not. We comment on the application of our construction to the study of the large charge sector of conformal field theories with non-Abelian symmetries.