CB: 2. Energy states, vacuum of free theory. T-ordering and Feynman propagator. Conserved charge. Charged particles and anti-particles.

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## Quantum Field Theory III: Gauge Theory

DT: 2. Interaction representation and Dyson formula.

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Wick's theorem. CB: 4. Evolution of states, S-matrix, probability amplitude. Dirac Hamiltonian and Dirac action.

Properties of spinors. Dirac equation and covariance. Algebra of gamma-matrices. Spinor representation of the Lorentz group. Orbital and spin angular momentum tensors. Pauli-Lubanski vector. Spin and spin projections. Free solutions of the Dirac equation. Spin sums and bilinears. Field decomposition. Canonical anti-commutation relations. CB: 3. Examples of scattering amplitudes. Discrete symmetries. Chiral interactions. Majorana spinors.

Dynamical invariants. Quantisation and propagator of a massive vector field. Linear polarisation. Spin vector and circular polarisation. Ward identity. DT: 6. Gauge invariance and gauge fixing Lagrangian of QED. Gauge principle. I treat the idea of effective field theory both in general and by use of the specific case of the linear sigma model. Effective field theory 1 — Notes and Video — What is effective field theory, locality, QED effective Lagrangian, the energy expansion, linear sigma model, a low energy calculation and its effective Lagrangian. Effective field theory 2 — Notes and Video — the exponential representation, recalculating the scattering amplitude, path integral connection, integrating out at tree level, start of matching.

Effective field theory 3 — Notes and Video — Integrating out scalar, heat kernel, general form of effective L, which parameters to use, matching the effective theory and the full theory.

Anomalies 1 — Notes and Video — currents in path integrals, path integrals and symmetries, scale invariance in the Standard Model, The trace anomaly, calculating the path integral jacobian. Anomalies 2 — Notes and Video — obtaining the trace relation, Feynman diagram approach, interpreting the trace anomaly, the simplest derivation via running charge, axial U 1 problem, starting the chiral anomaly calculation. Anomalies 3 — Notes and Video — shift of integration variable, the pi to 2 gamma story, anomalies and gauge currenta.

Standard Model 1 Notes and Video — quantum numbers, U 1 ambiguity, anomaly conditions, hypercharge assignments. These are two lectures which give a superficial overview of the structure of supersymmetric theories and the MSSM. These two lectures develop general relativity in a manner similar to our treatment of gauge theories. Now to physics. Physics is all about Nature. And mathematics is just a language used to explain Nature. The relation between mathematics and physics is that of poetry and the language used to express that poetry.

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There is no inherent relation. This means that math and physics are not tightly bound, just as poetry is not bound to any specific language. Shakespeare could have used any language to express the same beautiful thoughts.

## Quantum Field Theory III: Gauge Theory: A Bridge Between Mathematicians And Physicists

And if it ever turns out that extraterrestrials have a better language to explain Nature I for one would rush to master it and throw our terrestrial mathematics into the dust-bin. This hints at a mismatch between math and physics. One of the differences between physics and mathematics is that physics is more intuitive, and long mathematical proofs won't help if the intuition is not there.

In fact, physics is a reality-check on math - it controls maths runaway flights into pure logic. I guess this is what Einstein and Feynman always said. And it is exactly here that a lot of bridges between math and physics have collapsed. Probably the mismatch lies in the brains of mathematicians and physicists. So, paradoxically again, in order to build true bridges between math and physics, some psychological study of the minds of mathematicians and physicists is needed.

This gives some indication of the difficulty of building these bridges. It is not a bilateral but a multilateral task - a sort of multidisciplinary study. Seeing that Prof.

## Relativistic Quantum Field Theory III | Physics | MIT OpenCourseWare

Zeidler needs pages to deal with this bilateral task alone, it is no wonder that people dare not plunge into the murky waters of multilateralism - bilateralism is dark enough a territory to mess with. The reason I am excited about "Zeidler Program" is that almost every time I read something from the 2 volumes of his series, I end up seeing some connection between physics and math which I did not see before, and this sets me "thinking" at least in my limited ways.

This cannot be said of many other books where all you can do is stare at the "most general formalism expressed in extremely terse notation". All you can carry away from such "masterpieces" is pseudo-knowledge consisting of some memorized terms and this is the most dangerous form of knowledge. Yet the reason I am not passing a technical judgement on the first 2 volumes of his program is that I want to wait till volume 3 Gauge theory and volume 4 Quantum Mathematics appear on the stage. They will be the making or breaking points of "Zeidler Program". Only they will demonstrate what kind of bridges he has built between poor, old, and senile Electromagnetism and his new, flashy, and rich cousin called Principal Fiber Bundle, and between a man called Witten and a man called Witten again, that is, between Witten the physicist and Witten the mathematician.

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It is over such troubled waters that many a bridges have been washed away in the past. So I wish Prof. Zeidler all luck. To be continued after the appearance of volumes 3 and Rattan Mann Oslo, Norway. My background in math and physics is not good enough to do a good review of this book. It looks at QED from a big picture point of view which I like. He probably does a good job of it, I'm not in a position to say.

### Course Features

I hope someone will come along soon who can do a better job of reviewing the good parts of the book. My concern is that at the page level, it has a lot of problems. There are a large number of typos, sometimes in strategic places. I suppose that can't be helped. However, there is at least one definition that is simply incorrect.

### Bestselling Series

Fortunately, that becomes obvious right away. Although Schwartz spaces and tempered distributions are used in several places, they are not defined at all. Instead it refers you to the definition in volume I which I don't have. On the other hand, the Heaviside function is defined five times.