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.     

Implications of Analyticity to the Solution of Schwinger-Dyson Equations in Minkowski Space

We discuss some recent developments in nonperturbative studies of quantum field theory (QFT) using the Schwinger-Dyson equations formulated directly in Minkowski space. We begin with the introduction of essential ideas of the integral representation in QFT and a discussion of the renormalization in this approach. The technique based on the integral representation of Green’s functions is exploited to solve Schwinger-Dyson equations in several models of quantum field theory, e.g., in scalar models and in strong coupling QED₃₊₁ in the quenched and in the unquenched approximation. The phenomenon of dynamical chiral symmetry breaking in regularized theory is touched. In QCD, the analyticity of the gluon propagator on the complex momentum square plane is exploited to continue some recent lattice data to the timelike momentum axis. We find a contribution to the non-positive absorptive part in the Landau-gauge gluon propagator which is in agreement with some other new recent analyses.     

Phase transition in three-dimensional quantum electrodynamics at <Emphasis Type="Italic">T</Emphasis> ≠ 0

Dynamic mass generation in 3D quantum electrodynamics (QED₃) is considered at T ≠ 0. To solve the Schwinger–Dyson equation for the Matsubara electron Green’s function, the ladder approximation is used and the corresponding photonic function is taken in the Landau gauge. In this case, the instant approximation is used for the photonic function. It is established that the process of dynamical mass generation in QED₃ at T ≠ 0 is accompanied by a phase transition. Formal analogy of transitions in the coupling constant is revealed at T ≠ 0 in QED₃, at T = 0 in QED₄, and in graphene theory. Critical values of the coupling constant and temperature, calculated numerically based on an approximate analytical solution of the Schwinger–Dyson equation are of the same orders of magnitude.     

Structural Aspects of the Fermion-Boson Mapping in Two-Dimensional Gauge and Anomalous Gauge Theories with Massive Fermions

Using a synthesis of the functional integral and operator approaches we discuss the fermion-boson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In QED₂ with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In anomalous chiral QED₂ with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of Θ-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess-Zumino field replicates the theory, changing neither its algebraic content nor its physical content.     

Discussing the U(1)-Problem of QED2without Instantons

We construct QED₂with mass and flavor and an extra Thirring term. The vacuum expectation values are carefully decomposed into clustering states using the U(1)-axial symmetry of the considered operators and a limiting procedure. The properties of the emerging expectation functional are compared to the proposedθ-vacuum of QCD. The massive theory is bosonized to a generalized Sine–Gordon model (GSG). The structure of the vacuum of QED₂manifests itself in symmetry properties of the GSG. We study the U(1)-problem and derive a Witten–Veneziano-type formula for the masses of the pseudoscalars determined from a semiclassical approximation.     

Causal phase in QED3

The operator S in Fock space which describes the scattering and particle production processes in an external time-dependent electromagnetic potentialA can be constructed from the one-particleS-matrix up to a physical phase λ[A]. In this work we determine this phase for QED in (2+1) dimensions by means of causality and show that no ultraviolet divergences arise, in contrast to the usual formalism of QED₃.     

Transverse Ward-Takahashi identities and full vertex functions in different representations of QED_3

We derive the transverse Ward-Takahashi identities(WTI) of N-dimensional quantum electrodynamics by means of the canonical quantization method and the path integration method, and subsequently attempt to prove that QED_3 is solvable based on the transverse and longitudinal WTI, indicating that the full vector and tensor vertices functions can be expressed in terms of the fermion propagators in QED_3. Further, we discuss the effect of different γ matrix representations on the full vertex function.     

Fermionic representation of the Wess-Zumino term and the chiral Schwinger model

The quantum structure of the chiral Schwinger model is studied by fermionization of the Wess-Zumino field. The model contains a hidden parameter a reflecting the ambiguity in the definition of the gauge anomaly. It is shown that, for the special value a = 2, this chiral model is equivalent to massless QED₂ in the sence that they share the same gauge field and the same (left-handed) chiral fermion. The fermionic representation of the Wess-Zumino term provides a natural way to summarize the current algebras and yields a regularization-independent current-algebraic characterization of the model.     

Analytic study of θ vacua on the lattice

A new definition of the topological charge density for four-dimensional lattice gauge theory is given. Using a systematic expansion we find a cusp in the vacuum energy at θ = π signaling the spontaneous breaking of CP there. Unlike its two-dimensional analogue (QED₂), QCD confines at θ = π. As a by-product an expression for the topological mass term for (2+1)-dimensional lattice gauge theory is obtained.     

No parity anomaly in massless QED3: A BPHZL approach

In this Letter we call into question the perturbatively parity breakdown at 1-loop for the massless QED₃ frequently claimed in the literature. As long as perturbative quantum field theory is concerned, whether a parity anomaly owing to radiative corrections exists or not shall be definitely proved by using a renormalization method independent of any regularization scheme. Such a problem has been investigated in the framework of BPHZL renormalization method, by adopting the Lowenstein–Zimmermann subtraction scheme. The 1-loop parity-odd contribution to the vacuum-polarization tensor is explicitly computed in the framework of the BPHZL renormalization method. It is shown that a Chern–Simons term is generated at that order induced through the infrared subtractions — which violate parity. We show then that, what is called “parity anomaly”, is in fact a parity-odd counterterm needed for restauring parity.     

