Square-Root Operator Quantization and Nonlocality: A Review

A square-root-operator formalism is developed for quantum systems described with nonrelativistic and relativistic equations of motion. Spectral representation for Green's functions are designed for particles with spin 0, with the implication of its generalization to other spin values. Nonlocal operators suggest that a duality exists between physical particles and dual partners, which are tachyonic mathematical particles. It is shown that nonlocal operators result naturally from square-root operators, with the implication that microcausality holds only asymptotically. Applications help enlighten the formalism in order to envisage realistic situations with Schrödinger equations, Higgs fields, vacuum fluctuations, extra-dimensional methods in the potential theory, and electromagnetic interactions of extended charges and their consequences. It turns out that the innermost structure of these extended charges is associated with nonlocal photon propagators. It is shown that the propagator arisen from the charged torus potential consists of two different parts: a nonlocal photon propagator and a propagator of neutrino-like particles, which is described by square-root-operator equation. We examine the potential of the torus and its propagator as the appearance of superfields in terms of the photon and the massless fermion (photino).     

What can be tested in quantum electrodynamics?

In this paper we examine the theoretical foundations underlying the testing of quantum electrodynamics. We show that for the photon propagator (together with the contiguous vertices) it is not necessary to introduce ad hoc modifications in sufficiently accurate scattering experiments. Energy, momentum transfer, and accuracy determine the tested length in a model-independent way. The situation is quite different with the electron propagator. If gauge invariance is taken for granted, the electron propagator cannot be tested with processes where diagrams with open electron lines are important in the lowest order of perturbation theory. These processes can only give limits for anomalous moment and multiphoton parts of the vertices. On the other hand, processes with closed electron loops (vacuum polarization), such as photon-photon and Delbrück scattering, as well as photon splitting or corresponding low-energy, high-precision experiments can give limits also for the electron propagator. But in these cases only less accurate limits can be obtained, which depend on the modification model. Hence testing of the electron propagator, i.e., roughly speaking, the Dirac equation, is much more difficult than testing of the photon propagator, i.e, Maxwell's equations.Dedicated to the memory of Prof. Wolfgang Yourgrau (1908–1979).Presented at the 1975 International Symposium on Lepton and Photon Interactions at High Energies, Stanford University, Stanford, California.     

Equilibrium and non-equilibrium hard thermal loop resummation in the real time formalism

We investigate the use of the hard thermal loop (HTL) resummation technique in non-equilibrium field theory. We use the Keldysh representation of the real time formalism (RTF). We derive the HTL photon self energy and the resummed photon propagator. We show that no pinch singularities appear in the non-equilibrium HTL effective propagator. We discuss a possible regularization mechanism for these singularities at higher orders. As an example of the application of the HTL resummation method within the RTF we discuss the damping rate of a hard electron. Received: 9 April 1998 / Published online: 21 September 1998     

Vacuum Polarisation Effects in the Lorentz Violating Electrodynamics

In this work we reconsider the one loop calculation for the vacuum polarisation tensor in the Lorentz violating quantum electrodynamics. The electron propagator is “dressed” by a Lorentz breaking extra term in the fermion Lagrangian density. We check gauge invariance and use the Schwinger–Dyson equation to discuss the full photon propagator. After a discussion on a possible photon mass shift, we show how a finite quantum correction can be chosen in a unique way in order to ensure—in the spirit of spontaneously broken theories—the standard normalisation conditions for the vacuum polarisation tensor. Then we comment on possible observable physical consequences on the Lamb-shift.     

Photon propagator,monopoles, and the thermal phase transition in three dimensional compact QED

We investigate the gauge boson propagator in the three dimensional compact Abelian gauge model in the Landau gauge at finite temperature. The presence of the monopole plasma in the confinement phase leads to the appearance of an anomalous dimension in the momentum dependence of the propagator. The anomalous dimension as well as an appropriate ratio of photon wave function renormalization constants with and without monopoles is observed to be an order parameter for the deconfinement phase transition. We discuss the relation between our results and the confining properties of the gluon propagator in non-Abelian gauge theories.     

