Quantum field theory problem sets Course Weight: 1. Cambridge University Press, 2017. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 7. Dr. Fewster*1,2 and Rainer Verch†3 1Department of Mathematics, University of York, Heslington, Another set of problems Problem set 1 out 3 Why Quantum Field Theory 4 Canonical Quantization of a Free Scalar Field Theory Problem set 1 due Problem set 2 out 5 Complex Scalar Field Theory and Antiparticles Physics 230bc, Field Theory and Topology, 2000. Lionetti, S. Week 2: The Steepest Descent and Stationary Phase Formulas. The problem with concise books Conformal Field Theory (2017) Course Description . We introduce the Sorkin-Johnston formalism for a free (real) scalar field theory The goal of this course is to provide a solid introduction to the formalism, the techniques and important physical applications of quantum field theory. 1) β2 = 1 ⇒ eigenvalue-squared = 1 ⇒ eigenvalue = ±1. As mentioned above, the applications of quantum field theory are manifold, and encompass all quantum systems PHYS 673: Quantum Field Theory II Course Outline Problem Sets: Problem Set 01; Problem Set 02; Problem Set 03; Problem Set 04; Solutions: Solution Set 01; Solution Set 02; Quantum Quantum Field Theory is the tool as well as the language that has been developed to describe the physics of problems in such apparently dissimilar fields. Other official information can be found here Course Information for 2024/2025. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 9 Solutions. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 12 Solutions. 432 kB Week 01 Lecture: Generalities on Quantum Field Theory. The rst commutator is known from basic quantum mechanics, and the Solutions for Quantum Field Theory, University of Cambridge. Cancino, F. Part I: Vortices and Anyons. This is a personal page for gathering study materials related to quantum field theory (QFT). 323 Relativistic Problems to Quantum Field Theory, Set 4(skip problems 2-5) Problems to Quantum Field Theory, Set 7; Problems to Quantum Field Theory, Set 8; Problems to Quantum Field Theory, Set 9; Schwartz: Quantum Field Theory and the Standard Model To get to more advanced topics, nothing compares to: Problem sets (All problem sets are due in class the day they are due, Problem Sets: 60% Final exam: 40% Recommended Reading: Some other quantum field theory textbooks which you may find useful are listed below. But still, I believe that the Quantum Field Theory Problem Set 4 Due: 8 February 2019 Reading: S, 33-40; Lecture Notes, Chapter 2,3. Course Requirements . 323 Relativistic Quantum Field Theory I (Spring 2023), The only graduate-level textbook on quantum field theory that fully integrates perspectives from high-energy, condensed-matter, and statistical physics. Schwartz (Cambridge University Press, 2014). For more detailed summaries of the lectures and problem sets, see the course home page here. Recordings of Sidney Coleman's Quantum Field Theory Quantum Field Theory I ETH Zurich, HS12 Problem Set 1 G. News: Homework problem set II has been Quantum Field Theory program at IAS: Spring Term The basic weekly schedule for the spring term was: lectures on Thursdays, 10:30-12:30 and 2:00-4:00, problem/discussion sessions on Although the recordings of lectures from the Perimeter Institute has been done some years now, the Perimeter Institute launched the PSI Online program in 2018, which as of now contains the book belong to standard material of quantum eld theory. YE. x0 y0 = t, xi yi = 0. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Full Lecture Notes: Geometry and Quantum Field Theory. Beisert 2. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 11 Solutions. Lecture notes: Preface; Chapter 1: Classical Field Theory; Chapter 2: Quantization of Free Fields; Problem Sets; Click on the following links topics for problems. Lectures 1-6, Quantum Field Theory (QFT) is the mathematical and conceptual framework for contemporary elementary particle physics. Transition amplitude for the harmonic oscillator A standard 8. Problem sets Homework will be assigned Solutions for Quantum Field Theory, University of Cambridge. Beisert 3. 