Hidden spurious sources in axial gauge propagators

We show that charge carrying propagators in axial gauges involve spurious sources that move along the rays of gauge fixing. Although these spurious sources are hidden in the axial gauge in question, they are manifest when the same propagator is viewed in other gauges. Therefore, they influence the propagation of the dynamical fields. Thus the naive electron propagator in axial gauge quantum electrodynamics does not have the spectrum of a free, mass-renormalized electron. We confine our remarks to quantum electrodynamics here. In the sequel the implication for axial gauge quark and gluon propagators in quantum chromodynamics is discussed. Gauge-independent propagators do not suffer this affliction.     

Homogeneous propagators for massless half-integer spin fields in 3+2 De Sitter space

Investigation of the massive propagators allows us to exhibit indecomposable representations appearing with masslessness. By direct examination of the propagators, we prove that massless fields in 3+2 De Sitter space propagate on the light cone. Indeed, it will be shown that a choice of gauge, in which all propagation is confined to the light cone, exists and, in this context, explicit expressions of homogeneous propagators for massless half-integer spin fields are obtained.     

Two-point fermion correlation functions at finite density

The general form of two-point fermion correlation functions at finite density is examined. Examples of particular interest are correlation functions of nucleonic interpolating fields, used in QCD sum-rule studies, and nucleon propagators in hadronic field theories. The constraints of Lorentz covariance, parity, and time-reversal on the form of the correlators are derived by focusing on spectral functions. Discrepancies with other treatments in the literature are discussed.     

Polymer topology and Chern-Simons field theory

In this paper the statistical mechanical problem of two topologically linked polymers is related to a topological Ginzburg-Landau model coupled to two Chern-Simons field theories. The Chern-Simons fields play the role of propagators of the topological interactions. The effects of the topological constraints is investigated using the method of effective potential in one-loop approximation.     

Low magnetic fields for flow propagators in permeable rocks

Pulsed field gradient NMR flow propagators for water flow in Bentheimer sandstone are measured at low fields (1H resonance 2 MHz), using both unipolar and bipolar variants of the pulsed gradient method. We compare with propagators measured at high fields (1H resonance 85 MHz). We show that (i) measured flow propagators appear to be equivalent, in this rock, and (ii) the lower signal to noise ratio at low fields is not a serious limitation. By comparing different pulse sequences, we study the effects of the internal gradients on the propagator measurement at 2 MHz, which for certain rocks may persist even at low fields.     

Aspects of holography in the AdS/CFT correspondence

We study quantities which are important for the realization of the holographic principle in the AdS/CFT correspondence: boundaries, geodesics and the propagators of scalar fields. They should play a role in the holographic setup in the BMN limit as well. We review the backgrounds and their relations that are relevant in the AdS/CFT correspondence and in its BMN limit. We describe the realization of the holographic principle in the AdS/CFT correspondence and summarize proposals of how to translate it in the BMN limit. We analyze the boundaries, geodesics and propagators of scalar fields in detail and observe how they behave in the limiting process from AdS₅×S⁵ to the 10‐dimensional plane wave, which is the spacetime in the BMN limit.     

Republication of: Propagators,commutators and anti-commutators in general relativity

This is an English translation of A. Lichnerowicz’ 1964 paper “Propagateurs, commutateurs et anticommutateurs en relativité générale”. It was based on lectures at a Les Houches school, and gave a classic summary of the author’s work on quantum propagators in curved space-times, introducing tensorial and spinorial propagators which generalise the flat space propagators of Jordan and Pauli. It gives the quantum commutators for the Maxwell and Dirac fields and for perturbations of the gravitational field, and numerous intermediate formulae. The results are basic to quantum field theory in curved space-times. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by G. Esposito and by a brief biography written by M. A. H. MacCallum.     

Radiative Corrections to Non-Abelian Gauge Theory in Homogeneous Self-Dual Backgrounds

We study the Euclidean version of non-Abelian gauge theories in homogeneous background fields with due regard of negative and zero modes of the gauge field kernel. For general gauge group and general background but without external currents we prove a relation between the propagators belonging to different gauge fixings. Specializing to a self-dual homogeneous background we derive nonperturbatively the propagators. Next we calculate the matter field contribution to the renormalized polarization tensor using a modified dimensional regularization scheme. We prove the validity of a modified Ward identity.     

Consistent real-time propagators for any spin,mass, temperature and density

The time-path method in finite temperature field theory is extended to arbitrary covariant fields. Explicit expressions for the free thermal propagators are obtained using the multi-mass Klein-Gordon divisor. The key formula which shows that the interacting theory is free of singularities is derived. Finally, a simple method for the determination of free massless propagators is given.     

