Gamow state vectors as functionals over subspaces of the nuclear space

Exponentially decaying ‘Gamow state’ vectors are obtained from S-matrix poles in the lower half of the second sheet and are defined as functionals over a subspace of the nuclear space Φ. Exponentially growing ‘Gamow state’ vectors are obtained from S-matrix poles in the upper half of the second sheet and are defined as functionals over another subspace of Φ. On functionals over these two subspaces the dynamical group of time development splits into two semigroups.     

Holographic Schwinger effect

We study tunneling pair creation of W bosons by an external electric field on the Coulomb branch of N=4 supersymmetric Yang-Mills theory. We use AdS/CFT holography to find a generalization of Schwinger's formula for the pair production rate to the strong coupling, planar limit which includes the exchange of virtual massless particles to all orders. We find that the pair creation formula has an upper critical electric field beyond which the process is no longer exponentially suppressed. The value of the critical field is identical to that which occurs in the Born-Infeld action of probe D3-branes in the AdS(5)×S(5) background, where AdS(5) and S(5) are 5-dimensional anti-de Sitter space and the 5-sphere, respectively.     

The Schwinger terms and the gravitational anomaly

A new type of Schwinger term appearing in commutators of energy-momentum tensors is shown for chiral fermions in two-dimensional flat Minkowski space-time. Preserving the Jacobi identity, the Schwinger terms which correspond to gravitational anomalies appear in places different from the conformal anomaly. A relation to Faddeev's argument is also discussed.     

The Schwinger Model on the Torus

The classical and quantum aspects of the Schwinger model on the torus are considered. First we find explicitly all zero modes of the Dirac operator in the topological sectors with nontrivial Chern index and its spectrum. In the second part we determine the regularized effective action and discuss the propagators related to it. Finally we calculated the gauge invariant averages of the fermion bilinears and correlation functions of currents and densities. We show that in the infinite volume limit the well-known result for the chiral condensate can be obtained and the clustering property can be established. We also briefly discuss some new results on the Schwinger model which have been obtained recently.     

R~4 corrections to holographic Schwinger effect

We consider R4 corrections to the holographic Schwinger effect in an AdS black hole background and a confining D3-brane background. The potential between a test particle pair are performed for both backgrounds. We find there is no potential barrier in the critical electric field, which means that the system becomes catastrophically unstable. It is shown that for both backgrounds, increasing the inverse 't Hooft coupling parameter 1/λ enhances the Schwinger effect. We also discuss the possible relation between the Schwinger effect and the viscosity-entropy ratioη/s in strong coupling.     

The Schwinger effect and possibilities for its observation using optical and X-ray lasers

The probability W of e ⁺ e ^? pair production from a vacuum in an intense variable electric field generated with powerful optical or X-ray lasers is calculated. Two characteristic ranges are considered: γ ? 1 and γ ? 1, where γ is the adiabaticity parameter. The probability W is shown to increase sharply with γ (at a fixed field strength F). The dependence of W and the momentum spectrum of electrons and positrons on the laser pulse shape is discussed in detail. Numerical calculations were performed for a laser pulse with a Gaussian envelope and for some pulsed fields.     

The Young Julian Schwinger. III. Schwinger Goes to Berkeley

In this series of articles the early life and work of the young Julian Schwinger is explored. After a brilliant beginning at Columbia University, where he received his Ph.D., Schwinger went to work with J. Robert Oppenheimer in Berkeley. His stay, work, and interactions with Oppenheimer are discussed.     

On the normalization of Gamow functions

It is proved that the definitions of the norm given by Berggren and Romo are identical. Regularization in ref. ¹) with any convergence factor of the form

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leads to the same result. The existence of the norm is also established for the proton. The norm for neutrons is analytically given.     

Holographic Schwinger effect in spinning black hole backgrounds

We perform a potential analysis for the holographic Schwinger effect in spinning Myers-Perry black holes.We compute the potential between the produced pair by evaluating the classical action of a string attached on a probe D3-brane at an intermediate position in the AdS bulk.We find that increasing the angular momentum reduces the potential barrier,thus enhancing the Schwinger effect,consistent with previous findings obtained via the local Lorentz transformation.In particular,these effects are m...     

