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.     

Quantum Chromodynamics in 1+3 Dimensions at High Temperature: Dimensional Reduction Revisited

The gluon sector of QCD in 1+3 dimensions in analyzed at high temperature (much larger than the critical ones) thereby generalizing previous results by other authors. The imaginary time formalism is used. The analysis is carried out to all orders in an improved perturbation theory which includes all second-order internal quark loops in the “free” gluon propagators. General results are given for the leading high temperature contributions to all renormalized connected gluon Green's functions (for fixed external threemomenta, much smaller than the temperature). The latter are generated by a new (dimensionally reduced) high-temperature partition function Z_HT, which corresponds to: i) the Yang-Mills (“magnetic”) gluon field coupled to a massive scalar (“electric”) gluon field, all in 3 spatial dimensions and at zero imaginary time, ii) the quark field, which continues to depend on imaginary time, coupled to the above gluon fields Z_HT also depends on the renormalized quark masses and gauge coupling constant at zero temperature, the second order quark-loop contributions to the zero-temperature renormalization constants for the gluon field and the three and four gluon vertices and on new gluon mass terms. The latter correspond to a finite number of diagrams in the improved perturbation theory at high temperature. Z_HT could be useful as the starting point for further non-perturbative studies. For the pure Yang-Mills plus ghosts theory (no quarks), it is conjectured that contributions to Green's functions depending on external momenta due to internal electric gluons could be regarded, as subdominant. Arguments are given in order to justify that conjecture. Then, the above Z_HT can be simplified and another high-temperature generating functional depending only on magnetic gluon fields is given. For the full theory including quarks, the possibility of neglecting contributions due to internal quark loops is discussed: certain infrared divergences beyond the oneloop level appear to imply that such a simplification, although not discarded, is rather hard to establish.     

Why dilatation generators do not generate dilatations

We show that the Ward identities associated with broken scale invariance contain anomalies in renormalized perturbation theory. In low orders, these anomalies can be absorbed into a redefinition of the scale dimensions of the fields in the theory, but in higher orders this is not possible. Also, these anomalies cannot be removed by studying the Green's functions for objects other than canonical fields, e.g., currents. These results are established to first nontrivial order in perturbation theory by explicit Feynman calculations (which give us information at all momentum transfers), and in higher orders by the method of Callan and Symanzik (which gives information only at zero momentum transfer). The two approaches are consistent within their common domain of validity. Two appendices contain self-contained treatments of the formal canonical theory of scale and conformal transformations and of the derivation of Ward identities. In another appendix, we derive the Callan-Symanzik equations for Green's functions of currents, and show that no redefinition of scale dimension is necessary for these objects, although the other anomalies remain.     

Perturbation theory for QED bound states

A new method is presented for deriving a systematic perturbative expansion for QED bound states, which does not rely upon solving any new or old equation. The starting point is a given nonperturbative zeroth order Green's function, obtained by a suitable “relativistic dressing” of the nonrelativistic Green's function for the Schrödinger equation with Coulomb potential, which embodies the Coulombic bound states and is known. The comparison with the complete Green's function as given by standard perturbative QED gives a perturbative kernel which is then used for the expansion of the QED Green's function in terms of the given non-perturbative zeroth order Green's function.     

Can MBPT and QED be merged in a systematic way?

The possiblities of merging QED with the standard many-body perturbation theory (MBPT) for atomic systems in a rigorous and systematic way are analysed. Time-dependent MBPT, based on the time-evolution operator, a technique well developed particularly in nuclear theory, is used and somewhat reformulated to be consistent with the covariant QED formalism. An effective QED Hamiltonian, free from singularities, is constructed. The procedure can be applied to degenerate and quasi-degenerate systems (extended model space), which is not possible with the standard QED technique based upon the S-matrix formulation. To include in the model space closely lying energy levels, such as fine-structure levels, can have a dramatic effect on the convergence rate. The electron-electron interaction is investigated in detail, and it is shown that it can be separated into irreducible multi-photon interactions, which in principle can be iterated as in standard MBPT. Singularities do not appear, and a simple procedure for evaluating residual finite contributions is described. Comparison is made with the closely related Green's function technique. The procedure is presently being tested on the fine-structure levels of He-like ions.     