精确计算电子重整化链图传播下的Compton散射微分截面

采用电子与光子电磁相互作用最小耦合模型,对电子重整化链图传播下Compton散射微分截面作了严格解析计算,获得精确理论结果;并将该计算结果与电子树图和重整化单圈图传播下Compton散射微分截面作对比分析,获得了有关辐射修正的重要信息.此研究结果对精确描述Compton散射现象以及对电磁相互作用所呈现的复杂内部过程的深入探讨,都将从一个重要研究侧面给出理论计算研究方面某些可供借鉴与参考之处.     

W-Boson contribution to photon polarization operator in an external magnetic field

We calculated the one-loop contribution of w-bosons to the photon propagator in a constant homogeneous magnetic field. We obtain the probability for the creation of a pair of W-bosons by a polarized photon and the radiative shift of the photon mass in the external field above.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, No. 5, pp. 84–89, May, 1986.The authors would like to thank Professor I. E. Dzyaloshinskii for a fruitful discussion of the results of this work.     

Gauge Invariance of a Critical Number of Flavours in QED3

The fermion propagator in an arbitrary covariant gauge can be obtained from the Landau gauge result via a Landau–Khalatnikov–Fradkin transformation. This transformation can be written in a practically useful form in both configuration and momentum space. It is therefore possible to anticipate effects of a gauge transformation on the propagator’s analytic properties. These facts enable one to establish that if a critical number of flavours for chiral symmetry restoration and deconfinement exists in noncompact QED3, then its value is independent of the gauge parameter. This is explicated using simple forms for the fermion–photon vertex and the photon vacuum polarisation. The illustration highlights pitfalls that must be avoided in order to arrive at valid conclusions. Landau gauge is seen to be the covariant gauge in which the propagator avoids modification by a non-dynamical gauge-dependent exponential factor, whose presence can obscure truly observable features of the theory.     

Field statistics in a generalization of the Jaynes-Cummings model

Photon statistics in a generalization of the Jaynes-Cummings model, suitable for Raman scattering is considered. Expressions for stability and frequency shift of radiation fields are calculated. Also, the propagator of the system is evaluated and with the help of it correlation functions of photon numbers are calculated.     

The quantum electrodynamics of the nucleon

The Nuclear Force between a statistical assemblage of nucleon pairs is calculated directly for pseudo-scalar meson exchange. The Nucleon (proton) is treated as a particle with an extended structure. The model of the proton used is the one determined by high energy electron-proton scattering experiments.The self-energy process for such a proton is examined first for the emission and re-absorption of a photon. An appropriate photon propagator is derived for such a system using variational techniques. It is shown that the integrals that occur in the self-energy process converge without any of the difficulties associated with the point charge model. This shows the divergences in Quantum Electrodynamics (for nucleons) do not exist when nucleons are treated as particles with a structure.The pseudo-scalar meson propagator is derived using similar methods and the exchange force is calculated. It is shown that only certain diagrams need be considered when a stable nuclear bond is being calculated. The corrections to the Nuclear Force, which are self-energy processes involving emission and re-absorption of Virtual pseudoscalar mesons, are shown to converge for strong coupling.     

Stability of the Landau–Fermi Liquid Theory

The stability of the Landau–Fermi liquid theory is investigated. It has been shown that if the interaction function of the Fermi system is a finite function of the angle between the momenta of two particles at the Fermi surface, then the liquid can be stable. We have shown that the absolute value of the expansion coefficients of the interaction functions in Legendre polynomials are decreasing function of the coefficients indices. We solve the stability condition for one photon exchange (OPE) in an electron gas. The results show that we must use the massive boson propagator (higher order corrections to the photon propagator). Similar to previous works (Abrikosov et al. in Method of Quantum Field Theory in Statistical Physics, Pergamon, Elmsford, 1965), our result is proportional to g ². The density and temperature dependence of results is occulted in the effective mass of the system.     

