arXiv subjects

U. D. Jentschura

Publications and source records attributed to U. D. Jentschura.

At least 73 records · Page 4Linked to original sources

arXiv2014

Fine-Structure Constant for Gravitational and Scalar Interactions

Starting from the coupling of a relativistic quantum particle to the curved Schwarzschild space-time, we show that the Dirac--Schwarzschild problem has bound states and calculate their energies including relativistic corrections. Relativistic effects are shown to be suppressed by the gravitational fine-structure constant alpha_G = G m_1 m_2/(hbar c), where G is Newton's gravitational constant, c is the speed of light and m_1 and m_2 >> m_1 are the masses of the two particles. The kinetic corrections due to space-time curvature are shown to lift the familiar (n,j) degeneracy of the energy levels of the hydrogen atom. We supplement the discussion by a consideration of an attractive scalar potential, which, in the fully relativistic Dirac formalism, modifies the mass of the particle according to the replacement m -> m (1 - λ/r), where r is the radial coordinate. We conclude with a few comments regarding the (n,j) degeneracy of the energy levels, where n is the principal quantum number, and j is the total angular momentum, and illustrate the calculations by way of a numerical example.

gr-qc↗

arXiv2014

The Numerically Optimized Regulator and the Functional Renormalization Group

We aim to optimize the functional form of the compactly supported smooth (CSS) regulator within the functional renormalization group (RG), in the framework of bosonized two-dimensional Quantum Electrodynamics (QED_2) and of the three-dimensional O(N=1) scalar field theory in the local potential approximation (LPA). The principle of minimal sensitivity (PMS) is used for the optimization of the CSS regulator, recovering all the major types of regulators in appropriate limits. Within the investigated class of functional forms, a thorough investigation of the CSS regulator, optimized with two different normalizations within the PMS method, confirms that the functional form of a regulator first proposed by Litim is optimal within the LPA. However, Litim's exact form leads to a kink in the regulator function. A form of the CSS regulator, numerically close to Litim's limit while maintaining infinite differentiability, remains compatible with the gradient expansion to all orders. A smooth analytic behaviour of the regulator is ensured by a small, but finite value of the exponential fall-off parameter in the CSS regulator. Consequently, a compactly supported regulator, in a parameter regime close to Litim's optimized form, but regularized with an exponential factor, appears to have favorable properties and could be used to address the scheme dependence of the functional renormalization group, at least within the the approximations employed in the studies reported here.

hep-th↗

arXiv2014

Neutrino Helicity Reversal and Fundamental Symmetries

A rather elusive helicity reversal occurs in a gedanken experiment in which a massive left-handed Dirac neutrino, traveling at a velocity u < c, is overtaken on a highway by a speeding vehicle (traveling at velocity v with u < v < c). Namely, after passing the neutrino, looking back, one would see a right-handed neutrino (which has never been observed in nature). The Lorentz-invariant mass of the right-handed neutrino is still the same as before the passing. The gedanken experiment thus implies the existence of right-handed, light neutrinos, which are not completely sterile. Furthermore, overtaking a bunch of massive right-handed Dirac neutrinos leads to gradual de-sterilization. We discuss the helicity reversal and the concomitant sterilization and de-sterilization mechanisms by way of an illustrative example calculation, with a special emphasis on massive Dirac and Majorana neutrinos. We contrast the formalism with a modified Dirac neutrino described by a Dirac equation with a pseudoscalar mass term proportional to the fifth current.

hep-ph↗

arXiv2014

Light Sea Fermions in Electron-Proton and Muon-Proton Interactions

The proton radius conundrum [R. Pohl et al., Nature vol.466, p.213 (2010) and A. Antognini et al., Science vol.339, p.417 (2013)] highlights the need to revisit any conceivable sources of electron-muon nonuniversality in lepton-proton interactions within the Standard Model. Superficially, a number of perturbative processes could appear to lead to such a nonunversality. One of these is a coupling of the scattered electron into an electronic as opposed to a muonic vacuum polarization loop in the photon exchange of two valence quarks, which is present only for electron projectiles as opposed to muon projectiles. However, we can show that this effect actually is part of the radiative correction to the proton's polarizability contribution to the Lamb shift, equivalent to a radiative correction to double scattering. We conclude that any conceivable genuine nonuniversality must be connected with a nonperturbative feature of the proton's structure, e.g., with the possible presence of light sea fermions as constituent components of the proton. If we assume an average of roughly 0.7*10^(-7) light sea positrons per valence quark, then we can show that virtual electron-positron annihiliation processes lead to an extra term in the electron-proton versus muon-proton interaction, which has the right sign and magnitude to explain the proton radius discrepancy.

physics.atom-ph↗

arXiv2014

From First Principles of QED to an Application: Hyperfine Structure of P States of Muonic Hydrogen