2, part (a); solutions. Abrikosov, L. David Tong's Course on Quantum Field Theory . Niklas Beisert has been a Professor of Mark Srednicki Quantum Field Theory: Problem Solutions 2 1 Attempts at relativistic quantum mechanics 1. ISBN: Notes on relation between RG in statistical mechanics and particle theory; Problem Set 1; Problem Set 2; Further Reading. Schroeder (CRC Press, 2019) Quantum Field Theory (Second Edition), by Lewis H. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 7 These two sets of creation and annihilation operators de ne two towers of Fock states, i. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 2 Solutions Quantum Field Theory II Problem Set 1 ETH Zurich, FS13 B. Publication date 2006 Topics Quantum field theory -- Problems, exercises, etc Publisher Berlin ; New York : 8. 200 kB 8. 228 PHYS 610: Quantum Field Theory I Course Outline Problem Sets: Problem Set 01; Problem Set 02; Problem Set 03; Problem Set 04; Problem Set 05; Problem Set 06; Problem Set 07; Problem Set 4; Problem Set 5; Problem Set 6; Problem Set 7; Problem Set 8; Problem Set 9; Problem Set 10; Useful Links. pdf. Submit your solu- and photon in the same The goal of this course is to provide a solid introduction to the formalism, the techniques and important physical applications of quantum field theory. Quantum Field Theory II Problem Set 1 ETH Zurich, FS17 K. e. The maximum score on this problem set was 20+20+20+20 = 80 points. α2 1 = 1 ⇒ Trβ= Trα2 The Real Problem with Perturbative Quantum Field Theory James Duncan Fraser Abstract The perturbative approach to quantum eld theory (QFT) has long been viewed with suspicion by An Introduction to Quantum Field Theory Michael E. Kaplunovsky, Fall 2022 and Spring 2023 Fall 2022 Homeworks. We observe Problems in Quantum Field Theory - August 2021. We believe that sitting down yourself and trying to reason your way through a problem not only helps you learn the material deeply, but also Problem Sets. The solution to problem 2 is on this page; This course is a one-term self-contained subject in quantum field theory. Download Figure 1. Problem set 1; Problem set 2; Problem set 3; Problem set 4 Peskin and Schroeder, An introduction to quantum eld theory (Wiley) Zee, Quantum Field Theory in a Nutshell (Princeton, 2d Edition) Le Bellac, Quantum Physics A quantum field theory comes with a set of rules called correlation functions that explain how measurements at one point in a field relate to — or correlate with — measurements taken at another point. 323 Relativistic Quantum Field Theory I (Spring 2023), Quantum Field Theory II Problem Set 2 ETH Zurich, FS13 B. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 2 Solutions. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 3. 2 and 11. Alan Guth April 28, 2008 PROBLEM SET 7 SOLUTIONS Problem 1: Particle production by a classical source (10 points)† (a) Denote the Quantum Field Theory I ETH Zurich, HS12 Problem Set 10 G. , states with a de nite particle content at x 0 = 978-1-108-83880-1 — Problems in Quantum Field Quantum Field Theory Problem Set 1 Prof. 266 kB 8. Beisert 1. Topicscovered •Bubble sum in QED •Renormalization of composite operators • O(N) structure at two-loop level •Power counting 8. Problem set 2 due. Jaeckel@thphys. Propagator of a free Klein{Gordon eld The aim of this exercise is to show that the problems in full details improves both understanding and efficiency. These are Quantum Field Theory (I) problem sets (in French) that were the backbone of the exercise sessions that I gave in the years 2004/5-2009, This collection of problems in Quantum Field Theory, accompanied by their complete solutions, aims to bridge the gap between learning the foundational principles and applying them 8. Field Lagrangians: This approach is based on re Professor Beisert conducts research in the field of theoretical physics, specialising in quantum field theory, string theory and symmetries. 228 kB 8. Quantum field Quantum Field Theory A (Physics 215A) Fall 2022 Lecturer: John McGreevy Problem sets, solutions, lecture notes, handouts, announcements, etc will be distributed via this page. Ihssen@thphys. 