Vacuum birefringence in strong magnetic fields: (I) Photon polarization tensor with all the Landau levels

Photons propagating in strong magnetic fields are subject to a phenomenon called the “vacuum birefringence” where refractive indices of two physical modes both deviate from unity and are different from each other. We compute the vacuum polarization tensor of a photon in a static and homogeneous magnetic field by utilizing Schwinger’s proper-time method, and obtain a series representation as a result of double integrals analytically performed with respect to proper-time variables. The outcome is expressed in terms of an infinite sum of known functions which is plausibly interpreted as summation over all the Landau levels of fermions. Each contribution from infinitely many Landau levels yields a kinematical condition above which the contribution has an imaginary part. This indicates decay of a sufficiently energetic photon into a fermion–antifermion pair with corresponding Landau level indices. Since we do not resort to any approximation, our result is applicable to the calculation of refractive indices in the whole kinematical region of a photon momentum and in any magnitude of the external magnetic field.     

Fermionic determinant with a linear domain wall in 2+1 dimensions

We consider a Dirac field in 2+1 Euclidean dimensions, in the presence of a linear domain wall defect in its mass, and a constant electromagnetic field. We evaluate the exact fermionic determinant for the situation where the defect is assumed to be rectilinear, static, and the gauge field is minimally coupled to the fermions. We discuss the dependence of the result on the (unique) independent geometrical parameter of this system, namely, the relative orientation of the wall and the direction of the external field. We apply the result for the determinant to the evaluation of the vacuum energy.     

Exact two-loop vacuum polarization correction to the Lamb shift in hydrogenlike ions

We present a calculation scheme for the two-loop vacuum polarization correction of order to the Lamb shift of hydrogenlike high-Z atoms. The interaction with the external Coulomb field is taken into account to all orders in . By means of a modified potential approach the problem is reduced to the evaluation of effective one-loop vacuum polarization potentials. An expression for the energy shift is deduced within the framework of partial wave decomposition performing appropriate subtractions. Exact results for the two-loop vacuum polarization contribution to the Lamb shift of K- and L-shell electron states in hydrogenlike Lead and Uranium are presented. Received: 10 August 1997 / Revised: 31 October 1997 / Accepted: 18 November 1997     

Pseudospin and spin symmetries in 1+1 dimensions: The case of the Coulomb potential

The problem of fermions in 1+1 dimensions in the presence of a pseudoscalar Coulomb potential plus a mixing of vector and scalar Coulomb potentials which have equal or opposite signs is investigated. We explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. We show the relation between spin and pseudospin symmetries by means of charge-conjugation and γ⁵${\gamma }^5$ chiral transformations. The cases of pure pseudoscalar and mixed vector–scalar potentials, already analyzed in previous works, are obtained as particular cases. The results presented can be extended to 3+1 dimensions.     

The Schwinger model: A view from the temporal gauge

We present a new operator solution of the Schwinger model, i.e., of massless quantum electrodynamics in 1 + 1 dimensions in the temporal gauge A⁰ = 0. This gauge is well-suited for the treatment of static external charges. The energy functional reflects the immediate onset of pair creation of massless fermions. We show that every point charge is screened completely by a Yukawa-like polarization charge cloud of radius $\text{π}\text{e}$, e the coupling constant.     

Current algebra representation for the 3+1 dimensional Dirac-Yang-Mills theory

The structure of the current algebra representation in the state space of fermions in an external Yang-Mills field in 3+1 space-time dimensions is analyzed; the topology of the vector space is determined by a countable family of semi-definite inner products. We show that there is no hermitian non-trivial Hilbert space representation such that the energy is bounded from below. The structure of the Hilbert space for the quantized coupled Dirac-Yang-Mills system is discussed and the existence of the vacuum vector and the cancellation of commutator anomalies is described in terms of complex line bundles over infinite-dimensional Grassmannians.     

Photodetachment of H- in a static electric field

We derive a formula using closed-orbit theory for the photodetachment cross-section of H^- in the presence of a static electric field when there is an arbitrary angle θ_L between the laser polarization direction and the static electric field. This formula generalizes the previous result for laser polarization parallel to the static electric field, the effect of laser polarization direction appears as a factor cos²(θ_L) in the amplitude of the oscillation. A photodetachment cross-section formula valid above and below detachment threshold is proposed.     

Power-law spin correlations in a perturbed spin model on a honeycomb lattice

We consider the spin-1/2 model on the honeycomb lattice in the presence of a weak magnetic field hα < 1. Such a perturbation destroys the exact integrability of the model in terms of gapless fermions and static Z2 fluxes. We show that it results in the appearance of a long-range tail in the irreducible dynamic spin correlation function: ∝ h(z)(2)f(t,r), where f(t,r) ∝ [max(t,r)]-4 is proportional to the density polarization function of fermions.     

Static potential of a point charge in reduced QED<Subscript>3+1</Subscript>

The potential of a point source placed on a flat surface is calculated in the context of reduced QED₃₊₁, and the effective charge behavior is investigated with allowance for the polarization of vacuum. Both approximate analytical and numerical methods are used in calculations. It is established that the behavior of the examined potential at short and long distances from the source does not deviate significantly from the Coulomb behavior of vacuum massless and massive fermions. Other deviations of the results obtained from the well-known standard QED₃₊₁ and QED₂₊₁ data are also discussed.     

Vacuum polarization and color charge shielding in the external source problem of QCD2 with massless quarks

An approximate treatment of vacuum polarization in the external source problem of two-dimensional QCD with massless quarks is proposed. The static response to a static external source is determined with and without vacuum polarization. In the former case and if the gauge group is SU(2), a static solution is obtained only if the external source is essentially abelian. Complete shielding of the external charge sets in with the screening length equal to the inverse of the Schwinger mass. This shielding is enforced for special, self-screening external charges.     

Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD

The QCD vacuum condensates and various vacuum susceptibilities are all important parameters which characterize the nonperturbative properties of the QCD vacuum. In the QCD sum rules external field formula, various QCD vacuum susceptibilities play important roles in determining the properties of hadrons. In this paper, we review the recent progress in studies of vacuum susceptibilities together with their applications to the chiral phase transition of QCD. The results of the tensor, the vector, the axial–vector, the scalar, and the pseudo-scalar vacuum susceptibilities are shown in detail in the framework of Dyson–Schwinger equations.     

Vacuum Effects on Massive Spinor Fields: S 1× R 3 Topology

The aim of this work was to investigate the role played by an external field on the Casimir energy density for massive fermions under S ¹× R ³ topology. Both twisted- and untwisted-spin connections are considered and the calculation in a closed form is performed using an alternative approach based on the combination of the analytic regularization method and the Euler–Maclaurin summation formula. It is shown that no mass scale appears in the final result and, therefore, Casimir effect arises only from the boundary conditions and vacuum fluctuations induced by the coupling with the external field. PACS numbers: 11.10.Wx     

Microscopic Conductivity of Lattice Fermions at Equilibrium. Part II: Interacting Particles

We apply Lieb–Robinson bounds for multi-commutators we recently derived (Bru and de Siqueira Pedra, Lieb–Robinson bounds for multi-commutators and applications to response theory, 2015) to study the (possibly non-linear) response of interacting fermions at thermal equilibrium to perturbations of the external electromagnetic field. This analysis leads to an extension of the results for quasi-free fermions of (Bru et al. Commun Pure Appl Math 68(6):964–1013, 2015; Bru et al. J Math Phys 56:051901-1–051901-51, 2015) to fermion systems on the lattice with short-range interactions. More precisely, we investigate entropy production and charge transport properties of non-autonomous C*-dynamical systems associated with interacting lattice fermions within bounded static potentials and in presence of an electric field that is time and space dependent. We verify the 1st law of thermodynamics for the heat production of the system under consideration. In linear response theory, the latter is related with Ohm and Joule’s laws. These laws are proven here to hold at the microscopic scale, uniformly with respect to the size of the (microscopic) region where the electric field is applied. An important outcome is the extension of the notion of conductivity measures to interacting fermions.     

Evolution of coupled fermions under the influence of an external axial-vector field

The evolution of coupled fermions interacting with external axial-vector fields is described with the help of the classical field theory. We formulate the initial conditions problem for the system of two coupled fermions in (3+1)-dimensional space-time. This problem is solved using perturbation theory. We obtain in the explicit form the expressions for the leading and next to leading order terms in the expansion over the strength of the external fields. It is shown that in the relativistic limit the intensity of the fermion field coincides with the transition probability in the two neutrinos system interacting with moving and polarized matter. PACS 14.60.Pq; 03.50.-z     

Topological transitions in multi-band superconductors

The search for Majorana fermions has been concentrated in topological insulators or superconductors. In general, the existence of these modes requires the presence of spin–orbit interactions and of an external magnetic field. The former implies in having systems with broken inversion symmetry, while the latter breaks time reversal invariance. In a recent paper, we have shown that a two-band metal with an attractive inter-band interaction has non-trivial superconducting properties, if the k$k$-dependent hybridization is anti-symmetric in the wave-vector. This is the case, if the crystalline potential mixes states with different parities as for orbitals with angular momentum l$l$ and l+1$l+1$. In this paper we take into account the effect of an external magnetic field, not considered in the previous investigation, in a two-band metal and show how it modifies the topological properties of its superconducting state. We also discuss the conditions for the appearance of Majorana fermions in this system.     

Relativistic distribution function for particles with spin at local thermodynamical equilibrium

We present an extension of relativistic single-particle distribution function for weakly interacting particles at local thermodynamical equilibrium including spin degrees of freedom, for massive spin 1/2 particles. We infer, on the basis of the global equilibrium case, that at local thermodynamical equilibrium particles acquire a net polarization proportional to the vorticity of the inverse temperature four-vector field. The obtained formula for polarization also implies that a steady gradient of temperature entails a polarization orthogonal to particle momentum. The single-particle distribution function in momentum space extends the so-called Cooper–Frye formula to particles with spin 1/2 and allows us to predict their polarization in relativistic heavy ion collisions at the freeze-out.     

The index of scattering operators of Dirac equations

A new index formula of Atiyah Singer type for scattering operators is proved. The index corresponds to the vacuum polarization of the Fermion (on the Minkowski space) coupled to an external non abelian gauge field.     

Polarized light propagating in a magnetic field as a probe for millicharged fermions

Possible extensions of the standard model of particle physics suggest the existence of particles with small, unquantized electric charge. Photon-initiated pair production of millicharged fermions in a magnetic field would manifest itself as a vacuum magnetic (VM) dichroism. We show that laser polarization experiments searching for this effect yield, in the mass range below 0.1 eV, much stronger constraints on millicharged fermions than previous laboratory searches. VM birefringence due to virtual pair production gives a slightly better constraint for masses between 0.1 and a few eV. We comment on the possibility that the VM dichroism observed by PVLAS arises from pair production of such millicharged fermions rather than from single production of axionlike particles. Such a scenario can be confirmed or firmly excluded by a search for invisible decays of orthopositronium with a branching-fraction sensitivity of about 10(-9).