# lie group (blogs) — RSS Amplifier Recent posts from the 2 feeds in the RSS Amplifier directory that cover lie group. Page: Feed: --- ## [The last of the mixing angles](https://robwilson1.wordpress.com/2026/08/20/the-last-of-the-mixing-angles/) _2026-08-20 · Robert A. Wilson · Hidden assumptions_ For years I have struggled to find any ideas at all for explaining the mixing angle between the down and bottom quarks. It is measured experimentally at around .201 degrees, which is so small it gets lost in the noise whenever you start to look for it. But now that I have a proper model \[…\] ## [The Dirac model of quantum antigravity](https://robwilson1.wordpress.com/2026/08/15/the-dirac-model-of-quantum-antigravity/) _2026-08-15 · Robert A. Wilson · Hidden assumptions_ It is well known that Dirac predicted antiparticles. It is also well known that the properties he predicted for them turned out not to be correct. It is well known that his theory of the electron does a pretty good job of describing what happens when an electron and a proton get together to form \[…\] ## [The myth of intrinsic spin](https://robwilson1.wordpress.com/2026/08/12/the-myth-of-intrinsic-spin/) _2026-08-12 · Robert A. Wilson · Hidden assumptions_ The phrase “intrinsic spin” is, of course, an oxymoron. Spin is always relative, always measured with respect to something else, and can never be intrinsic. Nevertheless, “intrinsic spin” is an important concept in quantum mechanics, and apparently it has some real physical meaning. So I want to examine how such an obvious oxymoron can be \[…\] ## [Groundhog Day](https://robwilson1.wordpress.com/2026/08/10/groundhog-day-2/) _2026-08-10 · Robert A. Wilson · Hidden assumptions_ Back in the Good Old Days of E8 theories, when I first met Corinne Manogue and Tevian Dray, they began their construction of a model by putting the Lorentz group (in the form Spin(3,1)) in the middle of Spin(12,4), leaving Spin(9,3) which they split into Spin(6)=SU(4) and Spin(3,3)=SL(4,R). Now if you take the compact part \[…\] ## [I am a hoarder](https://robwilson1.wordpress.com/2026/08/06/i-am-a-hoarder/) _2026-08-06 · Robert A. Wilson · Hidden assumptions_ Or, to put it another way, I am a pure mathematician. You see, that’s what pure mathematicians do. They hoard interesting things, in the hope that they might come in useful one day. Pure mathematicians are essential parts of the ecosystem, because applied mathematicians throw away everything (mathematical) that they don’t think is useful. But \[…\] ## [Quantisation of SL(4,R)](https://robwilson1.wordpress.com/2026/08/02/quantisation-of-sl4r/) _2026-08-02 · Robert A. Wilson · Hidden assumptions_ If it really is true that the group SL(4,R) describes the symmetries of spacetime on all scales, then it is necessary to quantise SL(4,R). Certainly not everyone agrees with me that it is possible to quantise a non-compact Lie group, as quantisation usually implies compactness in some way or other. That, I think, is why \[…\] ## [Conventions](https://robwilson1.wordpress.com/2026/07/28/conventions/) _2026-07-28 · Robert A. Wilson · Hidden assumptions_ I have a lot of trouble with conventions. In mathematics and in physics “convention” means a decision that was taken at some point about a notation or a definition, that people generally adhere to in order to make communication easier. But sometimes, different groups of people make different decisions about the same thing, and that \[…\] ## [Sparrows and dunnocks](https://robwilson1.wordpress.com/2026/07/26/sparrows-and-dunnocks/) _2026-07-26 · Robert A. Wilson · Hidden assumptions_ At a young age, perhaps around 10, my brother got interested in bird-watching. Two specific memories that stay with me are these two exchanges (they