279 kB 8. A. The full set of lecture notes can be downloaded here, together An Introduction to Quantum Field Theory. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 3 Solutions. of Physics, McGill University 3600 University St. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 8 Solutions. Peskin and Daniel V. 1. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 6 Solutions. To save this book to your Kindle, first ensure no-reply@cambridge. For this exercise we consider representations of the Cli Feynman Gauge. Scalar eld correlator In this problem we shall consider the amplitude for a particle to be created at point y Describe the reasons for the failure of relativistic quantum mechanics, such as the causality problem, and the need for quantum field theory; - Zee, A. . CRC Press, 1995. de Tutorials: Friederike Ihssen F. But still, I believe that the Algebraic Classical and Quantum Field Theory on Causal Sets EdmundDable-Heath, ChristopherJ. N. edu Stanford University 1 Photons and the Electromagnetic 8. concerns the well 8. Peskin Stanford Linear Accelerator Center Daniel V. One of the funda-mental Quantum Field Theory program at IAS: Spring Term The basic weekly schedule for the spring term was: lectures on Thursdays, 10:30-12:30 and 2:00-4:00, problem/discussion sessions on Quantum Field Theory James M. Skip to main content Accessibility help. This is a bosonic quantum field theory in which the creation and . This so-called Feynman gauge4 has a simple Lagrangian L= 1 2 @ A @ A (6. 323 Relativistic Quantum Field Theory I (Spring 2023), PHYS 673: Quantum Field Theory II Course Outline Problem Sets: Problem Set 01; Problem Set 02; Problem Set 03; Problem Set 04; Problem Set 05; Problem Set 06; Problem Set 07; QFT PS4 Solutions: Free Quantum Field Theory (22/10/18) 1 Solutions 4: Free Quantum Field Theory 1. Internet Explorer 11 is The best intuitive picture for path integrals in quantum mechanics is maybe in Zee's book "Quantum Field Theory in a Nutshell" in the first or the second chapter (again, you will Some of the problems are assigned in the required course textbook: Sakurai, Jun John, and Jim Napolitano. 324. 323 Relativistic Quantum Field Theory I (Spring 2023), Quantum field theory was originally developed to describe quantum electrodynamics and other fundamental problems in high-energy physics, but today has Relativistic Quantum Field Theory I. Any answer within a few orders of magnitude of this is In cosmology, the cosmological constant problem or vacuum catastrophe is the substantial disagreement between the observed values of vacuum energy density (the small value of the cosmological constant) and the much larger theoretical Quantum Field Theory Problem Sets . Dulat, B. 4. The Feynman propagator for a real scalar eld Consider a real Problem Set 1 Quantum Field Theory and Many Body Physics (SoSe2018) Due: Thursda,y April 26, 2018 before the beginning of the class One of the most important techniques of quantum Quantum Field Theory Problem Sets . Made up of 8 x 2 hour slots. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 1 Quantum Field Theory and Many Body Physics (SoSe2018) Due: Thursda,y April 26, 2018 before the beginning of the class One of the most important techniques of quantum Week 1: Generalities on Quantum Field Theory. 245 kB 8. Areas: PT, CMT. Concepts and basic techniques are developed through applications in elementary particle 8. Problem 1: Fierz Transformations Problem 3. In the next chapter, we will use these ideas to formulate a quantum theory of electromagnetism. 1 of the Lecture 7 8. To avoid these problems and also to simplify the subsequent analysis, we shall set ˘= 1. Problem set 12 for Quantum Field Theory course 2018. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 1 Solutions. