Transverse Vector Vertex Function and Transverse Ward-Takahashi Relations in QED

The transverse vector vertex function in momentum space in four-dimensional QED is derived in terms of a set of transverse Ward-Takahashi relations for the vector and the axial-vector vertices in the case of massless fermion.It is demonstrated explicitly that the transverse vector vertex function derived this way to one-loop order leads to the same result as one obtained in perturbation theory. This provides a basic approach to determine the transverse part of basic vertex function from the symmetry relations of the system.     

Transverse Vector Vertex Function and Transverse Ward-Takahashi Relations in QED

The transverse vector vertex function in momentum space in four-dimensional QED is derived in terms of a set of transverse Ward-Takahashi relations for the vector and the axial-vector vertices in the case of massless fermion. It is demonstrated explicitly that the transverse vector vertex function derived this way to one-loop order leads to the same result as one obtained in perturbation theory. This provides a basic approach to determine the transverse part of basic vertex function from the symmetry relations of the system.     

Dispersive derivation of the trace anomaly

We present a simple derivation of the one-loop trace anomaly in spinor QED through dispersion relations, avoiding completely any ultraviolet regularization. The anomaly can be expressed as a convergent sum rule for the imaginary part of a relevant formfactor. In the massless limit, the imaginary part produces a delta-function singularity at zero external momentum squared. Such a treatment reveals an “infrared face” of the trace anomaly, in striking similarity with the well-known case of the axial anomaly.     

Implicit regularization beyond one-loop order: gauge field theories

We extend a constrained version of implicit regularization (CIR) beyond one-loop order for gauge field theories. In this framework, the ultraviolet content of the model is displayed in terms of momentum loop integrals order by order in perturbation theory for any Feynman diagram, while the Ward–Slavnov–Taylor identities are controlled by finite surface terms. To illustrate, we apply CIR to massless abelian gauge field theories (scalar and spinorial QED) to two-loop order and calculate the two-loop beta-function of spinorial QED. PACS  11.10.Gh; 11.15.Bt; 11.15.-q     

A convergent series for the QED effective action

The one-loop effective action of QED obtained by Heisenberg and Euler and by Schwinger has been expressed by an asymptotic perturbative series which is divergent. In this Letter we present a nonperturbative but convergent series of the effective action. With the convergent series we establish the existence of the manifest electric-magnetic duality in the one-loop effective action of QED.     

Effective potential for the massless KPZ equation

In previous work we have developed a general method for casting a classical field theory subject to Gaussian noise (that is, a stochastic partial differential equation (SPDE)) into a functional integral formalism that exhibits many of the properties more commonly associated with quantum field theories (QFTs). In particular, we demonstrated how to derive the one-loop effective potential. In this paper we apply the formalism to a specific field theory of considerable interest, the massless KPZ equation (massless noisy Burgers equation), and analyze its behavior in the ultraviolet (short-distance) regime. When this field theory is subject to white noise we can calculate the one-loop effective potential and show that it is one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions, and fails to be ultraviolet renormalizable in higher dimensions. We show that the one-loop effective potential for the massless KPZ equation is closely related to that for λφ⁴ QFT. In particular, we prove that the massless KPZ equation exhibits one-loop dynamical symmetry breaking (via an analog of the Coleman–Weinberg mechanism) in 1 and 2 space dimensions, and that this behavior does not persist in 3 space dimensions.     

Propagation of vacuum polarized photons in topological black hole spacetimes

The one-loop effective action for QED in curved spacetime contains equivalence principle violating interactions between the electromagnetic field and the spacetime curvature. These interactions lead to a dependence of the photon velocity on the motion and polarization directions. In this paper we investigate the gravitational analogue to the electromagnetic birefringence phenomenon in the static and radiating topological black hole backgrounds. For the static topological black hole spacetimes, the velocity shift of photons is the same as that in Reissner-Nordström black holes. This reflects the fact that the propagation of vacuum polarized photons is not sensitive to the asymptotic behavior and topological structure of spacetimes. For the massless topological black hole and BTZ black hole, the light cone condition remains unchanged. In the radiating topological black hole backgrounds, the light cone condition is changed even for the radially directed photons. The velocity shifts depend on the topological structures. Due to the null fluid, the velocity shift of photons no longer vanishes at the apparent horizons as well as the event horizons. However, the “polarization sum rule” is still valid.     