Gamow Vectors and Time Asymmetry

We prove that Gamow vectors are important toolsin the quantum theory of irreversibility. We use themathematical formalism of rigged Hilbert spaces. Wediscuss some spectral formulas that include Gamow vectors as well as some results concerningGamow vectors. The role of the time-reversal operator isstudied. The formalism can be applied to formulate asense of irreversibility in cosmology.     

Particle self-bunching in the Schwinger effect in spacetime-dependent electric fields

Nonperturbative electron-positron pair creation (the Schwinger effect) is studied based on the Dirac-Heisenberg-Wigner formalism in 1+1 dimensions. An ab initio calculation of the Schwinger effect in the presence of a simple space- and time-dependent electric field pulse is performed for the first time, allowing for the calculation of the time evolution of observable quantities such as the charge density, the particle number density or the total number of created particles. We predict a new self-bunching effect of charges in phase space due to the spatial and temporal structure of the pulse.     

Effective Field Theory and the Gamow Shell Model

We combine halo/cluster effective field theory (H/CEFT) and the Gamow shell model (GSM) to describe the 0⁺ ground state of ⁶He as a three-body halo system. We use two-body interactions for the neutron-alpha particle and two-neutron pairs obtained from H/CEFT at leading order, with parameters determined from scattering in the p_3/2 and s₀ channels, respectively. The three-body dynamics of the system is solved using the GSM formalism, where the continuum states are incorporated in the shell model valence space. We find that in the absence of three-body forces the system collapses, since the binding energy of the ground state diverges as cutoffs are increased. We show that addition at leading order of a three-body force with a single parameter is sufficient for proper renormalization and to fix the binding energy to its experimental value.     

The consistency of the Chiral Schwinger Model

The Chiral Schwinger Model is solved using path integral methods. It is shown that the theory has a consistent solution despite the presence of a chiral anomaly if a suitable regularization procedure is used.     

Dynamical Schwinger effect and high-intensity lasers. Realising nonperturbative QED

We consider the possibility of experimental verification of vacuum e⁺e^- pair creation at the focus of two counter-propagating optical laser beams with intensities 10²⁰–10²² W/cm²^{22}~{\rm W/cm}^2, achievable with present-day petawatt lasers, and approaching the Schwinger limit: 10²⁹ W/cm²^{29}~{\rm W/cm}^2 to be reached at ELI. Our approach is based on the collisionless kinetic equation for the evolution of the e⁺ and e^- distribution functions governed by a non-Markovian source term for pair production. As possible experimental signals of vacuum pair production we consider e⁺e^- annihilation into γ-pairs and the refraction of a high-frequency probe laser beam by the produced e⁺e^- plasma. We discuss the dependence of the dynamical pair production process on laser wavelength, with special emphasis on applications in the X-ray domain (X-FEL), as well as the prospects for μ⁺μ^- and π⁺π^- pair creation at high-intensity lasers. We investigate perspectives for using high-intensity lasers as “boosters” of ion beams in the few-GeV per nucleon range, which is relevant, e.g., to the exploration of the QCD phase transition in laboratory experiments.     

The Young Julian Schwinger. II. Julian Schwinger at Columbia University

In this series of articles the life and work of the young Julian Schwinger are explored. In this second article in the series, Schwinger's work at Columbia University, up to the completion of his doctorate and a little after, is discussed. Schwinger soon matured into a brilliant theoretical physicist.     

The gauge transformations of the Schwinger model

We determine the group of implementable local gauge transformations of massless quantum electrodynamics in two space-time dimensions in the covariant Landau gauge. It splits into an infinite discrete set of disjoint classes. The unitary operators representing the implementable gauge transformations are constructed explicitly. A subset of these operators does not reduce to multiples of the identity in the physical Hilbert space constructed according to the usual rules. The disappearance of the fermionic degrees of freedom is related to this fact. Combined with the properties of the global chiral transformations, it provides a better understanding of the model's vacuum structure.     

The Schwinger model and its axial anomaly

The Schwinger model (quantum electrodynamics with massless fermions in one spatial dimension) is solved, supposing that space is a circle. This clarifies aspects of the usual version of the model, where space is a line, without changing the physics. The Hamiltonian formalism is used. On a circle, an abelian gauge field has one physical degree of freedom, and the gauge covariant Dirac operator, which couples the fermions to this degree of freedom, exhibits spectral flow. The relationship between the spectral flow and the axial anomaly is explained. Some variants of the Schwinger model are also discussed.