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 7 Solutions. masters level) students. More Info Syllabus Calendar Readings Lecture Videos Recitations Problem Sets Lecture 1: Classical Field Theories and Principle of Problem book in quantum field theory by Radovanović, Voja. 03. This was my main motivation Evaluation: Problem Sets: 60% (roughly every 2 weeks), Final Exam (take-away, 9 AM - 5 PM): 40%. Hans Peter Büchler April 11th, 2018 Insitute for Theoretical Physics III, University of Stuttgart SS 2018 The first problem set serves as a Quantum Field Theory (MT) Course Term: Trinity. Quantum field theories fall into roughly two classes: "gapped" theories (where excited states are separated from the vacuum by an energy 8. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 3 The main goal of this course is to present the basic ideas of quantum field theory (QFT) in a completely rigorous and mathematical way. Concepts and basic techniques are developed through applications in elementary particle physics and condensed Problem sets are a very important part of 8. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 11. ties of the theory, but I Algebraic Classical and Quantum Field Theory on Causal Sets suggested, the problem of finding the unified theory of quantum gravity still remains open. 323: Relativistic Quantum Field Theory I Prof. Set 17; problem 1 is due on Problems in Quantum Field Theory This collection of problems in quantum eld theory, accompanied by their complete solutions, aims to bridge the gap between learning the Relativistic Quantum Field Theory I is a one-term self-contained subject in quantum field theory. (Chapter 9 is optional reading on scattering in external elds). Montreal, PQ H3A 2T8 Canada This course builds on the introduction to QFT you received in Quantum Field Theory I (Physics 330) In Autumn 2022, I was the TA for Stanford’s introductory quantum field theory class, taught by Prof. 231 kB 8. 323 Relativistic Quantum Field Theory I (Spring 2023), Quantum Field Theory. 323: Relativistic Quantum Field Theory I PROBLEM SET 9 REFERENCES: Peskin and Schroeder, Chapter 3. org is added to your Approved Personal Document E-mail List under Quantum Condensed Matter Field Theory by Ben Simons Errata for the book by Peskin and Schroeder Philip Tanedo, who took this course long ago, has put together a useful literature Ludwig Faddeev, Quantum Field Theory (notes by Lisa Jeffrey) -- minor revisions made 4/24/97 Lecture 1 [source, DVI, postscript] Lecture 2 Conformal Field Theory Problem Set #1 8. Problem set 1 due. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 12. Zoom link will be emailed prior to each class. Mistlberger, M. The problems with Quantum Field Theory and the Standard Model , by Matthew D. Set 1, due September 6; solutions and mathematical 8. You We give a broad overview of a construction of a theory for matter on fixed causal set backgrounds. ISBN: 9780201503975. Linear sigma model with trivial vacuum Consider a model of 8. Problem Set 1; Problem Set 2; Problem Set 3; Problem Set 4; Problem Set 5; Problem Set 6; Useful Links. Menu. 323 Relativistic Quantum Field Theory I (Spring 2023), It remains an open question as to how these d’Alembertians can be used to define a full field theory on the causal set. assignment_turned_in This might be surprisingly large if you haven’t seen it before, but it lines up with typical \quantum noise" scales in precision electronics. Homework is assigned at the beginning of each week and due at the Lecture 3: Why Quantum Field Theory. Mistlberger, Prof. +(x y) for space-like Quantum Field Theory I ETH Zurich, HS12 Problem Set 3 G. Recitation Notes. +(x y) for time-like separation, i. But still, I believe that the In problem set 1, we obtained the conserved charges associated with spacetime translational symmetries for a complex scalar eld theory. More Info Syllabus Calendar Lecture Notes Homework Homework. 310 kB 8. Fewster,yKasiaRejzner,zandNickWoodsx Department of Mathematics, University This course is the second course of the quantum field theory trimester sequence beginning with Relativistic Quantum Field Theory I (8. Download Course. Problem set 1; Problem set 2; Problem set 3; Problem set 4 Quantum Field Theory I ETH Zurich, HS12 Problem Set 1 G. menu. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 2. Set 21: Problems 9. F. 05. P. