Student Friendly Quantum Field Theory 22
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I find it counterproductive when people treat the formulation of relativistic QFTs as a matter of second quantization. It confuses learners into thinking that it involves going beyond the general principles of quantum theory. The real change is going from situations where the wave function formulation is often the most convenient (for non-relativistic situations) to a Heisenberg-picture formulation with heavy emphasis on its time-dependent operators.
lun,In textbooks this shows up as the fact that the Legendre transform from velocity to momentum variables is only one-to-one in special circumstances. Even for free field theories this becomes a problem, typically first seen when you try to quantize the theory of a free photon, and find that the canonical momentum for the time-like component of the vector field is zero.
This is simply not the case. You just use products of fields (not necessarily at the same space-time point) that have the quantum numbers to add or remove one of the bound state particles you are interested in. For example in QCD, if you want to find an S-matrix element or an operator matrix element involving protons, you would use a product of three fields for the up quark for an outgoing proton, and the hermitian conjugate field product for an incoming proton.Then you apply the LSZ method unchanged.That is, you examine Green functions that include these fields. In momentum space, corresponding to the bound state there is a pole in the external momentum of the field product. In coordinate space, there is the corresponding asymptotic large-time oscillatory behavior.Essentially the same idea is used in lattice QCD to calculate matrix elements of operators between hadron states. The important difference is that instead of the oscillating asymptotic behavior in Minkowski coordinate space, one has exponential decay corresponding to the mass of the particle.
By incorporating extensive student input and innovative teaching methodologies, this book aims to make the process of learning quantum field theory easier, and thus more rapid, profound, and efficient, for both students and instructors. Comprehensive explanations are favored over conciseness, every step in derivations is included, and 'big picture' overviews are provided throughout. See the first two chapters at www.quantumfieldtheory.info.The book is intended for physics students, typically at the graduate level. Student responses to the book include: \"[This] book ... makes quantum field theory much easier to understand!\"\"Thanks for ... making quantum field theory clearer!\"\"Awesome. .. approach and presentation .. just awesome !!!\"Best presentation of QFT I have ever seen .... marvelous!!!.\" transforms learning QFT from being a hazardous endeavor to actually being an enjoyable thing to do.\"\"Great job .. extremely clear ... guided me through many ambiguities .. I wasn't able to work out with any other book.\"\"..truly special... extraordinary text. For me, ... a big relief .. finding [this] text.\"The book focuses on the canonical quantization approach, but also provides an introductory chapter on path integrals. It covers fundamental principles of quantum field theory, then develops quantum electrodynamics in depth. 153554b96e
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