Asymptotic analysis | Perturbation theory

Perturbation problem beyond all orders

In mathematics, perturbation theory works typically by expanding unknown quantity in a power series in a small parameter. However, in a perturbation problem beyond all orders, all coefficients of the perturbation expansion vanish and the difference between the function and the constant function 0 cannot be detected by a power series. A simple example is understood by an attempt at trying to expand in a Taylor series in about 0. All terms in a naïve Taylor expansion are identically zero. This is because the function possesses an essential singularity at in the complex -plane, and therefore the function is most appropriately modeled by a Laurent series -- a Taylor series has a zero radius of convergence. Thus, if a physical problem possesses a solution of this nature, possibly in addition to an analytic part that may be modeled by a power series, the perturbative analysis fails to recover the singular part. Terms of nature similar to are considered to be "beyond all orders" of the standard perturbative power series. (Wikipedia).

Video thumbnail

Quantum Field Theory 4d - Second Quantization IV

We end our discussion of second quantization with the details of perturbation theory.

From playlist Quantum Field Theory

Video thumbnail

Transcendental Functions 17 The Indefinite Integral of 1 over u du Example 2.mov

More example problems involving the integral of 1 over u, du.

From playlist Transcendental Functions

Video thumbnail

Transcendental Functions 17 The Indefinite Integral of 1 over u du Example 1.mov

Example problems involving the integral of u to the power negative 1 du.

From playlist Transcendental Functions

Video thumbnail

Maxim Kazarian - 3/3 Mathematical Physics of Hurwitz numbers

Hurwitz numbers enumerate ramified coverings of a sphere. Equivalently, they can be expressed in terms of combinatorics of the symmetric group; they enumerate factorizations of permutations as products of transpositions. It turns out that these numbers obey a huge num

From playlist ­­­­Physique mathématique des nombres de Hurwitz pour débutants

Video thumbnail

Maxim Kazarian - 1/3 Mathematical Physics of Hurwitz numbers

Hurwitz numbers enumerate ramified coverings of a sphere. Equivalently, they can be expressed in terms of combinatorics of the symmetric group; they enumerate factorizations of permutations as products of transpositions. It turns out that these numbers obey a huge num

From playlist ­­­­Physique mathématique des nombres de Hurwitz pour débutants

Video thumbnail

Maxim Kazarian - 2/3 Mathematical Physics of Hurwitz numbers

Hurwitz numbers enumerate ramified coverings of a sphere. Equivalently, they can be expressed in terms of combinatorics of the symmetric group; they enumerate factorizations of permutations as products of transpositions. It turns out that these numbers obey a huge num

From playlist ­­­­Physique mathématique des nombres de Hurwitz pour débutants

Video thumbnail

Gérald DUNNE - Resurgent Trans-series Analysis of Hopf Algebraic Renormalization

In the Kreimer-Connes Hopf algebraic approach to renormalization, for certain QFTs the Dyson-Schwinger equations can be reduced to nonlinear differential equations. I describe methods based on Ecalle's theory of resurgent trans-series to extract non-perturbative information from these Dyso

From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday

Video thumbnail

Michael Green -- String Scattering Amplitudes, Feynman diagrams, and M-theory

This workshop seeks to explore connections between geometric flows and other areas of mathematics and physics. Geometric flows refer to ways in which geometry can be deformed smoothly in time, rather analogous to the way in which the geometry of the surface of a balloon becomes smooth and

From playlist Research Lectures

Video thumbnail

Mechanics of Dimples & Jets from an Axisymmetric, Collapsing Wave Trough by Ratul Dasgupta

DISCUSSION MEETING WAVES, INSTABILITIES AND MIXING IN ROTATING AND STRATIFIED FLOWS (ONLINE) ORGANIZERS: Thierry Dauxois (CNRS & ENS de Lyon, France), Sylvain Joubaud (ENS de Lyon, France), Manikandan Mathur (IIT Madras, India), Philippe Odier (ENS de Lyon, France) and Anubhab Roy (IIT M

From playlist Waves, Instabilities and Mixing in Rotating and Stratified Flows (ONLINE)