may not be verbatim): At the time, of course, I was just a by-stander, without the experience to know who was right. But with more than half a century of \[…\] ## [Weyl groups](https://robwilson1.wordpress.com/2026/07/26/weyl-groups/) _2026-07-26 · Robert A. Wilson · Hidden assumptions_ Weyl groups are the standard method in physics of relating continuous and discrete groups. They are named after Hermann Weyl, whose work in the first half of the 20th century was of enormous importance for both mathematics and physics. He was the first to propose the gauge principle for physical theories, and is particularly known \[…\] ## [Quantum field theory](https://robwilson1.wordpress.com/2026/07/25/quantum-field-theory-2/) _2026-07-25 · Robert A. Wilson · Hidden assumptions_ The special theory of relativity established the principle that a unified force field could in at least one case (electromagnetism) be represented by a Lie algebra, that is the adjoint representation of a Lie group, in this case the Lorentz group. The unification here established that the magnetic field is a subalgebra, but the electric \[…\] ## [AI News Summaries & Audio (Sponsored)](https://crawlproof.com/a/F2iBV0b0ykx8) _2026-07-25 · **Sponsored**_ Tap an article for an AI summary and an audio briefing. ## [Furry's Theorem, Part 1: Why an Odd Number of Photons Can't Come From Nothing](https://rohankulkarni.me/posts/notes/furrys-theorem-part-1/) _2026-07-25 · Rohan Kulkarni_ A path-integral and diagrammatic proof that any correlation function of an odd number of photon fields vanishes exactly — the photon is C-odd, the vacuum is C-even, and QED conserves C — plus the three places the proof most often goes wrong. ## [Furry's Theorem, Part 2: What It Buys You](https://rohankulkarni.me/posts/notes/furrys-theorem-part-2/) _2026-07-25 · Rohan Kulkarni_ Spending Furry's theorem: no photon tadpole, no three-photon vertex, why Euler–Heisenberg has only even powers of F, whole classes of Feynman diagrams deleted for free, why light doesn't scatter off light until fourth order, and where the theorem breaks near a magnetar. ## [The trouble with quantum mechanics](https://robwilson1.wordpress.com/2026/07/19/the-trouble-with-quantum-mechanics/) _2026-07-19 · Robert A. Wilson · Hidden assumptions_ The trouble with quantum mechanics, as I have had occasion to remark before, lies in the identification of SU(2) with Spin(3). It is undeniable that these two groups are mathematically equivalent, but it is not undeniable that they are physically equivalent. The assumption that they are physically equivalent was made in 1925, and has never \[…\] ## [Self-Energy, 1PI Diagrams, and the Dyson Resummation](https://rohankulkarni.me/posts/notes/self-energy-dyson-resummation/) _2026-05-02 · Rohan Kulkarni_ How perturbation theory actually computes the field strength renormalization Z and the shift from bare mass m₀ to physical mass m, by resumming all 1PI insertions into the full propagator i/(p² − m₀² − M²(p²)). ## [Why Renormalization Is Needed: The Källén–Lehmann Spectral Representation](https://rohankulkarni.me/posts/notes/field-strength-renormalization/) _2026-05-01 · Rohan Kulkarni_ A non-perturbative derivation showing that the analytic structure of the interacting two-point function forces field strength renormalization Z and a physical mass m ≠ m₀ — long before any loops or infinities appear. ## [Starting MSc Physics at Heidelberg — What We Wish We Knew Earlier](https://rohankulkarni.me/posts/blogs/heidelberg_msc_guide/) _2026-04-15 · Rohan Kulkarni_ A practical companion to a video I made in collaboration with STARGAZER on beginning the MSc Physics program at Heidelberg University — covering courses, research groups, admin, and life in the city. ## [Lie Groups and