The purpose of this article is twofold. First, we attempt to give a brief overview of the different application areas of quantum electrodynamics (QED). These include fundamental physics (prediction of atomic energy levels), where the atom may be exposed to additional external fields (hyperfine splitting and g factor). We also mention QED processes in highly intense laser fields, and more applied areas like Casimir and Casimir--Polder interactions. Both the unifying aspects as well as the differences in the the theoretical treatment required by these application areas (such as the treatment of infinities) are highlighted. Second, we discuss an application of the formalism in the fundamentally interesting area of the prediction of energy levels, namely, the hyperfine structure of P states of muonic hydrogen.

physics.atom-ph↗

arXiv2013

Weighing the Neutrino

We investigate the potential of short-baseline experiments in order to measure the dispersion relation of the (muon) neutrino, with a prospect of eventually measuring the neutrino mass. As a byproduct, the experiment would help to constrain parameters of Lorentz-violating effects in the neutrino sector. The potential of a high-flux laser-accelerated proton beam (e.g., at the upcoming ELI facility), incident on a thick target composed of a light element to produce pions, with a subsequent decay to muons and muon-neutrinos, is discussed. We find a possibility for a muon neutrino mass measurement of unprecedented accuracy.

hep-ph↗

arXiv2013

Foldy-Wouthuysen Transformation, Scalar Potentials and Gravity

We show that care is required in formulating the nonrelativistic limit of generalized Dirac Hamiltonians which describe particles and antiparticles interacting with static electric and/or gravitational fields. The Dirac-Coulomb and the Dirac-Schwarzschild Hamiltonians, and the corrections to the Dirac equation in a non-inertial frame, according to general relativity, are used as example cases in order to investigate the unitarity of the standard and "chiral" approaches to the Foldy-Wouthuysen transformation, and spurious parity-breaking terms. Indeed, we find that parity-violating terms can be generated by unitary pseudo-scalar transformations ("chiral" Foldy-Wouthuysen transformations). Despite their interesting algebraic properties, we find that "chiral" Foldy-Wouthuysen transformations change fundamental symmetry properties of the Hamiltonian and do not conserve the physical interpretation of the operators. Supplementing the discussion, we calculate the leading terms in the Foldy-Wouthuysen transformation of the Dirac Hamiltonian with a scalar potential (of the (1/r)-form and of the confining radially symmetric linear form), and obtain compact expressions for the leading higher-order corrections to the Dirac Hamiltonian in a non-inertial rotating reference frame "Mashhoon term").

gr-qc↗

arXiv2013

Thermal Correction to the Molar Polarizability of a Boltzmann Gas

Metrology in atomic physics has been crucial for a number of advanced determinations of fundamental constants. In addition to very precise frequency measurements, the molar polarizability of an atomic gas has recently also been measured very accurately. Part of the motivation for the measurements is due to ongoing efforts to redefine the International System of Units (SI) for which an accurate value of the Boltzmann constant is needed. Here, we calculate the dominant shift of the molar polarizability in an atomic gas due to thermal effects. It is given by the relativistic correction to the dipole interaction, which emerges when the probing electric field is Lorenz transformed into the rest frame of the atoms that undergo thermal motion. While this effect is small when compared to currently available experimental accuracy, the relativistic correction to the dipole interaction is much larger than the thermal shift of the polarizability induced by blackbody radiation.

physics.atom-ph↗

arXiv2013

Generalized Householder Transformations for the Complex Symmetric Eigenvalue Problem

We present an intuitive and scalable algorithm for the diagonalization of complex symmetric matrices, which arise from the projection of pseudo--Hermitian and complex scaled Hamiltonians onto a suitable basis set of "trial" states. The algorithm diagonalizes complex and symmetric (non--Hermitian) matrices and is easily implemented in modern computer languages. It is based on generalized Householder transformations and relies on iterative similarity transformations T -> T' = Q^T T Q, where Q is a complex and orthogonal, but not unitary, matrix, i.e, Q^T equals Q^(-1) but Q^+ is different from Q^(-1). We present numerical reference data to support the scalability of the algorithm. We construct the generalized Householder transformations from the notion that the conserved scalar product of eigenstates Psi_n and Psi_m of a pseudo-Hermitian quantum mechanical Hamiltonian can be reformulated in terms of the generalized indefinite inner product [integral of the product Psi_n(x,t) Psi_m(x,t) over dx], where the integrand is locally defined, and complex conjugation is avoided. A few example calculations are described which illustrate the physical origin of the ideas used in the construction of the algorithm.

quant-ph↗

arXiv2013

Nonrelativistic Limit of the Dirac-Schwarzschild Hamiltonian: Gravitational Zitterbewegung and Gravitational Spin-Orbit Coupling