Video thumbnail

Studying thermal QCD matter on the lattice (LQCD1 - Lecture 1) by Peter Petreczky

PROGRAM THE MYRIAD COLORFUL WAYS OF UNDERSTANDING EXTREME QCD MATTER ORGANIZERS: Ayan Mukhopadhyay, Sayantan Sharma and Ravindran V DATE: 01 April 2019 to 17 April 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Strongly interacting phases of QCD matter at extreme temperature and

From playlist The Myriad Colorful Ways of Understanding Extreme QCD Matter 2019

Video thumbnail

Fractionalized fermionic quantum criticality by Lukas Janssen

PROGRAM FRUSTRATED METALS AND INSULATORS (HYBRID) ORGANIZERS Federico Becca (University of Trieste, Italy), Subhro Bhattacharjee (ICTS-TIFR, India), Yasir Iqbal (IIT Madras, India), Bella Lake (Helmholtz-Zentrum Berlin für Materialien und Energie, Germany), Yogesh Singh (IISER Mohali, In

From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)

Video thumbnail

Alexandre Tkatchenko - Many-body perturbation theory and wavefunction methods: A Physics perspective

Recorded 08 March 2022. Alexandre Tkatchenko of the University of Luxembourg presents "Many-body perturbation theory and wavefunction methods: A Physics perspective" at IPAM's Advancing Quantum Mechanics with Mathematics and Statistics Tutorials. Learn more online at: http://www.ipam.ucla.

From playlist Tutorials: Advancing Quantum Mechanics with Mathematics and Statistics - March 8-11, 2022

Video thumbnail

Introduction to Resurgence, Trans-series and Non-perturbative Physics III by Gerald Dunne

Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to

From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography

Video thumbnail

The Orientation Dynamics of Sedimenting Anisotropic Particles in a Stratified by Ganesh Subramanian

DISCUSSION MEETING WAVES, INSTABILITIES AND MIXING IN ROTATING AND STRATIFIED FLOWS (ONLINE) ORGANIZERS: Thierry Dauxois (CNRS & ENS de Lyon, France), Sylvain Joubaud (ENS de Lyon, France), Manikandan Mathur (IIT Madras, India), Philippe Odier (ENS de Lyon, France) and Anubhab Roy (IIT M

From playlist Waves, Instabilities and Mixing in Rotating and Stratified Flows (ONLINE)

Video thumbnail

Signatures of Deconfined Quantum Criticality in a spin-1 Model on the Square ... by Vikas Vijigiri

DISCUSSION MEETING 8TH INDIAN STATISTICAL PHYSICS COMMUNITY MEETING ORGANIZERS: Ranjini Bandyopadhyay (RRI, India), Abhishek Dhar (ICTS-TIFR, India), Kavita Jain (JNCASR, India), Rahul Pandit (IISc, India), Samriddhi Sankar Ray (ICTS-TIFR, India), Sanjib Sabhapandit (RRI, India) and Prer

From playlist 8th Indian Statistical Physics Community Meeting-ispcm 2023

Video thumbnail

Lecture 06-Jack Simons Electronic Structure Theory- Møller-Plesset perturbation theory

Determining the CI amplitudes using Moller-Plesset perturbation theory (MPn); Brillouin theorem; strengths and weaknesses of MPn; non-convergence of MPn can give crazy results. (1)Jack Simons Electronic Structure Theory- Session 1- Born-Oppenheimer approximation http://www.youtube.com/

From playlist U of Utah: Jack Simons' Electronic Structure Theory course

Video thumbnail

Mike Boyle - Nonnegative matrices : Perron Frobenius theory and related algebra (Part 3)

Nonnegative matrices : Perron Frobenius theory and related algebra (Part 3) Licence: CC BY NC-ND 4.0Lecture I. I’ll give a complete elementary presentation of the essential features of the Perron Frobenius theory of nonnegative matrices for the central case of primitive matrices (the "Perr

From playlist École d’été 2013 - Théorie des nombres et dynamique

Related pages

Radius of convergence | Laurent series | Perturbation theory | Asymptotic expansion | Power series | Essential singularity | Taylor series | Flat function