Photon dispersion in a strong magnetic field

In an external magnetic field analytical properties are studied of the photon polarization tensor calculated as the electron-positron loop in the Furry picture. The polarization tensor is reexpressed as a sum over singular contributions coming from e⁺e^?-pair photocreation in semidiscrete Landau states. The solutions of the photon dispersion equation (i.e., the one for the poles of the photon propagator) are described. The shape of the photon dispersion curve obtained is responsible for the effect of photon deflection by a strong magnetic field. No physically reliable solutions, apart from spurions, are found for the longitudinal photon mode. An infinite number of solutions with complex space-momentum are found, with no apparnet ghosts among them. An attempt is made to interprete the former in terms of possible bound and quasibound states of electron and positron pairs.     

Quantum Field Theoretic Treatment of the Casimir Effect at T > 0. Real Time Formalism — Free Field Approximation

The framework of real time quantum field theory at finite temperature is generalized to include boundary conditions for the electromagnetic field strength tensor. In the perturbation theory the usual Feynman rules remain, only the photon propagator is modified. As a first application the Casimir effect is studied in the free field approximation and the known results are rederived with the new method.     

Radiative muon capture in medium-heavy nuclei

Radiative muon capture in nuclei is thoroughly investigated in view of its sensitivity to the pseudoscalar coupling constant g_P. In the photon energy domain of interest (k ? 60 MeV) the effective one-body hamiltonian in use is shown essentially to hold true, with minor corrections due to the muon propagator in the nuclear field and to the two-step process. The closure approximation is avoided by appropriately integrating the response function calculated in the Fermi gas model, in the energy-momentum transfer plane.Theoretical predictions in medium-heavy nuclei of the high-energy photon spectrum, of photon polarization, and of muon-spin photon angular correlation are given for various values of the pseudoscalar coupling constant.     

Vacuum Polarization Tensor for QED in the Light Front Gauge

The use of light front coordinates in quantum field theories (QFT) always brought some problems and controversies. In this work we explore some aspects of its formalism with respect to the employment of dimensional regularization in the computation of the photon’s self-energy at the one-loop level and how the fermion propagator has an important role in the outcoming results.     

热密QED中的德拜质量

从QED中光子传播子的Schweinger-Dyson方程出发,得到一个有用的德拜质量和热力学压强之间的关系.利用这个关系以及有限温度与有限化学势下的相关压强计算了德拜质量的双圈修正.其结果显示双圈修正减少了德拜屏蔽质量.最后还讨论了QED等离子体中的磁质量     

Note on hadronic shadowing effects in high energy photon-nucleus interactions

A simple model is proposed to describe the hadronic shadowing effects observed in total photon-nucleus cross sections at high energies. The model combines the existence of hadronic components in the photon propagator with the Glauber theory of multiple scattering, without paying explicit reference to the ? - dominance picture. Some consequences of the present treatment are discussed and compared to previous work.     

Photon sector of quantum electrodynamics at high temperature in two spatial dimensions

The photon sector of quantum electrodynamics (QED) in two spatial dimensions is analyzed at high temperature to all orders of perturbation theory. Imaginary-time formalism is used. The photon self-energy and propagator at finite temperature with vanishing frequency is calculated to the second order of perturbation theory. Based upon the latter, an improved perturbation theory which incorporates Debye screening is formulated. By virtue of the latter and gauge invariance, infrared finitness holds. The temperature dependence of any contribution to the connected Green's functions in the improved perturbation theory is analyzed systematically. At very high temperature, the photon sector becomes equivalent to a very massive scalar boson field plus a massless electromagnetic field and both become decoupled: all connected Green's functions containing, at least, one closed fermion loop with four or more vertices are shown to tend to zero.     

Dimensional regularization of massless quantum electrodynamics in spherical spacetime

The quantization and renormalization of massless electrodynamics in a spacetime of constant curvature are discused. A formalism is presented which is valid in an arbitrary number of dimensions and therefore allows the use of dimensional regularization. In the discussion of the photon propagator it is found that anomalous mass terms dependent on the curvature arise, although these vanish in four dimensions. Further, the gauge-fixing term in the Lagrangian has the unconventional feature of not being a perfect square. The renormalizability of the theory is then demonstrated to one loop order, and the renormalization constants are shown to retain their flat spacetime values. Finally, expansions for the renormalized electron and photon propagators in terms of appropriate spherical harmonics are derived.