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We give a detailed treatment of electromagnetic signals generated by gravitational waves (GWs) in resonant cavity experiments. Our investigation corrects and builds upon previous studies by carefully accounting for the gauge dependence of relevant quantities. We work in a preferred frame for the laboratory, the proper detector frame, and show how to resum short-wavelength effects to provide analytic results that are exact for GWs of arbitrary wavelength. This formalism allows us to firmly establish that, contrary to previous claims, cavity experiments designed for the detection of axion dark matter only need to reanalyze existing data to search for high-frequency GWs with strains as small as $h\sim 10^{-22}-10^{-21}$. We also argue that directional detection is possible in principle using readout of multiple cavity modes. Further improvements in sensitivity are expected with cutting-edge advances in superconducting cavity technology., Comment: 20 pages + appendix, 7 figures, matches journal version

We calculate the three- and four-loop corrections to the massless fermion propagator in three-dimensional quenched Quantum Electrodynamics with four-component fermions. The three-loop correction is finite and gauge invariant but the four-loop one has singularities except in the Feynman gauge where it is also finite. Our results explicitly show that, up to four loops, gauge-dependent terms are completely determined by lower order ones in agreement with the Landau-Khalatnikov-Fradkin transformation., Comment: 11+4 pages

The Landau-Khalatnikov-Fradkin (LKF) transformation is a powerful and elegant transformation allowing to study the gauge dependence of the propagator of charged particles interacting with gauge fields. With the help of this transformation, we derive a non-perturbative identity between massless propagators in two different gauges. From this identity, we find that the corresponding perturbative series can be exactly expressed in terms of a hatted transcendental basis that eliminates all even Euler $\zeta$-functions. This explains the mystery of even $\zeta$-values observed in multi-loop calculations of Euclidean massless correlators for almost three decades now. Our construction further allows us to derive an exact formula relating hatted and standard $\zeta$-functions to all orders of perturbation theory., Comment: (v2) 9 pages, no figure, published in PRD, few edits in text (some per referee's comments) and references added, no change in results. (v1) 9 pages, no figure

This letter examines diagrammatic cancellations for Quantum Electrodynamics (QED) in the general linear gauge. These cancellations combine Feynman graphs of various topologies and provide a method to reconstruct the gauge dependence of the electron propagator from the result of a particular gauge by means of a linear Dyson-Schwinger equation. We use this method in combination with dimensional regularization to demonstrate how the 3-loop ${\epsilon}$-expansion in the Feynman gauge determines the ${\epsilon}$-expansions for all gauge parameter dependent terms to 4 loops.

Dynamical chiral symmetry breaking (D$\chi$SB) is studied within ($2+1$)-dimensional QED with $N$ four-component fermions. The leading and next-to-leading orders of the $N$ expansion were computed exactly in Refs.~[\onlinecite{Gusynin:2016som,Kotikov:2016prf}] in an arbitrary non-local gauge. In this addendum to [\onlinecite{Kotikov:2016prf}], we show that the resummation of the wave-function renormalization constant at the level of the gap equation yields a {\it complete} cancellation of the gauge dependence of the critical fermion flavour number resulting in: $N_c= 2.8469$, which is such that D$\chi$SB takes place for $N, Comment: (v2) 3+epsilon pages, published in PRD, 2 references added, no change in results (v1) 3 pages, no figure. addendum to arXiv:1609.06912

Analytic calculations in the infrared regime of nonabelian gauge theories are hampered by the presence of Gribov copies which results in some ambiguity in the gauge-fixing procedure. This problem shares strong similarities with the issue of finding the true ground state among a large number of metastable states, a typical situation in the field of statistical physics of disordered systems. Building on this analogy, we propose a new gauge-fixing procedure which, we argue, makes more explicit the influence of the Gribov copies. A 1-loop calculation shows that the dynamics of these copies can lead to the spontaneous generation of a gauge-dependent gluon mass., 5 pages, 1 figure

CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior Nesta tese expomos primeiramente um breve histórico-motivacional para a construção de uma teoria de gravitação quântica, bem como, rápidas revisões orientadas sobre elementos de teorias quânticas de campos e sobre a técnica de Schwinger-Dewitt. De posse destas ferramentas, discutimos a dependência de calibre e da parametrização para uma teoria quântica de gravitação em um espaço-tempo de dimensão arbitrária D. Com este objetivo, calculamos explicitamente as correções quânticas a 1-loop, da ação efetiva da teoria, considerando a parametrização mais geral possível para a métrica quântica. Essa parametrização contém inicialmente sete parâmetros, sendo que alguns deles serão fixados através da condição de fixação de calibre, o que torna o nosso cálculo um pouco mais simples. Por fim, para esta teoria, confirmamos a validade de um teorema geral, o qual garante a independência das divergências on-shell, a 1-loop, com respeito às ambiguidades nas escolhas de calibre e de parametrização da métrica quântica. In this thesis we first present a brief historical-motivational for a construction of a theory of quantum gravitation, as well as quick reviews oriented on elements of quantum field theory and Schwinger- Dewitt technique. In possession of these tools, the gauge and parametrization dependence is discussed in quantum gravity in an arbitrary dimension D. Explicit one-loop calculations are performed within the most general parametrization of quantum metric with seven arbitrary parameters. On the other hand, some of the gauge fixing parameters are fixed to make the calculations relatively simple. We confirm the general theorem stating that the on shell local terms in the one-loop effective action are independent of the gauge and parametrization ambiguity.

Some precisions are given about the definition of the Hamiltonian operator H and its transformation properties, for a linear wave equation in a general spacetime. In the presence of time-dependent unitary gauge transformations, H as an operator depends on the gauge choice. The other observables of QM and their rates also become gauge-dependent unless a proper account for the gauge choice is done in their definition. We show the explicit effect of these non-uniqueness issues in the case of the Dirac equation in a general spacetime with the Schwinger gauge. We show also in detail why, the meaning of the energy in QM being inherited from classical Hamiltonian mechanics, the energy operator and its mean values ought to be well defined in a general spacetime., Comment: 25 pages, conforms exactly with the published version. arXiv admin note: text overlap with arXiv:1312.6707

We evaluate the one-graviton loop contribution to the vacuum polarization on de Sitter background in a 1-parameter family of exact, de Sitter invariant gauges. Our result is computed using dimensional regularization and fully renormalized with BPHZ counterterms, which must include a noninvariant owing to the time-ordered interactions. Because the graviton propagator engenders a physical breaking of de Sitter invariance two structure functions are needed to express the result. In addition to its relevance for the gauge issue this is the first time a covariant gauge graviton propagator has been used to compute a noncoincident loop. A number of identities are derived which should facilitate further graviton loop computations., Comment: 61 pages, 1 figure, 11 tables, version 2 (63 pages) revised for publication in CQG

We employ a recent, general gauge computation of the one loop graviton contribution to the vacuum polarization on de Sitter to solve for one loop corrections to the photon mode function. The vacuum polarization takes the form of a gauge independent, spin 2 contribution and a gauge dependent, spin 0 contribution. We show that the leading secular corrections derive entirely from the spin 2 contribution., Comment: 41 pages, no figures, uses LaTeX2e

We report on an explicit on-shell framework to renormalize the fermion-flavour mixing matrices in the Standard Model and its extensions, at one-loop level. It is based on a novel procedure to separate the external-leg mixing corrections into gauge-independent self-mass and gauge-dependent wave-function renormalization contributions., Comment: to appear in Proceedings of Lepton-Photon 2009, Hamburg, Germany

Calculations of atomic axial tensors (AATs) using the localized orbital/local origin (LORG) method are presented. The accuracy of the AATs obtained from this method is compared to the accuracy obtained in calculations using the common origin (GO) method, the distributed origin (DO) method, and the London method for four small molecules, at two basis set levels (VD/3P and DZ/POL). LORG and DO AATs are of comparable accuracy. The LORG method enables AATs to be broken down into contributions from individual localized orbitals, and this is illustrated in a calculation on formic acid, for which we also present a localized orbital decomposition of the atomic polar tensors (APTs). The same calculation is used to detail the local contributions to the AATs, which are omitted in the approximate localized molecular orbital (LMO) model.