Lie Algebras, Part IV: The Poincaré Group and the Classification of Particles](https://rohankulkarni.me/posts/notes/poincare-group/) _2026-04-06 · Rohan Kulkarni_ Exploring the Poincaré group, its Casimir operators, and Wigner's classification of elementary particles by mass and spin/helicity. ## [Lie Groups and Lie Algebras, Part III: Spinors, Fields, and the Representations That Matter](https://rohankulkarni.me/posts/notes/lorentz-representations/) _2026-04-05 · Rohan Kulkarni_ Decomposing the Lorentz algebra into su(2) ⊕ su(2), classifying representations by (j+, j-), and understanding Weyl, Dirac, and Majorana spinors in relativistic field theory. ## [Lie Groups and Lie Algebras, Part II: The Lorentz Group](https://rohankulkarni.me/posts/notes/lorentz-group/) _2026-04-04 · Rohan Kulkarni_ Exploring the Lorentz group O(3,1), its disconnected components, its defining invariant metric, and its fundamental representations in relativistic physics. ## [Lie Groups and Lie Algebras, Part I](https://rohankulkarni.me/posts/notes/lie-groups-lie-algebras/) _2026-04-03 · Rohan Kulkarni_ Building the language of Lie groups and their representations from the ground up — generators, structure constants, representations, Casimir operators, and the exponential map. ## [Brisk AI News Briefings (Sponsored)](https://crawlproof.com/a/w36y0PbISFBc) _2026-04-02 · **Sponsored**_ Read AI summaries and listen to audio briefings for top stories. ## [Faddeev–Popov Quantization (Abelian), Part 2: The Trick, the Propagator, and What Counts as Gauge Fixing](https://rohankulkarni.me/posts/notes/faddeev-popov-abelian-part-2/) _2026-04-02 · Rohan Kulkarni_ We derive the Faddeev–Popov identity using a discrete warm-up, insert it into the path integral, extract the gauge-fixed photon propagator, and ask: what other gauge-fixing terms are allowed? ## [Faddeev–Popov Quantization (Abelian), Part 1: The Overcounting Problem](https://rohankulkarni.me/posts/notes/faddeev-popov-abelian-part-1/) _2026-04-01 · Rohan Kulkarni_ Why you can't just write down the path integral for a gauge theory and call it a day — the operator you can't invert, the orbits you can't avoid, and the geometric picture that makes gauge fixing click. ## [Dark Energy Beyond Scalars, Part IV: Perturbations, Gauge Invariance, and What Propagates](https://rohankulkarni.me/posts/notes/dark-energy-p-forms-part4/) _2025-12-23 · Rohan Kulkarni_ Decomposing the fluctuations of massive vectors and massless 2-forms to determine their physical degrees of freedom and observational signatures. ## [Dark Energy Beyond Scalars, Part III: The Cosmological Principle Meets Higher-Rank Fields](https://rohankulkarni.me/posts/notes/dark-energy-p-forms-part3/) _2025-12-21 · Rohan Kulkarni_ Applying the cosmological principle to massive vectors and massless 2-forms to see if they can drive the expansion of the Universe. ## [Dark Energy Beyond Scalars, Part II: Gauge Symmetry, Mass, and Degrees of Freedom](https://rohankulkarni.me/posts/notes/dark-energy-p-forms-part2/) _2025-12-20 · Rohan Kulkarni_ A deep dive into gauge symmetry, equations of motion, constraints, and degrees of freedom for massive vectors and massless 2-forms. ## [Dark Energy Beyond Scalars, Part I: Why p-Forms?](https://rohankulkarni.me/posts/notes/dark-energy-p-forms/) _2025-12-19 · Rohan Kulkarni_ An introduction to using higher-rank tensor fields like vectors and 2-forms as dark energy candidates, going beyond the scalar field quintessence. ## [Cosmology (Heidelberg, WiSe 24/25)](https://rohankulkarni.me/posts/teaching/cosmology_heidelberg_wise24-25/) _2024-10-15 · Rohan Kulkarni_ Tutorial notes for the M.Sc. Cosmology core course at Heidelberg University — covers GR basics, FLRW cosmology, perturbation theory, and inflation.