Total charge screening

Solutions of classical massless scalar electrodynamics with a large external charge which exhibit total charge screening, that is, in which the charge in the field exactly neutralizes the external charge, are found. These solutions have lower energy than the unscreened Coulomb potential. The relation to the color screening problem in QCD is discussed.     

Damping of plasma oscillations in hot gluon matter

The computation of the damping constant of QCD plasma oscillations is discussed in the physical Coulomb and temporal axial gauges in the framework of a consistent linear response analysis. To bare one-loop order the waves damp by decaying into two massless gluons, and the two gauges give the same result for the damping constant. It is pointed out that, due to the infrared behaviour of the theory, higher-order corrections will modify the result and an example showing how they may do this by turning the gluons effectively massive is given.     

QED effective action in Krein space quantization

The one-loop effective action of QED is calculated by the Schwinger method in Krein space quantization. We show that the effective action is naturally finite and regularized. It also coincides with the renormalized solution which was derived by Schwinger.     

Photon-Z mixing in the Weinberg-Salam model: Effective charges and the a = −3 gauge

We study some properties of the Weinberg-Salam model connected with the photon-Z mixing. We solve the linear Dyson-Schwinger equations between full and 1PI boson propagators. The task is made easier by the two-point function Ward identities that we derive to all orders and in any gauge. Some aspects of the renormalization of the model are also discussed. We display the exact mass-dependent one-loop two-point functions involving the photon and Z field in any linear ξ-gauge. The special gauge a = ξ^?1 = ?3 is shown to play a peculiar role. In this gauge, the Z field is multiplicatively renormalizable (at the one-loop level), and one can construct both electric and weak effective charges of the theory from the photon and Z propagators, with a very simple expression similar to that of the QED Petermann, Stueckelberg, Gell-Mann and Low charge.     

Topological charge from thermodynamics in two dimensions

It is shown that in the weak coupling limit the partition function of massless (QED)₂ in a finite volume is identical to that of a bose field if the boson topological charge is identified with the fermion number. Generalizations to theories with U(N) gauge symmetry, fractional fermion number, and the Schwinger model for any coupling are also discussed.     

Canonical quantization theory of general singular QED system of Fermi field interaction with generally decomposed gauge potential

Quantization theory gives rise to transverse phonons for the traditional Coulomb gauge condition and to scalar and longitudinal photons for the Lorentz gauge condition. We describe a new approach to quantize the general singular QED system by decomposing a general gauge potential into two orthogonal components in general field theory, which preserves scalar and longitudinal photons. Using these two orthogonal components, we obtain an expansion of the gauge-invariant Lagrangian density, from which we deduce the two orthogonal canonical momenta conjugate to the two components of the gauge potential. We then obtain the canonical Hamiltonian in the phase space and deduce the inherent constraints. In terms of the naturally deduced gauge condition, the quantization results are exactly consistent with those in the traditional Coulomb gauge condition and superior to those in the Lorentz gauge condition. Moreover, we find that all the nonvanishing quantum commutators are permanently gauge-invariant. A system can only be measured in physical experiments when it is gauge-invariant. The vanishing longitudinal vector potential means that the gauge invariance of the general QED system cannot be retained. This is similar to the nucleon spin crisis dilemma, which is an example of a physical quantity that cannot be exactly measured experimentally. However, the theory here solves this dilemma by keeping the gauge invariance of the general QED system.     