Phase transition in the superconducting state in Gd-rich pseudoternary compounds (La1-xGdx)1.0Mo6Se8

A pronounced lambda-type specific heat anomaly in the superconducting state is reported for Gd-rich pseudoternary compounds (La_1-xGd_x)_1.0Mo₆Se₈. The anomaly is very similar to that previously reported for the compound Gd_1.2Mo₆Se₈. Both the temperature of the lambda anomaly (≈ 3.5 K) and the Curie-Weiss temperature were found to be nearly independent of x. In addition, evidence for the occurence of magnetic ordering at 0.8 K in Gd_1.2Mo₆Se₈ is presented. These observations support our earlier conjecture that the lambda anomaly at 3.5 K does not arise from magnetic ordering of the Gd³⁺ ions. The anomaly appears instead to be due to a different type of phase transition which is associated with the presence of the localized 4f electrons of the Gd³⁺ ions, but the exact nature of the transition remains to be established.     

First-principles study of the mechanisms of the pressure-induced dielectric anomalies in ferroelectric perovskites

The pressure-induced giant dielectric anomaly at 0 K of ABO₃ perovskites is investigated at the Hartree-Fock, density-functional theory and hybrid levels. Its mechanism is analyzed in terms of thermodynamic phase stability, structural and phonon contributions and Born effective charges. It is shown that the IR-active soft phonon is responsible for the anomaly. This mode always involves a displacement and a deformation of the oxygen octahedra, while the roles of A and B ions vary among the materials and between high- and low-pressure phase transitions. A sharp increase in the phonon amplitude near the phase transition gives rise to the dielectric anomaly. The use of hybrid functionals is required for agreement with experimental data. The calculations show that the dielectric anomaly in the pressure-induced phase transitions of these perovskites is a property of the bulk material.     

Quantizing QED2 on the light-cone

The method of discretized light-cone quantization (DLCQ) is applied to quantum electrodynamics in one space and one time dimension (QED₂) with different initial conditions. This leads to different representations of the operators of the constants of motion. Within the fermion-antifermion approximation we perform analytically the transition to the continuum limit and show that the discrete massive and massless representations are equivalent. We compare a semiclassical calculation of the number of bound states with the results obtained in the continuum limit. Furthermore a discrete bosonized version of QED₂ is discussed.     

On the character of chiral symmetry breaking and fermion vacuum structure in QED<Subscript>3</Subscript>

Equation for the Bethe-Salpeter wave function of the Goldstone boson in QED₃ is considered in the ladder approximation with the use of the Landau gauge for the photon propagator. With the help of standard simplifications, the existence of nonzero solutions for this equation is demonstrated, which testifies to the production of the above-described boson in the process of chiral symmetry breaking. At the same time, it is demonstrated that only one of the entire set of solutions describing the Goldstone boson corresponds to the stable ground state; this solution has the greatest fermion mass. In the remaining cases, the compound boson state with zero mass is excited, and all other states having smaller energies appear tachyon states and hence are unstable. The fermion condensate is calculated; it is demonstrated that in the examined case, it is finite. Based on the foregoing, conclusions are drawn about spontaneous rather than dynamic character of chiral symmetry breaking in QED₃, complex structure of fermion vacuum for the examined model, and at the same time, simple structure of the massive phase vacuum.     

Fermion Condensates in Lower Dimensional Gauge Theories

Combining a unitary transformation,the variational method and the exact ground state of pure gauge Hamiltonian.we investigate syst matically the vacumm structure and spintaneous chiral-symmetry breaking in (1+1) and (2+1) dimensional Hamiltonian lattice gauge theories with fermions,and obtain nice scaling behaviors for 〈ψψ〉 extending to the weak coupling regime.This paper not only reproduces well the exact value in the continuum Schwinger model,but also predicts the values for the fermion condensates in QCD₂,QED₃ and QCD₃.     

An alternative approach to dynamical mass generation in QED3

Some quantum properties of QED₃ are studied with the help of an exact evolution equation of the effective action with the bare fermion mass. The resulting effective theory and the occurrence of a dynamical mass are discussed in the framework of the gradient expansion.     

Radiative processes as a condensation phenomenon and the physical meaning of deformed canonical structures

We study the radiative corrections of QED₃ from the dual point of view and show that this process is the exact dual to the Julia–Toulouse mechanism introduced by Quevedo and Trugenberger [F. Quevedo, C.A. Trugenberger, Nucl. Phys. B 501 (1997) 143] some years ago. We discuss the physics behind this mechanism that involves condensation of topological defects. It is shown that the dual Stuckelberg mechanism is responsible for the “rank-jump” phenomenon that transforms the scalar field (dual to Maxwell in this dimensionality) into the vectorial self-dual field. This phenomenon is studied using the ideas of noncommutative fields theory that examines possible deformations of the canonical structure of some well-known models in (2+1)D$(2+1)\mathrm{D}$. A deformation is constructed linking the massless scalar field theory with the self-dual theory. This is the exact dual of the known deformation connecting the Maxwell theory with the Maxwell–Chern–Simons theory. Duality, radiative corrections, the Julia–Toulouse mechanism and canonical deformations are then used to establish a web of relations between the mentioned theories and to propose a physical picture of the deformation procedure adopted.     

Superconducting EuBa2Cu3O7. A Mössbauer study

EuBa₂Cu₃O₇ shows a sharp transition to zero resistance atT _sc =85(1) K. Europium is entirely trivalent. The¹⁵¹Eu Mössbauer recoilless fraction in the range 4–300 K is well-fitted by a Debye model withT _sc = 85(1) K. There is no anomaly around 240 K, nor atT _sc , and therefore no significant change in the vibrational amplitude of the rare-earth ion. Another sample doped with 1%⁵⁷Fe, shows two ferric quadrupole doublets associated with Fe³⁺ on Cu₁ and Cu₂ sites. There is no sign of any magnetic order down to 4.2 K.     

Effective potential, the structure of fermion vacuum, and the mechanism of chiral symmetry breaking in QED3

Elementary-particle Physics and Field Theory

Effective potential, the structure of fermion vacuum, and the mechanism of chiral symmetry breaking in QED₃