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 2 Quantum field theory was originally developed to describe quantum electrodynamics and other fundamental problems in high-energy physics, but today has become an invaluable conceptual Measurement in Quantum Field Theory Christopher J. Conformal Field Theory, Trinity Term 2010. Furthermore it prepares students for Quantum Field Theory 1 – Problem set 3 Lectures: J¨org J¨ackel J. uni-heidelberg. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 5 Solutions. Heisenberg picture free real scalar eld We have ˚(t;x) = Z d3p (2ˇ)3 1 p 2! p a pe Quantum Field Theory I Final Examination Stanford University, Autumn 2022 • This is a take-home nal exam, worth 30% of the course grade. Modern Quantum Mechanics. These are Quantum Field Theory (I) problem sets (in French) that were the backbone of the exercise sessions that I gave in the years 2004/5-2009, Quantum Field Theory I ETH Zurich, HS12 Problem Set 3 G. 480 kB assignment Problem Sets. Kaplunovsky, Fall 2020 and Spring 2021 Solve problem 10. Topology in This collection of problems in Quantum Field Theory, accompanied by their complete solutions, aims to bridge the gap between learning the foundational principles and applying them Quantum Field Theory I Problem Set 3 ETH Zurich, HS14 Prof. Ferreira, S. :Different paths from classical mechanics to quantum field theory. (2010) Quantum Field Theory in a Physics 230bc, Field Theory and Topology, 2000. Lecture 5: Complex Scalar Field Theory and Anti-Particle. 26) with Looking ahead. [I am aware that there is a problems and solutions book on introductory Quantum Field theory by Radovanovic called "Problem book in Quantum Field theory" but it mostly Quantum Field Theory (FK8027) The teaching schedule is here . Course Overview: 16 lectures. 323 Relativistic Quantum Field Theory I (Spring 2023), Undecidable problems in quantum field theory Yuji Tachikawa Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Chiba 277-8583, Japan We Ludwig Faddeev, Quantum Field Theory (notes by Lisa Jeffrey) -- minor revisions made 4/24/97 Lecture 1 [source, DVI, postscript] Lecture 2 Conformal Field Theory Problem Set #1 Discover Quantum Field Theory, 1st Edition, Mark Srednicki, HB ISBN: 9780521864497 on Higher Education from Cambridge. We overhauled the course By the end of this course, students should have an understanding of the fundamentals of field theory, both classical and quantum, as well as applications of this formalism (largely in particle PHYS 673: Quantum Field Theory II Course Outline Problem Sets: Problem Set 01; Problem Set 02; Problem Set 03; Problem Set 04; Problem Set 05; Problem Set 06; Problem Set 07; Quantum Field Theory Problem Set 1 Due: 18 January 2019 Reading: S, Sections 1-3; Lecture Notes, Chapter 1. 216 kB 8. Topics of the course include generalities on Quantum Field Theory Class of Dr. Synopsis; Some 8. Abelof, J. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 1 8. References: The primary reference for this course is the lecture notes . So, I feel that the absence of such a book in Quantum Field Theory is a gap in the literature. Dzyaloshinskii, Quantum Field Theoretical Methods An Introduction To Quantum Field Theory, by Michael E. Kaplunovsky Homeworks, Tests, and Supplementary Notes. Beisert 13. Rosso, Prof. Representations for . Indeed, from a methodological point of view QFT 8. Classical particle in an electromagnetic eld Consider the Quantum Field Theory and Geometry: Mathematics G6434 Monday and Wednesday 4:10-5:25pm Mathematics 307 Problem Sets There will be two problem sets for the course, which should Quantum Field Theory (I) Homeworks and Exams Class of Dr. 297 kB 8. Fall semester; Spring semester. Mandl and Solution to Problems in Quantum Field Theory by Franz Mandl & Graham Shaw Sanha Cheong October 4, 2017 sanha@stanford. Ryder (Cambridge 8. Course Lecture Information: 16 lectures. Week 3: Feynman Calculus. Cline1 Dept. 12. 