scholarly journals GAUGE-INVARIANT VARIABLES IN GENERAL-RELATIVISTIC PERTURBATIONS: GLOBALIZATION AND ZERO-MODE PROBLEM

2012 ◽  
Vol 21 (11) ◽  
pp. 1242004 ◽  
Author(s):  
KOUJI NAKAMURA
Keyword(s):  
Perturbation Theory ◽  
Zero Mode ◽  
Higher Order ◽  
Gauge Invariant ◽  
General Relativistic ◽  
Essential Problem ◽  
Invariant Perturbation Theory

An outline of a proof of the local decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts on an arbitrary background spacetime is briefly explained. We explicitly construct the gauge-invariant and gauge-variant parts of the linear metric perturbations based on some assumptions. We also point out the zero-mode problem is an essential problem to globalize of this decomposition of linear metric perturbations. The resolution of this zero-mode problem implies the possibility of the development of the higher-order gauge-invariant perturbation theory on an arbitrary background spacetime in a global sense.

scholarly journals Gauge invariant perturbation theory via homotopy transfer

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Christoph Chiaffrino ◽  
Olaf Hohm ◽  
Allison F. Pinto
Keyword(s):  
Perturbation Theory ◽  
Lie Algebras ◽  
Closed String ◽  
Cosmological Perturbation ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Cosmological Perturbation Theory ◽  
Invariant Perturbation Theory ◽  
General Gauge ◽  
Algorithmic Procedure

Abstract We show that the perturbative expansion of general gauge theories can be expressed in terms of gauge invariant variables to all orders in perturbations. In this we generalize techniques developed in gauge invariant cosmological perturbation theory, using Bardeen variables, by interpreting the passing over to gauge invariant fields as a homotopy transfer of the strongly homotopy Lie algebras encoding the gauge theory. This is illustrated for Yang-Mills theory, gravity on flat and cosmological backgrounds and for the massless sector of closed string theory. The perturbation lemma yields an algorithmic procedure to determine the higher corrections of the gauge invariant variables and the action in terms of these.

scholarly journals Pair production processes and flavor in gauge-invariant perturbation theory

2017 ◽  
Vol 32 (38) ◽  
pp. 1750212 ◽  
Author(s):  
Larissa Egger ◽  
Axel Maas ◽  
René Sondenheimer
Keyword(s):  
Perturbation Theory ◽  
Standard Model ◽  
Pair Production ◽  
Bound State ◽  
Gauge Invariant ◽  
Quantum Numbers ◽  
The Standard Model ◽  
Invariant States ◽  
The Impact ◽  
Invariant Perturbation Theory

Gauge-invariant perturbation theory is an extension of ordinary perturbation theory which describes strictly gauge-invariant states in theories with a Brout–Englert–Higgs effect. Such gauge-invariant states are composite operators which have necessarily only global quantum numbers. As a consequence, flavor is exchanged for custodial quantum numbers in the Standard Model, recreating the fermion spectrum in the process. Here, we study the implications of such a description, possibly also for the generation structure of the Standard Model. In particular, this implies that scattering processes are essentially bound-state–bound-state interactions, and require a suitable description. We analyze the implications for the pair-production process [Formula: see text] at a linear collider to leading order. We show how ordinary perturbation theory is recovered as the leading contribution. Using a PDF-type language, we also assess the impact of sub-leading contributions. To lowest order, we find that the result is mainly influenced by how large the contribution of the Higgs at large [Formula: see text] is. This gives an interesting, possibly experimentally testable, scenario for the formal field theory underlying the electroweak sector of the Standard Model.

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