Gauge independent quantum gravitational corrections to Maxwell’s equation

We consider quantum gravitational corrections to Maxwell’s equations on flat space background. Although the vacuum polarization is highly gauge dependent, we explicitly show that this gauge dependence is canceled by contributions from the source which disturbs the effective field and the observer who measures it. Our final result is a gauge independent, real and causal effective field equation that can be used in the same way as the classical Maxwell equation.

Gauge invariance, polar coordinates and inflation

We point out the necessity of resolving the apparent gauge dependence in the quantum corrections of cosmological observables for Higgs-like inflation models. We highlight the fact that this gauge dependence is due to the use of an asymmetric background current which is specific to a choice of coordinate system in the scalar manifold. Favoring simplicity over complexity, we further propose a practical shortcut to gauge-independent inflationary observables by using effective potential obtained from a polar-like background current choice. We demonstrate this shortcut for several explicit examples and present a gauge-independent prediction of inflationary observables in the Abelian Higgs model. Furthermore, with Nielsen’s gauge dependence identities, we show that for any theory to all orders, a gauge-invariant current term gives a gauge-independent effective potential and thus gauge-invariant inflationary observables.

Quantum gauge theories

This chapter, which is the last chapter in Part I, is devoted to an extensive discussion of quantum gauge theories, which is based on functional integrals and Lagrangian quantization. After introducing the notion of a Yang-Mills gauge theory, the Faddeev-Popov method (also known as the DeWitt-Faddeev-Popov procedure) is explained. Starting from this point, the BRST symmetry is formulated, and the corresponding Ward identities (called Slavnov-Taylor identities in some cases) established. More specialized subjects, such as the gauge dependence of effective action and the background field method, are dealt with in detail. In addition, Yang-Mills theory is analyzed as a primary example of general theorems concerning the renormalization of gauge theories.

A critical look at the electroweak phase transition

The electroweak phase transition broke the electroweak symmetry. Perturbative methods used to calculate observables related to this phase transition suffer from severe problems such as gauge dependence, infrared divergences, and a breakdown of perturbation theory. In this paper we develop robust perturbative tools for dealing with phase transitions. We argue that gauge and infrared problems are absent in a consistent power-counting. We calculate the finite temperature effective potential to two loops for general gauge-fixing parameters in a generic model. We demonstrate gauge invariance, and perform numerical calculations for the Standard Model in Fermi gauge.

Towards Higgs masses and decay widths satisfying the symmetries in the (N)MSSM

In models with an extended Higgs sector, such as the (N)MSSM, scalar states mix with one another. Yet, the concept of Higgs mixing is problematic at the radiative level, since it introduces both a scheme and a gauge dependence. In particular, the definition of Higgs masses and decay amplitudes can be impaired by the presence of gauge-violating pieces of higher order. We discuss in depth the origin and magnitude of such effects and consider two strategies that minimize the dependence on the gauge-fixing parameter and field-renormalization of one-loop order in the definition of the mass and decay observables, both in degenerate and non-degenerate scenarios. In addition, the intuitive concept of mixing and the simplicity of its definition in terms of two-point diagrams can make it tempting to include higher-order corrections on this side of the calculation, irrespectively of the order achieved in vertex diagrams. Using the global $$SU(2)_{\mathrm{L}}$$ S U ( 2 ) L -symmetry in the decoupling limit, we show that no improvement can be expected from such an approach at the level of the Higgs decays, but that, on the contrary, the higher-order terms may lead to numerically large spurious effects.

Composite and Background Fields in Non-Abelian Gauge Models

A joint introduction of composite and background fields into non-Abelian quantum gauge theories is suggested based on the symmetries of the generating functional of Green’s functions, with the systematic analysis focused on quantum Yang–Mills theories, including the properties of the generating functional of vertex Green’s functions (effective action). For the effective action in such theories, gauge dependence is found in terms of a nilpotent operator with composite and background fields, and on-shell independence from gauge fixing is established. The basic concept of a joint introduction of composite and background fields into non-Abelian gauge theories is extended to the Volovich–Katanaev model of two-dimensional gravity with dynamical torsion, as well as to the Gribov–Zwanziger theory.

Gauge Dependence of the S Molecular Orbital Space Decomposition of Optical Rotation

<div> <div> <div> <p>Optical rotation (OR) is a foundational technique for the detection and characterization of chiral molecules, but it is poorly understood how the observed property relates to the structure of the molecule. Over the years, several schemes have been developed to de- compose the OR into more chemically intuitive contributions. In this paper, we introduce two alternative formulations of our previously developed S molecular orbital space decomposition. These new expressions use the Modified Velocity Gauge-Magnetic (MVG-M) and -Electric (MVG-E) definitions of OR, rather than the Length Gauge Magnetic (LG-M) definition used in the original paper. Comparing these formulations across a small set of previously studied chiral molecules, we find that these different definitions produce consistent physical interpretations of the OR. These results further confirm the robustness of the S methodology for the investigation of structure-property relationships in chiral molecules.</p> </div> </div> </div>

Gauge Dependence of the S Molecular Orbital Space Decomposition of Optical Rotation

<div> <div> <div> <p>Optical rotation (OR) is a foundational technique for the detection and characterization of chiral molecules, but it is poorly understood how the observed property relates to the structure of the molecule. Over the years, several schemes have been developed to de- compose the OR into more chemically intuitive contributions. In this paper, we introduce two alternative formulations of our previously developed S molecular orbital space decomposition. These new expressions use the Modified Velocity Gauge-Magnetic (MVG-M) and -Electric (MVG-E) definitions of OR, rather than the Length Gauge Magnetic (LG-M) definition used in the original paper. Comparing these formulations across a small set of previously studied chiral molecules, we find that these different definitions produce consistent physical interpretations of the OR. These results further confirm the robustness of the S methodology for the investigation of structure-property relationships in chiral molecules.</p> </div> </div> </div>