The covariant-evolution-operator method in bound-state QED

The methods of quantum-electrodynamical (QED) calculations on bound atomic systems are reviewed with emphasis on the newly developed covariant-evolution-operator method. The aim is to compare that method with other available methods and also to point out possibilities to combine that with standard many-body perturbation theory (MBPT) in order to perform accurate numerical QED calculations, including quasi-degeneracy, also for light elements, where the electron correlation is relatively strong.As a background, the time-independent many-body perturbation theory (MBPT) is briefly reviewed, particularly the method with extended model space. Time-dependent perturbation theory is discussed in some detail, introducing the time-evolution operator and the Gell–Mann–Low relation, generalized to an arbitrary model space. Three methods of treating the bound-state QED problem are discussed. The standard S-matrix formulation, which is restricted to a degenerate model space, is discussed only briefly. Two methods applicable also to the quasi-degenerate problem are treated in more detail, the two-times Green's-function and the covariant-evolution-operator techniques. The treatment is concentrated on the latter technique, which has been developed more recently and which has not been discussed in more detail before. A comparison of the two-times Green's-function and the covariant-evolution-operator techniques, which have great similarities, is performed. In the appendix a simple procedure is derived for expressing the evolution-operator diagrams of arbitrary order.The possibilities of merging QED in the covariant evolution-operator formulation with MBPT in a systematic way is indicated. With such a technique it might be feasible to perform accurate QED calculations also on light elements, which is presently not possible with the techniques available.     

Proof for Gauge Independence of the Energy-Momentum Tensor in Quantum Electrodynamics

Proof is given for gauge independence of the (Belinfante's) symmetric energy-momentum tensor in QED. Under the covariant LSZ-formalism it is shown that expectation values, supplemented with physical state conditions, of the energy-momentum tensor are gauge independent to all orders of the purturbation theory (the loop expansion). A study is also made, in terms of the gauge invariant operators of electron (known as the Dirac's or Steinmann's electron) and photon, in expectation of gauge invariant result without any restriction. It is, however, shown that singling out gauge invariant quantities is merely synonymous to fixing a gauge, then there needs again a use of the asymptotic condition to obtain gauge independent results.     

Adsorbate-induced surface reconstructions of Pd 110 — do phonons contribute?

The free-energy contribution of phonons to surface reconstruction of Pd 110 is studied by Green's function methods. The adsorbate is modelled as a local perturbation to the dynamical matrix, the effect of which is solved from Dyson's equation. The phonons have a high entropy at the reconstructed surface, thus easing the reconstruction as the temperature increases. Adding an impurity atom with a low Debye temperature further enhances the entropy effect in favour of reconstruction.     

Optical Theorem in Quantum electrodynamics with Unstable Vacuum

All the results reffering to the relations of the optical theorem in QED with an external electromagnetic field with unstable vacuum are consistently given in this paper. The results obtained are true in all orders of perturbation theory. A generating functional is introduced for calculating total probabilities of any processes in QED with unstable vacuum.     

Remarks on the Renormalization Properties of Lorentz- and CPT-Violating Quantum Electrodynamics

In this work, we employ algebraic renormalization technique to show the renormalizability to all orders in perturbation theory of the Lorentz- and CPT-violating QED. Essentially, we control the breaking terms by using a suitable set of external sources. Thus, with the symmetries restored, a perturbative treatment can be consistently employed. After showing the renormalizability, the external sources attain certain physical values, which allow the recovering of the starting physical action. The main result is that the original QED action presents the three usual independent renormalization parameters. The Lorentz-violating sector can be renormalized by 19 independent parameters. Moreover, vacuum divergences appear with extra independent renormalization. Remarkably, the bosonic odd sector (Chern-Simons-like term) does not renormalize and is not radiatively generated. One-loop computations are also presented and compared with the existing literature.     