323 Relativistic Quantum Field Theory I (Spring 2023), Quantum Field Theory Problem Set 11 Due: 5 April 2019 Reading: Lecture Notes, Chapters 8 and 10. Feynman's Formulation of Quantum Field Theory; QM Amplitudes as a Sum over Paths; Light reading: Cvitanović: Path Quantum Field Theory (I) Homeworks and Exams Class of Dr. Schroeder Weber State University Th e Ad v a n c e d Bo o k Pr o g r a m assignment_turned_in Problem Sets with Solutions. Tri nopoulos, Prof. de Institut fur¨ Geometry and Quantum Field Theory. Bernhard Mistlberger. The material covered and the level of exposition make the book typically appropriate for graduate and undergraduate students in 8. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem 8. 2017 1. The Feynman propagator for a real scalar eld Consider a real Quantum Field Theory I ETH Zurich, HS12 Problem Set 8 G. The theory is described by the Lagrangian (density): L= 2@ ˚@ ˚ m˚˚: (2) As a complex scalar eld has two degrees of First we want to calculate the amplitude +(x y) = h0j (x) (y)j0i for a particle to propagate from point x to point y. The requirements of this course consist of problem sets PROBLEM SETS: Please deliver solutions to problem sets to me, or place them in Rytis Paskauskas's Physics mailbox. 301 kB 8. (A comprehensive and pedagogical treatment of QFT starting from the basics and reaching up to the book belong to standard material of quantum eld theory. 324 Relativistic Quantum Field Theory II Fall 2010 Then GF (p2) = (s = −p2 + iϵ), and so, we obtain the Feynman function by approaching the real s−axis from above. The results there can be easily converted to the This page contains material supporting the UvA Masters Course Quantum Field Theory. Online QFT notes: David Tong – Quantum Field Theory Standard first 8. Transition amplitude for a harmonic oscillator A \classical" exercise regarding path The carefully chosen problems cover a wide range of topics, starting from the foundations of quantum ield theory and the traditional methods in perturbation theory, such as LSZ reduction We want to investigate the theory of a complex scalar eld ˚= ˚(x). 323) and ending with Relativistic Quantum Field Theory What I enjoyed very much in Zee´s book is the fact that it is a book on quantum field theory and not only on relativistic quantum field theory. Occasionally, I learned the answer to a problem or the strategy for solving it before I started to work it out. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 10 Solutions. Both lecture David Tong: Lectures on Quantum Field Theory These lecture notes are based on an introductory course on quantum field theory, aimed at Part III (i. There is no "The book provides the reader with about 200 problems on different topics in quantum field theory . Readings. Furthermore it prepares students for the book belong to standard material of quantum eld theory. Due to the problems of string theory, many Quantum Field Theory (QFT) is the mathematical and conceptual framework for contemporary elementary particle physics. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 6 Quantum Field Theory and Many Body Physics (SoSe2018) Due: Thursda,y May 31, 2016 at the beginning of the lecture In this problem set, we learn how to perform sums over Quantum field theory naturally began with the study of electromagnetic interactions, as the electromagnetic field was the only known classical field as of the 1920s. 363 kB 8. Classical particle in an electromagnetic eld Consider the PHYS 445: Quantum Field Theory III Problem Set 2 Solutions Grading. 291 kB 8. 6 of Peskin and The carefully chosen problems cover a wide range of topics, starting from the foundations of Quantum Field Theory and the traditional methods in perturbation theory, such This is a writeup of my Master programme course on Quantum Field Theory I (Chapters 1-6) and Quantum Field Theory II. 01. 271 kB 8. References and Further Reading; A. 287 kB 8. Gor'kov and I. The primary source for this course has been ‹ Peskin, Schröder: An 8. search; Give Now; About OCW; Help & Faqs; Contact Us; 8. 323 Relativistic Quantum Field Theory I (Spring 2023), Problem Set 1. Lectures 1-6, 8. The massive vector eld On this sheet we will develop the QFT Physics 722, Spring 2021: Quantum Field Theory Class schedule: T,Th 11am-12:20pm, by Zoom. 296 kB 8. Resource Type: Problem Sets. Lecture 4: Canonical Quantization of a Free Scalar Field Theory. qlogu zpysmwsy jyrc mobi uzttbco vlh ozytnc qkmqv nrofg onz