I saw an interesting video on how groups were used by Garret in his model for a Theory of Everything. Here is the video. The group he used is an exotic Lie group commonly known as E8.

Group theory and Physics

Most of us have group theory in our degree course. Some time ago, I was pretty critical about pure math and its abstract nature ( having nothing to do with reality). I treated them as just mental fantasies, some of which tends to have a structure that agrees with the way nature nature worked.
I went around telling people about some paradoxes in set theory and how Godel's theorem implies that any system based on precise axioms and set of rules is fundamentally flawed. One famous paradox is Russel's paradox.

I now realize that how I felt back then was wrong. I felt that way partly because I am not good at Math and partly because I my thinking was very naive. Which is not really a bad thing, I always learn from my naiveties.
I am now doing a project in Lie Groups under a professor in my college. And I visit a person named Dr. Aravinda from TIFR. He's helping me out with Topology and Differential Geometry. This is amazing because two years ago I didn't think I would find anyone working on these topics ( and also willing to guide me).

Anyway, I thought I'll put up something here that I found worth reading. This is the preface to one of the books that he suggested:

" As a graduate student in experimental physics, I found the study of group theory considered to be a useless "high-brow" luxury. Furthermore all attempts to follow a lecture course resulted in a losing battle with cosets, classes, invariant subgroups, normal divisors and assorted lemmas. It was impossible to learn all the definitions of new terms defined in one lecture and remember them until the next lecture. The result was complete chaos.


It was a great surprise to find later on that (1) Techniques based on group theory can be useful; (2) They can be learned and used without memorizing the large number of definitions and lemmas which frighten the uninitiated. 

Angular momentum is presented in elementary quantum mechanics courses without a detailed analysis of the lie group of continuous rotations in three dimensions. The student learns about angular momentum multiplets and coupling angular momenta without realizing that these are irreducible representations of the rotation group.He also does not realize that the algebraic properties of other lie groups can be applied to physical problems in the same way as he used angular momentum algebra, with no need for classes, cosets etc. . . . . . . "
He then goes on to talk about further applications in creation and annihilation operators, and also talks about quasi spin etc..
The book is Lie groups for Pedestrians by Harry Lipkin.

Group theory is actually fun and beautiful ( a word I rarely use) , but again college takes the life out of it. I am actually lucky that this course is handled in my college by an expert in this topic, but even he is constrained because the college requires you to rush through all the theorems within one semester and one is not given enough time to understand the subtleties. But it is always best continue to reflect on it even after the course is done.





P.S: The weekend sessions have been going on. Everybody has just been too busy to put up the summary. We have had three sessions within a span of four days. Karthik made quite a lot of connections in classical mechanics during his class on friday. I conducted a test on saturday on whatever has been done, to judge the understanding so far. Today was Shruthi's session on QM, which was again taken up mostly by Karthik to make known previously unspoken things. 

CHANDRASEKHAR CENTENARY LECTURE

Title: From white  dwarfs  to  holography and quantum gravity


Date: 19th Oct, 4:00pm, CHEP Seminar Hall (IISC)


Abstract:
The talk aims to trace the influence of the Chandrasekhar limit
in  understanding  the physics of gravity. Here
is a summary of the salient points which will be covered
in the talk.


Around the time when Chandrasekhar was born ,
the white dwarf  was regarded  as  a bete noir by  astronomers.  During
1930-35 , Chandrasekhar proved that massive stars which have
run out their fuel , can not rest in peace as white dwarfs if their mass
exceeds 1.44 times the mass of the Sun , because  gravitation will
overwhelm all other forces and they  must collapse.
Recalling later developments, in  1982  during the Eddington centenary
lecture  Chandrasekhar said " the existence  for a limiting mass   is
inextricably woven into the present fabric of astronomical tapestry with
its complex designs of stellar evolution , nuclear burning in the
 high - density cores of certain stars  and gravitational collapse
leading to supernova phenomenon and the formation of neutron  stars of
nearly the same mass and of black holes. " .

In the  nineteen thirties  famous but older physicists  disliked the idea
of ultimate  collapse and disapproved of singularities of the equations of
physics. Along with the issue of stellar collapse there was also the
parallel  problem  regarding cosmological singularities present   in
models of the Universe . Are singularities rigorous results of equations
of physics or the work of maladroit  theorist  ?  The seminal  work of
Raychaudhuri  in the fifties , paved the way for Penrose  Hawking  and
Geroch , to prove a decade later
-1) the inevitability for collapse  into black hole  by a massive  star
on the one hand
2)  strengthened  the basis of big bang cosmology on the other . It is
consistent with astronomical data  to  assume that our  Universe
began with a singularity  .

Today thousands of white dwarfs with mass below Chandrasekhar limit are
known with their structure and properties well understood . They are an
important standard in astronomy.  Many stellar mass black holes are known
today.

Classical black holes absorb everything and  pose a problem for the second
law of thermodynamics .  Hawking's  discovery that in quantum theory ,
black holes must radiate  resolves this  but brings in fresh issues in its
wake  , challenging our  understanding of interface
between the inside and  outside of  a black hole .

Speaker: J. Pasupathy.
Affiliation: CHEP



I think we should all attend this lecture. Seems mouthwatering. Ciao