Advanced Quantum Field Theory: intuition with path integrals

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Emanuele Pesaresi

10:35:40

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1 - Path integrals and Quantum Mechanics

1 - Introduction to the course.mp4

05:41

2 - Course prerequisites.mp4

11:41

3 - ADVANCED-QFT-OSBORN-HUGH.pdf

3 - Path integral derivation.mp4

38:16

4 - Some intuition behind the path integral.mp4

16:35

4 - chap1.pdf

2 - QFT in zero dimensions

5 - Free field theory in zero dimensions.mp4

11:46

5 - chap2.pdf

6 - The current in the Free field theory in zero dimensions.mp4

13:31

7 - Wick theorem as a probabilistic theorem in QFT.mp4

15:57

8 - Integrals in perturbation theory.mp4

10:34

9 - Example of perturbation theory.mp4

20:37

10 - Feynman diagrams from a combinatoric perspective.mp4

19:58

11 - Feynman diagrams and orbit stabilizer theorem.mp4

25:12

12 - Wilsonian effective action.mp4

22:36

13 - Feynman rules with two fields and 4valent vertices.mp4

05:38

14 - Example of action with two fields.mp4

22:30

15 - Direct calculation of the effective action without Feynman rules.mp4

18:40

16 - Direct calculation of the correlation function without Feynman rules.mp4

17:27

17 - How renormalization comes forth.mp4

25:17

3 - QFT in 1 dimension

18 - QFT in one dimension action with two fields.mp4

19:09

18 - chap3.pdf

19 - Logarithm of a determinant.mp4

17:08

20 - Nonlocality of interactions in a onedimensional Quantum Field Theory.mp4

23:02

21 - 1non-commutativity-and-path-integrals.zip

21 - 2non-commutativity-and-path-integrals.zip

21 - Non commutativity and path integrals.mp4

19:46

22 - Correlation functions and time ordered products.mp4

16:19

4 - Theory of renormalization in physics

23 - RenormalizationChap.pdf

23 - Theory of the renormalization group.mp4

29:57

24 - Running of couplings and Callan Symanzik equation.mp4

08:26

25 - Anomalous dimensions part 1.mp4

14:12

26 - Anomalous dimensions part 2.mp4

22:47

27 - Scale invariant theories.mp4

20:07

28 - Massive scalar field and the Yukawa potential.mp4

17:11

29 - Derivation of the Yukawa potential from the Klein Gordon field in 3 dimension.mp4

27:10

30 - Renormalization group flow.mp4

11:04

31 - The local potential approximation example on the running of couplings.mp4

43:32

5 - Appendix

32 - Complex Gaussian integrals.mp4

18:01

33 - Lagrange duplication formula.mp4

06:36

34 - Relation between Beta and Gamma function.mp4

05:49

35 - Derivation of a green function from a differential equation.mp4

13:28

Description

Master Quantum Field Theory and Renormalization group with Path Integrals: Intuitive Insights & Practical Applications

What You'll Learn?

Master Path Integrals: Understand the concept of path integrals in Quantum Field Theory, and learn how they offer a unique perspective on the subject
Derive Feynman Rules: Gain the ability to derive Feynman rules naturally from the path integral formulation
Dive into Renormalization: Delve into the essential concept of renormalization, with a particular focus on the renormalization group.
Comprehend Non-Commutativity: Explore the non-commutative nature of Quantum Field Theory by examining how path integrals incorporate non-differentiable paths
Derive the Yukawa potential: while discussing renormalization, we will see how some theories give rise to long-range potentials and some others short-range ones
Discover the partition function: essential tool to the definition of path integrals
Learn how to use correlation functions, whose interpretation is related to Feynman diagrams and particle interactions
Learn how to use perturbation theory in QFT
Learn the orbit-stabilizer theorem, another key concept related to the interpretation of Feynman diagrams
Discover the effective action: this tool is key to understanding renormalization
Discover the Callan Symanzik equation, which appears in the theory of the renormalization group
Learn why "anomalous" dimensions arise in QFT

Who is this for?

Advanced (Master-level) Students

Physicists and Researchers: Professionals in the field of theoretical physics, including physicists, researchers, and academics, who wish to enhance their expertise in Quantum Field Theory.

Mathematics Enthusiasts, Mathematicians, interested in the intersection of advanced mathematics and theoretical physics, looking to explore the beauty of Quantum Field Theory from a mathematical perspective.

