42 research outputs found
An approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions
In this paper, we provide an approach for the calculation of one-loop
effective actions, vacuum energies, and spectral counting functions and discuss
the application of this approach in some physical problems. Concretely, we
construct the equations for these three quantities; this allows us to achieve
them by directly solving equations. In order to construct the equations, we
introduce shifted local one-loop effective actions, shifted local vacuum
energies, and local spectral counting functions. We solve the equations of
one-loop effective actions, vacuum energies, and spectral counting functions
for free massive scalar fields in , scalar fields in
three-dimensional hyperbolic space (the Euclidean Anti-de Sitter space
), in (the geometry of the Euclidean BTZ black hole), and in
, and the Higgs model in a -dimensional finite interval.
Moreover, in the above cases, we also calculate the spectra from the counting
functions. Besides exact solutions, we give a general discussion on approximate
solutions and construct the general series expansion for one-loop effective
actions, vacuum energies, and spectral counting functions. In doing this, we
encounter divergences. In order to remove the divergences, renormalization
procedures are used. In this approach, these three physical quantities are
regarded as spectral functions in the spectral problem.Comment: 37 pages, no figure. This is an enlarged and improved version of the
paper published in JHE
Computing the effective action with the functional renormalization group
The \u201cexact\u201d or \u201cfunctional\u201d renormalization group equation describes the renormalization group flow of the effective average action \u393 k. The ordinary effective action \u393 0 can be obtained by integrating the flow equation from an ultraviolet scale k= \u39b down to k= 0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang\u2013Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity. \ua9 2016, The Author(s)
Quantum corrections to Schwarzschild black hole
Using effective field theory techniques, we compute quantum corrections to spherically symmetric solutions of Einstein’s gravity and focus in particular on the Schwarzschild black hole. Quantum modifications are covariantly encoded in a non-local effective action. We work to quadratic order in curvatures simultaneously taking local and non-local corrections into account. Looking for solutions perturbatively close to that of classical general relativity, we find that an eternal Schwarzschild black hole remains a solution and receives no quantum corrections up to this order in the curvature expansion. In contrast, the field of a massive star receives corrections which are fully determined by the effective field theory
Measuring the gravitational field in General Relativity: From deviation equations and the gravitational compass to relativistic clock gradiometry
How does one measure the gravitational field? We give explicit answers to
this fundamental question and show how all components of the curvature tensor,
which represents the gravitational field in Einstein's theory of General
Relativity, can be obtained by means of two different methods. The first method
relies on the measuring the accelerations of a suitably prepared set of test
bodies relative to the observer. The second methods utilizes a set of suitably
prepared clocks. The methods discussed here form the basis of relativistic
(clock) gradiometry and are of direct operational relevance for applications in
geodesy.Comment: To appear in "Relativistic Geodesy: Foundations and Application", D.
Puetzfeld et. al. (eds.), Fundamental Theories of Physics, Springer 2018, 52
pages, in print. arXiv admin note: text overlap with arXiv:1804.11106,
arXiv:1511.08465, arXiv:1805.1067
Self-force: Computational Strategies
Building on substantial foundational progress in understanding the effect of
a small body's self-field on its own motion, the past 15 years has seen the
emergence of several strategies for explicitly computing self-field corrections
to the equations of motion of a small, point-like charge. These approaches
broadly fall into three categories: (i) mode-sum regularization, (ii) effective
source approaches and (iii) worldline convolution methods. This paper reviews
the various approaches and gives details of how each one is implemented in
practice, highlighting some of the key features in each case.Comment: Synchronized with final published version. Review to appear in
"Equations of Motion in Relativistic Gravity", published as part of the
Springer "Fundamental Theories of Physics" series. D. Puetzfeld et al.
(eds.), Equations of Motion in Relativistic Gravity, Fundamental Theories of
Physics 179, Springer, 201