We investigate the nonrelativistic limit of the gravitationally coupled Dirac Equation via a Foldy-Wouthuysen transformation. The relativistic correction terms have immediate and obvious physical interpretations in terms of a gravitational zitterbewegung, and a gravitational spin-orbit coupling. We find no direct coupling of the spin vector to the gravitational force, which would otherwise violate parity. The particle-antiparticle symmetry described recently by one of us in [Phys.Rev.A 87 (2013) 032101] is verified on the level of the perturbative corrections accessed by the Foldy-Wouthuysen transformation. The gravitational corrections to the electromagnetic transition current are calculated.

gr-qc↗

arXiv2013

Gravitationally Coupled Dirac Equation for Antimatter

The coupling of antimatter to gravity is of general interest because of conceivable cosmological consequences ("surprises") related to dark energy and the cosmological constant. Here, we revisit the derivation of the gravitationally coupled Dirac equation and find that the prefactor of a result given previously in [D.R. Brill and J.A. Wheeler, Rev. Mod. Phys., vol. 29, p. 465 (1957)] for the affine connection matrix is in need of a correction. We also discuss the conversion the curved-space Dirac equation from East-Coast to West-Coast conventions, in order to bring the gravitationally coupled Dirac equation to a form where it can easily be unified with the electromagnetic coupling as it is commonly used in modern particle physics calculations. The Dirac equation describes anti-particles as negative-energy states. We find a symmetry of the gravitationally coupled Dirac equation, which connects particle and antiparticle solutions for a general space-time metric of the Schwarzschild type and implies that particles and antiparticles experience the same coupling to the gravitational field, including all relativistic quantum corrections of motion. Our results demonstrate the consistency of quantum mechanics with general relativity and imply that a conceivable difference of gravitational interaction of hydrogen and antihydrogen should directly be attributed to a a "fifth force" ("quintessence").

hep-ph↗

arXiv2012

From Generalized Dirac Equations to a Candidate for Dark Energy

We consider extensions of the Dirac equation with mass terms m1+i*gamma5*m2 and i*m_1+gamma*m2. The corresponding Hamiltonians are Hermitian and pseudo-Hermitian ("gamma5 Hermitian"), respectively. The fundamental spinor solutions for all generalized Dirac equations are found in the helicity basis and brought into concise analytic form. We postulate that the time-ordered product of field operators should yield the Feynman propagator (i*epsilon prescription), and we also postulate that the tardyonic as well as tachyonic Dirac equations should have a smooth massless limit. These postulates lead to sum rules that connect the form of the fundamental field anticommutators with the tensor sums of the fundamental plane-wave eigenspinors and the projectors over positive-energy and negative-energy states. In the massless case, the sum rules are fulfilled by two egregiously simple, distinguished functional forms. The first sum rule remains valid in the case of a tardyonic theory and leads to the canonical massive Dirac field. The second sum rule is valid for a tachyonic mass term and leads to a natural suppression of the right-handed helicity states for tachyonic particles, and left-handed helicity states for tachyonic spin-1/2 antiparticles. When applied to neutrinos, the theory contains a free tachyonic mass parameter. Tachyons are known to be repulsed by gravity. We discuss a possible role of a tachyonic neutrino as a contribution to the accelerated expansion of the Universe ("dark energy").

hep-ph↗

arXiv2012

Quantum dynamics in atomic-fountain experiments for measuring the electric dipole moment of the electron with improved sensitivity

An improved measurement of the electron electric dipole moment (EDM) appears feasible using ground-state alkali atoms in an atomic fountain in which a strong electric field, which couples to a conceivable electron dipole moment (EDM), is applied perpendicular to the fountain axis. In a practical fountain, the ratio of the atomic tensor Stark shift to the Zeeman shift is a facto mu~100. We expand the complete time evolution operator in inverse powers of this ratio; complete results are presented for atoms of total spin F=3, 4, and 5. For a specific set of entangled hyperfine sublevels (coherent states), potential systematic errors enter only as even powers of 1/mu, making the expansion rapidly convergent. The remaining EDM mimicking effects are further suppressed in a proposed double-differential setup, where the final state is interrogated in a differential laser configuration, and the direction of the strong electric field also is inverted. Estimates of the signal available at existing accelerator facilities indicate that the proposed apparatus offers the potential for a drastic improvement in EDM limits over existing measurements, and for constraining the parameter space of supersymmetric (SUSY) extensions of the Standard Model.

physics.atom-ph↗

arXiv2012

Dirac Hamiltonian with Imaginary Mass and Induced Helicity-Dependence by Indefinite Metric

