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     

Real time thermal propagators for massive gauge bosons

We derive Feynman rules for gauge theories exhibiting spontaneous symmetry breaking using the real-time formalism of finite temperature field theory. We also derive the thermal propagators where only the physical degrees of freedom are given thermal boundary conditions. We analyse the abelian Higgs model and find that these new propagators simplify the calculation of the thermal contribution to the self energy.     

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.     

One-loop renormalizability of noncommutative U(1) gaugetheory with scalar fields

This paper uses the background field method to calculate one-loop divergent corrections to the gauge field propagators in noncommutative U(1) gauge theory with scalar fields. It shows that for a massless scalar field, the gauge field propagators are renormalizable to θ²-order, but for a massive scalar field they are renormalizable only to θ-order.     

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.     

Axial gauge propagators for quarks and gluons on the Polyakov-Wilson lattice

We discuss problems encountered in defining gauge-dependent propagators in a confining theory. For precision we use a finite Polyakov-Wilson lattice to define the Yang-Mills theory and to provide the ultraviolet and infrared regularization. Gauge fixing in a class of superaxial gauges is natural in this framework. A variety of approaches for defining the propagators for quarks and gluons is discussed and the propagators are evaluated explicitly in the strong coupling limit. We speculate upon the infrared behavior of these propagators in the weak coupling limit and upon the utility and validity of the Schwinger-Dyson equations for these propagators. In conclusion we propose that the leading infrared behavior is strongly gauge dependent and governed by the masses of low-lying color singlet states in the hadron spectrum. In the ultraviolet limit, however, with a properly constructed propagator, we find no reason to question the conventional wisdom derived from perturbation theory. Our conclusions should not depend in any fundamental way on the lattice formulation of the gauge theory, except insofar as that formulation serves to give precision to the continuum functional integration.     

Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge

We study the Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge, considering both the pure Coulomb gauge and the gauge where in addition the remaining constant gauge field is restricted to the Cartan algebra. We evaluate the corresponding Faddeev-Popov determinants, resolve Gauss’ law and derive the Hamiltonians, which differ in both gauges due to additional zero modes of the Faddeev-Popov kernel in the pure Coulomb gauge. By Gauss’ law the zero modes of the Faddeev-Popov kernel constrain the physical wave functionals to zero colour charge states. We solve the Schrödinger equation in the pure Coulomb gauge and determine the vacuum wave functional. The gluon and ghost propagators and the static colour Coulomb potential are calculated in the first Gribov region as well as in the fundamental modular region, and Gribov copy effects are studied. We explicitly demonstrate that the Dyson-Schwinger equations do not specify the Gribov region while the propagators and vertices do depend on the Gribov region chosen. In this sense, the Dyson-Schwinger equations alone do not provide the full non-abelian quantum gauge theory, but subsidiary conditions must be required. Implications of Gribov copy effects for lattice calculations of the infrared behaviour of gauge-fixed propagators are discussed. We compute the ghost-gluon vertex and provide a sensible truncation of Dyson-Schwinger equations. Approximations of the variational approach to the 3 + 1 dimensional theory are checked by comparison to the 1 + 1 dimensional case.     

The hydrogen atom in strong magnetic fields: Summation of the weak field series expansion: J. C. Le Guillou. Laboratoire de Physique Théorique et Hautes Energies,Université Paris VI, 75230 Paris Cedex 05, France; and J. Zinn-Justin. Service de Physique Théorique,Centre d'Etudes Nucléaires de Saclay, 91191 Gif-sur-Yvette,France

Multiple reflection expansions are derived for scalar, Dirac, and gauge field propagators obeying confining boundary conditions.     

Renormalization and asymptotic behavior in a finite quantum field theory with shadow states

In this paper we present a study of the renormalization problem in a finite quantum field theory with shadow states for a system of a physical scalar field interacting with a physical fermion field. In order to make the theory finite, two fermion shadow fields are introduced. We observe that the stability criterion of renormalization can not be satisfied simultaneously by both physical fields and shadow fields, if the finiteness of the theory is to be maintained. A physical interpretation of this result is given. Furthermore, we find that the effective complete propagators for large space-like momenta behave like free field propagators without the logarithmic factors observed in the non-abelian gauge theory.     

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.     

