We study the heat kernel for the Laplace type partial differential operator acting on smooth sections of a complex spin-tensor bundle over a generic $n$-dimensional Riemannian manifold. Assuming that the curvature of the U(1) connection (that we call the electromagnetic field) is constant we compute the first two coefficients of the non-perturbative asymptotic expansion of the heat kernel which are of zero and the first order in Riemannian curvature and of arbitrary order in the electromagnetic field. We apply these results to the study of the effective action in non-perturbative electrodynamics in four dimensions and derive a generalization of the Schwinger's result for the creation of scalar and spinor particles in electromagnetic field induced by the gravitational field. We discover a new infrared divergence in the imaginary part of the effective action due to the gravitational corrections, which seems to be a new physical effect.
We study the transformation of the dressed electron propagator and the general $N$-point functions under a change in the covariant gauge of internal photon propagators. We re-establish the well known Landau-Khalatnikov-Fradkin transformation for the propagator and generalise it to arbitrary correlation functions in configuration space, finding that it coincides with the analogous result for scalar fields. We comment on the consequences for perturbative application in momentum-space.
An approach that has been given promising results concerning investigations on the physics of graphene is the so-called reduced quantum electrodynamics. In this work we consider the natural generalization of this formalism to curved spaces. We employ the local momentum space representation. We discuss the validity of the Ward identity and study one-loop diagrams in detail. We show that the one-loop beta function is zero. As an application, we calculate the one-loop optical conductivity of graphene by taking into account curvature effects which can be incorporated locally. In addition, we demon…
We propose to develop the Kalb-Ramond theory in four-dimensional spacetime at the level of a classical field theory by following the same formal development steps as in Maxwell theory of standard electrodynamics. Solutions of Kalb-Ramond theory in the presence of static sources in various curved spacetimes are then analyzed. A question that we address here is that of a possible Kalb-Ramond polarization in curved spacetimes, like one can encounter a dielectric polarization in ordinary Maxwell electrodynamics in certain types of spacetimes.
Despite the large amount of work done in quantum field theory in curved space-times, there are not great many results available for perturbative calculations of particle processes in these systems. Such processes are expected to be important in the early stages of the universe, as well as near highly relativistic objects like black holes and, recently, in effective field theories of condensed matter systems. The difficulties with carrying out perturbative calculations in curved space-times are related to the practical difficulty of quantizing in curved space-times. This suggests the need for i…
In this paper, we give an update on divergent problems concerning the radiative corrections of quantum electrodynamics in $(3+1)$ dimensions. In doing so, we introduce a geometric adaptation for the covariant photon propagator by including a higher derivative field. This derivation, so-called generalized quantum electrodynamics, is motivated by the stability and unitarity features. This theory provides a natural and self-consistent extension of the quantum electrodynamics by enlarging the space parameter of spinor-gauge interactions. In particular, Haag$'$s theorem undermines the perturbative …
String geometry theory is one of the candidates of the non-perturbative formulation of string theory. In this paper, from the closed bosonic sector of string geometry theory, we derive path integrals of all order perturbative strings on all the string backgrounds, $G_{μν}(x)$, $B_{μν}(x)$, and $Φ(x)$, by considering fluctuations around the string background configurations, which are parametrized by the string backgrounds.
In this work, we provide a non-perturbative description of the phenomenon of dynamical mass generation in the case of quantum electrodynamics in $2+1$ dimensions. We will use the Kugo-Ojima-Nakanishi formalism to conclude that the physical Hilbert space of the asymptotic photon field is the same as that of the Maxwell-Chern-Simons.
We show how quantum many-body systems on hyperbolic lattices with nearest-neighbor hopping and local interactions can be mapped onto quantum field theories in continuous negatively curved space. The underlying lattices have recently been realized experimentally with superconducting resonators and therefore allow for a table-top quantum simulation of quantum physics in curved background. Our mapping provides a computational tool to determine observables of the discrete system even for large lattices, where exact diagonalization fails. As an application and proof of principle we quantitatively r…
Landau-Khalatnikov-Fradkin Transformations in Reduced Quantum Electrodynamics: Perturbative and Nonperturbative Dynamics of the Fermion Propagator
Quaid-i-Azam University（奎德-e-阿扎姆大学）；Air University（空军大学）；University of the Punjab（旁遮普大学）；Universidad Michoacana de San Nicolás de Hidalgo（圣尼古拉斯德伊达尔戈米却肯自治大学）；Universidad de Huelva（韦尔瓦大学）；Universidad Autónoma de Querétaro（克雷塔罗自治大学）；Universidad de Sonora（索诺拉大学）
We study 7D maximally supersymmetric Yang-Mills theory on curved manifolds that admit Killing spinors. If the manifold admits at least two Killing spinors (Sasaki-Einstein manifolds) we are able to rewrite the supersymmetric theory in terms of a cohomological complex. In principle this cohomological complex makes sense for any K-contact manifold. For the case of toric Sasaki-Einstein manifolds we derive explicitly the perturbative part of the partition function and speculate about the non-perturbative part. We also briefly discuss the case of 3-Sasaki manifolds and suggest a plausible form for…