It is of general theoretical interest to investigate the properties of superluminal matter wave equations for spin one-half particles. One can either enforce superluminal propagation by an explicit substitution of the real mass term for an imaginary mass, or one can use a matrix representation of the imaginary unit that multiplies the mass term. The latter leads to the tachyonic Dirac equation, while the equation obtained by the substitution m->i*m in the Dirac equation is naturally referred to as the imaginary-mass Dirac equation. Both the tachyonic as well as the imaginary-mass Dirac Hamiltonians commute with the helicity operator. Both Hamiltonians are pseudo-Hermitian and also possess additional modified pseudo-Hermitian properties, leading to constraints on the resonance eigenvalues. Here, by an explicit calculation, we show that specific sum rules over the spectrum hold for the wave functions corresponding to the well-defined real energy eigenvalues and complex resonance and anti-resonance energies. In the quantized imaginary-mass Dirac field, one-particle states of right-handed helicity acquire a negative norm ("indefinite metric") and can be excluded from the physical spectrum by a Gupta--Bleuler type condition.

hep-ph↗

arXiv2012

Quantum Electrodynamic Corrections to the g Factor of Helium P States

The Lande g factor describes the response of an atomic energy level to an external perturbation by a uniform and constant magnetic field. In the case of many-electron systems, the leading term is given by the interaction mu_B*(L+2S.B), where L and S are the orbital and spin angular momentum operators, respectively, summed over all electrons. For helium, a long-standing experimental-theoretical discrepancy for P states motivates a reevaluation of the higher-order terms which follow from relativistic quantum theory and quantum electrodynamics (QED). The tensor structure of relativistic corrections involves scalar, vector, and symmetric and anti-symmetric tensor components. We perform a tensorial reduction of these operators in a Cartesian basis, using an approach which allows us to separate the internal atomic from the external degrees of freedom (magnetic field) right from the start of the calculation. The evaluation proceeds in a Cartesian basis of helium eigenstates, using a weighted sum over the magnetic projections. For the relativistic corrections, this leads to a verification of previous results obtained using the Wigner-Eckhart theorem. The same method, applied to the radiative correction (Bethe logarithm term) leads to a spin-dependent correction which is different for singlet versus triplet P states. Theoretical predictions are given for singlet and triplet 2P and triplet 3P states and compared to experimental results where available.

physics.atom-ph↗

arXiv2012

Enhancement of Blackbody Friction due to the Finite Lifetime of Atomic Levels

The thermal friction force acting on an atom moving relative to a thermal photon bath is known to be proportional to an integral over the imaginary part of the frequency-dependent atomic (dipole) polarizability. Using a numerical approach, we find that blackbody friction on atoms either in dilute environments or in hot ovens is larger than previously thought by orders of magnitude. This enhancement is due to far off-resonant driving of transitions by low-frequency thermal radiation. At typical temperatures, the blackbody radiation maximum lies far below the atomic transition wavelengths. Surprisingly, due to the finite lifetime of atomic levels, which gives rise to Lorentzian line profiles, far off-resonant excitation leads to the dominant contribution to the blackbody friction.

physics.atom-ph↗

arXiv2012

Triple Compton effect: A photon splitting into three upon collision with a free electron

The process in which a photon splits into three after the collision with a free electron (triple Compton effect) is the most basic process for the generation of a high-energy multi-particle entangled state composed out of elementary quanta. The cross section of the process is evaluated in two experimentally realizable situations, one employing gamma photons and stationary electrons, and the other using keV photons and GeV electrons of an x-ray free electron laser. For the first case, our calculation is in agreement with the only available measurement of the differential cross section for the process under study. Our estimates indicate that the process should be readily measurable also in the second case. We quantify the polarization entanglement in the final state by a recently proposed multi-particle entanglement measure.

quant-ph↗

arXiv2012

Tachyonic Field Theory and Neutrino Mass Running

In this paper three things are done. (i) We investigate the analogues of Cerenkov radiation for the decay of a superluminal neutrino and calculate the Cerenkov angles for the emission of a photon through a W loop, and for a collinear electron-positron pair, assuming the tachyonic dispersion relation for the superluminal neutrino. The decay rate of a freely propagating neutrino is found to depend on the shape of the assumed dispersion relation, and is found to decrease with decreasing tachyonic mass of the neutrino. (ii) We discuss a few properties of the tachyonic Dirac equation (symmetries and plane-wave solutions), which may be relevant for the description of superluminal neutrinos seen by the OPERA experiment, and discuss the calculation of the tachyonic propagator. (iii) In the absence of a commonly accepted tachyonic field theory, and in view of an apparent "running" of the observed neutrino mass with the energy, we write down a model Lagrangian, which describes a Yukawa-type interaction of a neutrino coupling to a scalar background field via a scalar-minus-pseudoscalar interaction. This constitutes an extension of the standard model. If the interaction is strong, then it leads to a substantial renormalization-group "running" of the neutrino mass and could potentially explain the experimental observations.

physics.gen-ph↗