In-medium chiral perturbation theory

This talk will report about a systematical implementation of a chiral effective field theory in nuclear matter with explicit pion fields and in the presence of external sources[1]. Within the generating functional approach of Ref.[2] the so-called standard power counting rules for the calculation of in-medium pion properties are developed that apply if the residual nucleon energies are of the order of the pion mass. In addition, for the case of vanishing residual nucleon energies, a modified scheme (non-standard counting) is introduced. For both schemes the pertinent scales where the chiral expansions have to break down are established as well. We report about a systematic analysis of n-point in-medium Green functions up to and including next-to-leading order when the standard rules apply. These include the in-medium contributions to quark condensates, pion propagators, pion masses and couplings of the axial-vector, vector and pseudoscalar currents to pions.     

Polarized vector bosons on the de Sitter expanding universe

The quantum theory of the vector field minimally coupled to the gravity of the de Sitter spacetime is built in a canonical manner starting with a new complete set of quantum modes of given momentum and helicity derived in the moving chart of conformal time. It is shown that the canonical quantization leads to new vector propagators which satisfy similar equations as the propagators derived by Tsamis and Woodard (J Math Phys 48:052306, 2007) but having a different structure. The one-particle operators are also written down pointing out that their properties are similar with those found already in the quantum theory of the scalar, Dirac and Maxwell free fields.     

Hamiltonian quantization of the non-anomalous generalized Schwinger model

We quantize a generalized version of the Schwinger model, where the two chiral sectors couples with different strengths to theU(1) gauge field. Starting from a theory which includes a generalized Wess-Zumino term, we obtain the equal time commutation relation for physical fields, both the singular and non-singular cases are considered. The photon propagators are also computed in their gauge dependent and invariant versions.     

Matter fields in lattice gravity

The formulations of the scalar, spinor and gauge fields on a curved random lattice are discussed. A new fermion scheme — simplicial fermions — which is more natural in the presence of gravity, is introduced. Some of the propagators in D = 2 are evaluated numerically and are compared with the continuum limit.     

A Decoupling Theorem for the BPHZL-Scheme

Conditions are stated, which are sufficient for the heavy-mass-suppression of BPHZL- subtracted Feynman-integrals containing propagators of “heavy fields”. This result generalizes the Decoupling Theorems of Ambjørn, Manoukian and Landsman to cases, where massless fields (e.g., gauge fields) are present.     

Perturbation theory for the anomaly-free chiral Schwinger model

We apply perturbation theory to the gauge invariant version of the chiral Schwinger model. The cancellation of anomalies is shown explicitly in terms of Feynman diagrams. We calculate the exact propagators for the gauge field, for the Wess-Zumino field and for the mixing between these fields. Using these propagators, we demonstrate the existence of a massive state.     

Propagators for lattice gauge theories in a background field

We prove regularity and decay properties for propagators connected with the renormalization group method in lattice gauge theories. These propagators depend on an external gauge field configuration, called a background field.Research supported in part by the National Science Foundation under Grant PHY-82-0369     

Constraints on the IR behaviour of gluon and ghost propagator from Ward-Slavnov-Taylor identities

We consider the constraints of the Slavnov-Taylor identity of the IR behaviour of gluon and ghost propagators and their compatibility with solutions of the ghost Dyson-Schwinger equation and with the lattice picture.     

General aspects of stochastic quantum field theory for extended particles

Theories of free fields describing spin zero and1/2 extended particles are derived within the stochastic quantum field theory (SQFT) framework. Covariant SQFT analogs of free Schwinger functions and Feynman propagators are obtained, and explicit expressions for charge and four-momentum operators are derived which exhibit a remarkable formal resemblance to their local counterparts. It is shown that the essential results of the LSZ formalism for interacting fields also have their counterpart in SQFT, and that the same holds true of Wightman's reconstruction theorem. Fields on quantum space-time do not obey the local (anti)-commutativity postulate, but we argue that due to the uncertainty principle this postulate cannot be operationally justified as an expression of microcausality despite the customary identification of the two notions. An operationally consistent microcausality condition is proposed instead.This work was supported in part by an NRC research grant.     

Construction of homogeneous propagators for massive half-integer spin fields in 3+2 De Sitter space,with implications for the massless limit

In this Letter we obtain explicit expressions of homogeneous propagators for half-integer spin fields and their flat-space limits, showing that propagation is confined inside the light cone. Also, for lower values of spin, flat-space limits are given.     

Current density and field fluctuations in a conducting medium

We study thermal fluctuations in a conducting medium which may be spatially non-uniform and anisotropic. The fluctuation spectra for charge and current density, and for the electromagnetic fields, are expressed in terms of the basic propagators of the macroscopic equations. The theory is based on an application of the generalized Nyquist theorem.