Vextex Corrections and one σ Exchange Potential at Finite Temperature

By using the imaginary-time Green's function method in finite temperature field theory,we calculate the effects of the three-line vertex function on finite temperature one σ-meson exchange potential.It is found that the finite temperature coupling constant of the sigma-nucleon interaction decreases as the temperature increases,it approaches zero when temperature arrives at 210MeV.This result is quite similar to that the temperature dependence of coupling constant given by Nambu-Jona-Lasinia model at the quark level.     

The lattice dynamics of an anharmonic crystal

The theory of the physical properties of an anharmonic crystal is discussed by using the thermodynamic Green's functions for the phonons. A perturbation procedure is developed to obtain the Green's functions and it is shown that for some purposes a quasi-harmonic approximation is useful, in which the frequencies of the normal modes are those determined by infra-red or neutron spectrometry. The thermodynamic, elastic, dielectric and scattering properties of an anharmonic crystal are discussed in terms of the Green's functions, and detailed expressions are given for the more important contributions. Detailed numerical calculations are presented of the thermal expansion, dielectric properties and shapes of some of the inelastically scattered neutron groups, for sodium iodide and potassium bromide. The calculations, which give reasonable agreement with experiment, show that even at quite low temperatures, the lifetimes of some of the normal modes can be quite short. By using the quasi-harmonic approximation it is shown that the large temperature dependence of the normal modes in a ferroelectric crystal can be treated adequately.     

Merging of photons in the field of a multielectron atom: Higher orders of perturbation theory

The contribution of higher orders of relativistic quantum perturbation theory to the differential cross section for the merging of three X-ray photons into one photon in the field of a multielectron atom has been studied in the Tamm–Dankov approximation. It has been shown that higher orders do not change the physical results obtained in the leading (second) order of perturbation theory.     

Optimized perturbation theory in quantum electrodynamics

The optimized perturbation expansions, Grunberg's fastest apparent convergence and Stevenson's principle of minimal sensitivity, are applied to some low-energy QED quantities. The optimization does not disturb the experimentally established values, and, at higher orders, its effects are in the direction of reducing small differences between theoretical and experimental values.     

Green's functions on finite lattices and their connection to the infinite lattice limit

It is shown that the Green's function on a finite lattice in arbitrary space dimension can be obtained from that of an infinite lattice by means of a translation operator. Explicit examples are given for one- and two-dimensional lattices.     

η-meson in the Pseudoscalar Coupling at Finite Temperature

By means of the imaginary-time Green's function method in the finite-temperature field theory, the η-meson and nucleons interaction coupling constant, the effective mass of η-meson and the one η-meson exchange potential for the pseudoscalarcoupling at finite temperature are given. The results are compared with that given by the pseudovector coupling case.     

Curing fermion mass gauge variance in QED

The problem of the gauge dependence of the fermion mass in the Maxwell-Chern-Simons QED is revisited. Using Proca mass term as an intermediate infrared regulator we are demonstrating gauge-invariance of the fermion mass shell in QED in all orders of the perturbation theory.     

The renormalized σ model

A renormalization procedure of the boson σ model based on the finite field equations of Brandt-Wilson is given. We first show that the current operators appearing in the field equations, which are finite local limit of sums of nonlocal field products and suitable subtraction terms, can be chosen to be the same form as the one given for the symmetric limit except for the symmetry breaking constant source term itself. The set of integral equations derived from the field equations is shown to be equivalent to the usual Bogoliubov-Parasiuk-Hepp renormalization theory, and gives us immediately all the renormalized Green's functions in each order of perturbation theory in clear and straightforward fashion. We then analyze the structures of the model in detail. In particular, Ward identities are shown to be satisfied to all orders of perturbation theory. The Goldstone theorem is a particular consequence of these identities.     

Hard noncommutative loops resummation

The noncommutative version of the Euclidean g2phi4 theory is considered. By using Wilsonian flow equations the ultraviolet renormalizability can be proved to all orders in perturbation theory. On the other hand, the infrared sector cannot be treated perturbatively and requires a resummation of the leading divergences in the two-point function. This is analogous to what is done in the hard thermal loops resummation of finite temperature field theory. Next-to-leading order corrections to the self-energy are computed, resulting in O(g3) contributions in the massless case, and O(g6logg2) in the massive one.