Fixed point action for the massless lattice Schwinger model

We determine non-perturbatively the fixed-point action for fermions in the two-dimensional U(1) gauge (Schwinger) model. This is done by iterating a block spin transformation in the background of non-compact gauge field configurations sampled according to the (perfect) Gausian measure. The resulting action has 123 independent couplings, is bilinear in the Grassmann fields, gauge invariant by the compact gauge transporters considered, and localized within a 7 × 7 lattice centered around one of the fermions. We then simulate the model at various values of β and compare with results obtained with the Wilson fermion action. We find excellent improvement for the observables studied (propagators and masses).     

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.     

Accessing directly the properties of fundamental scalars in the confinement and Higgs phase

The properties of elementary particles are encoded in their respective propagators and interaction vertices. For a SU(2) gauge theory coupled to a doublet of fundamental complex scalars these propagators are determined in both the Higgs phase and the confinement phase and compared to the Yang–Mills case, using lattice gauge theory. Since the propagators are gauge dependent, this is done in the Landau limit of the ’t Hooft gauge, permitting to also determine the ghost propagator. It is found that neither the gauge boson nor the scalar differ qualitatively in the different cases. In particular, the gauge boson acquires a screening mass, and the scalar’s screening mass is larger than the renormalized mass. Only the ghost propagator shows a significant change. Furthermore, indications are found that the consequences of the residual non-perturbative gauge freedom due to Gribov copies could be different in the confinement and the Higgs phase.     

Supersymmetric anyon model coupled to the electromagnetic field

We construct a supersymmetric gauge model describing the electromagnetic interaction of anyons. This is done by means of the supersymmetric generalization of theU(1) ×U(1) gauge theory. The model contains the statisticalU(1) gauge field endowed with a Chern-Simons mass term and the electromagnetic field, both with the corresponding superpartners, coupled to matter fields. This constrained system is analyzed from the Hamiltonian point of view and the canonical quantization is found. The path-integral method is used to develop the perturbative formalism. We define suitable propagators and vertices and give the diagrammatics and the Feynman rules.     

Comment on real-time finite-temperature gauge field propagators

The gauge-fixing terms of the free, real-time thermal gauge field propagators corresponding to quantization in a covariant gauge obtained by Kobes, Semenoff, and Weiss are shown to be incorrect, apart from well-known signature ambiguities in the off-diagonal elements, and to differ from those obtained by Landsman using the method of the Klein-Gordon divisor. We obtain the correct forms which are then shown to coincide with Landsman's results by means of a distributional identity.     

Gravity and Spin Forces in Gravitational Quantum Field Theory

In the new framework of gravitational quantum field theory(GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93(2016) 024012-1, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newton's gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.     

Short distance propagators in a background field

We derive an operator expansion of the scalar, the spinor and the vector propagators in the presence of an arbitrary long range background field, using the Schwinger-DeWitt ‘proper time’ formalism. This has the advantage of keeping the expansion gauge covariant at all stages. These results may be used to calculate the leading background effects in the one-loop correlation functions.     

Gravity and Spin Forces in Gravitational Quantum Field Theory

In the new framework of gravitational quantum field theory (GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93 (2016) 024012-1, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newton's gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.     

Lorentz-invariant ensembles of vector backgrounds

We consider gauge field theories in the presence of ensembles of vector backgrounds. While Lorentz invariance is explicitly broken in the presence of any single background, here, the Lorentz invariance of the theory is restored by averaging over a Lorentz-invariant ensemble of backgrounds, i.e., a set of background vectors that is mapped onto itself under Lorentz transformations. This framework is used to study the effects of a non-trivial but Lorentz-invariant vacuum structure or mass dimension two vector condensates by identifying the background with a shift of the gauge field. Up to now, the ensembles used in the literature comprise configurations corresponding to non-zero field tensors together with such with vanishing field strength. We find that even when constraining the ensembles to pure gauge configurations, the usual high-energy degrees of freedom are removed from the spectrum of asymptotic states in the presence of said backgrounds in Euclidean and in Minkowski space. We establish this result not only for the propagators to all orders in the background and otherwise at tree level but for the full propagator.     

Real-time Feynman rules for gauge theories with fermions at finite temperature and density

We derive Feynman rules for gauge theories with fermions at finite temperature and density which use thermal propagators with real time arguments.