Physics Enthusiasts, passionate about the world of quantum physics and eager to deepen their understanding of Quantum Field Theory.

What You Need to Know?

Schrödinger equation

Operators, states, eigenstates, eigenvalues

familiarity with bra-ket notation

Classical theory of Fields (Lagrangian, action, etc)

Multivariable Calculus

Complex calculus (in particular, the Residue Theorem)

Familiarity with QFT and second quantization will enhance your learning experience

Special Relativity (and tensors)

More details

Description
Welcome to "Advanced Quantum Field Theory: Intuition with Path Integrals." In this course, we take a unique approach to delve deeper into the fascinating world of Quantum Field Theory (QFT). The foundations of this course are based on the notes of Professor David Skinner, although an original perspective will be given, which emphasizes intuition and the power of path integrals.
What You Will Learn:
Path Integrals Demystified: Explore Quantum Field Theory from a different angle, using path integrals as our guiding tool. Unlike the traditional "second quantization" approach, we won't begin with a classical field and then transform it into an operator, but rather, we'll start directly from the action and Lagrangian, offering a more intuitive understanding.
Summing Over Infinite Paths: In classical field theory, a single trajectory minimizes the action. Path integrals take us beyond this limitation. You'll grasp the essence of QFT by summing over countless possible paths, gaining insight into the fundamental role of uncertainty.
Zero-Dimensional QFT: We'll begin with simpler mathematics in a zero-dimensional QFT, paving the way for a natural derivation of Feynman rules directly from the path integral formulation.
Exploring Non-Commutativity: Delve into the concept of non-commutativity in Quantum Field Theory. Discover how path integrals naturally encompass non-commutative behaviors due to the summation over non-differentiable paths.
Renormalization Insights: Gain a deep understanding of renormalization, a crucial concept often overlooked in basic QFT courses. Explore the intricacies of the renormalization group, a fundamental aspect of Quantum Field Theory.
Course Content: the current course content covers path integrals, zero-dimensional QFT, one-dimensional QFT, and renormalization. The material may be expanded in the future to include additional sections.
Prerequisites: To fully benefit from this course, it's essential to have a grasp of:
SchrÃ¶dinger equation
operators
bra-ket notation
multivariable calculus and complex calculus
Classical Theory of fields
Special Relativity and tensors
Familiarity with QFT and second quantization will enhance your learning experience.
Enroll today and embark on a captivating journey into the heart of Quantum Field Theory. Discover the power of path integrals and develop a deep, intuitive understanding of this fascinating field. Join this course to reshape your perspective on Advanced Quantum Field Theory!
Who this course is for:
Advanced (Master-level) Students
Physicists and Researchers: Professionals in the field of theoretical physics, including physicists, researchers, and academics, who wish to enhance their expertise in Quantum Field Theory.
Mathematics Enthusiasts, Mathematicians, interested in the intersection of advanced mathematics and theoretical physics, looking to explore the beauty of Quantum Field Theory from a mathematical perspective.
Physics Enthusiasts, passionate about the world of quantum physics and eager to deepen their understanding of Quantum Field Theory.

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Physics

Emanuele Pesaresi

Instructor's Courses

I obtained my PhD in "Mechanics and Advanced Engineering Sciences" in 2021.I attained a Bachelor of Science and Master of Science in Mechanical engineering in 2015 and 2017 respectively, with honors from the University of Bologna.I was the teaching tutor for the course of Mechanics of Machines from the academic year 2018 until the end of 2021 at the University of Bologna (branch of Forlì).My passion for mathematics, physics and teaching has motivated me to lecture high school and university students.My approach as a teacher is to prove to students that memory is less important for an engineer, mathematician, or physicist, than learning how to tackle a problem through logical reasoning. I believe that a teacher of scientific subjects should try to develop his students’ curiosity about the subject, rather than just concentrating on acquisition of knowledge, however important that may also be. Students should be encouraged to dig deeper and build on their knowledge by continually questioning it, rather than accepting everything at face value without a thorough understanding.For enquiries (e.g. about tutoring, or advice related to the subjects spanned by my courses), you can either contact me on LinkedIn, or you can post questions in my courses' message boards, or you can also contact me via email or on my website.You can also find the updated versions of my courses on my website.

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