Topological vertex,string amplitudes and spectral functions of hyperbolic geometry

We study radiative corrections to massless quantum electrodynamics modified by two dimension-five LV interactions $\bar{\Psi } \gamma ^{\mu } b'^{\nu } F_{\mu \nu }\Psi $ and $\bar{\Psi }\gamma ^{\mu }b^{\nu } \tilde{F}_{\mu \nu } \Psi $ in the framework of effective field theories. All divergent one-particle-irreducible Feynman diagrams are calculated at one-loop order and several related issues are discussed. It is found that massless quantum electrodynamics modified by the interaction $\bar{\Psi } \gamma ^{\mu } b'^{\nu } F_{\mu \nu }\Psi $ alone is one-loop renormalizable and the result can be understood on the grounds of symmetry. In this context the one-loop Lorentz-violating beta function is derived and the corresponding running coefficients are obtained.     

QED corrections to the parity-nonconserving 6s-7s amplitude in 133Cs

The complete gauge-invariant set of the one-loop QED corrections to the parity-nonconserving 6s-7s amplitude in 133Cs is evaluated to all orders in alphaZ using a local version of the Dirac-Hartree-Fock potential. The calculations are performed in both length and velocity gauges for the absorbed photon. The total binding QED correction is found to be -0.27(3)%. The weak charge of 133Cs, derived using two most accurate values of the vector transition polarizability beta, is Q(W)=-72.57(46) for beta=26.957(51)a(3)(B) and Q(W)=-73.09(54) for beta=27.15(11)a(3)(B). The first value deviates by 1.1sigma from the prediction of the standard model, while the second one is in perfect agreement with it.     

Dynamical symmetry breaking in models with the Yukawa interaction

The models with a massless fermion and a self-interacting massive scalar field with the Yukawa interaction are discussed. The chiral condensate and the fermion mass are calculated analytically through a one-loop approximation in (1 + 1)-dimensions. It is shown that the models have a phase transition as a function of the squared mass of the scalar field.     

On the dynamical vacuum rearrangement and the problem of fermion mass generation

We discuss the conditions under which the dynamical fermion mass generation mechanism may occur. The analogy between the vacuum rearrangement in massless electrodynamics, which results in the generation of a physical fermion mass, and the vacuum rearrangement concerned with the fall into the Coulomb centre with a large charge (Z > 137) is considered.     

Structure of the two-point green function of the gauge field for N = 1 supersymmetric Yang-Mills theory regularized by higher covariant derivatives

For the most general renormalizable N = 1 supersymmetric Yang-Mills theory, regularized by higher derivatives, we investigate a contribution to the Gell-Mann-Low function from the two-loop diagrams, containing cubic interaction of the matter superfields. We find that all integrals with respect to the loop momentum in the massless case are factorized to the integrals of total derivatives and can be easily calculated. Thus, we explain the origin of the relation between the two-loop β-function and the one-loop anomalous dimension of the matter superfield.     

Space charge effect and mirror charge effect in photoemission spectroscopy

We report the observation and systematic investigation of the space charge effect and mirror charge effect in photoemission spectroscopy. When pulsed light is incident on a sample, the photo-emitted electrons experience energy redistribution after escaping from the surface because of the Coulomb interaction between them (space charge effect) and between photo-emitted electrons and the distribution of mirror charges in the sample (mirror charge effect). These combined Coulomb interaction effects give rise to an energy shift and a broadening which can be on the order of 10 meV for a typical third-generation synchrotron light source. This value is comparable to many fundamental physical parameters actively studied by photoemission spectroscopy and should be taken seriously in interpreting photoemission data and in designing next generation experiments.     

On the mass spectrum of noncommutative Schwinger model in Euclidean ℝ<Superscript>2</Superscript> space

The mass spectrum of noncommutative QED in two-dimensional Euclidean ?² space is derived first in a perturbative approach at one-loop level and then in a nonperturbative approach using the equivalent bosonized noncommutative effective action. It turns out that the mass spectrum of noncommutative QED in two dimensions reduces to a single non-interacting meson with mass \(M_{\gamma}=\frac{g}{\sqrt{\pi}}\), as in commutative Schwinger model.