“Quantum field theory is a very rich subject for mathematics as well as physics. But its development in the last seventy years has been mainly by physicists, and it is still largely out of reach as a rigorous mathematical theory despite important efforts in constructive field theory. So most of its impact on mathematics has not yet been felt. Yet in many active areas of mathematics, problems are studied that actually have their most natural setting in quantum field theory. Examples include Donaldson theory of four-manifolds, the Jones polynomial of knots and its generalizations, mirror symmetry of complex manifolds, elliptic cohomology, and many aspects of the study of affine Lie algebras.

To a certain extent these problems are studied piecemeal, with difficulty in understanding the relations among them, because their natural home in quantum field theory is not now part of the mathematical theory. To make a rough analogy (Figure1), one has here a vast mountain range, most of which is still covered with fog. Only the loftiest peaks, which reach above the clouds, are seen in the mathematical theories of today, and these splendid peaks are studied in isolation, because above the clouds they are isolated from one another. Still lost in the mist is the body of the range, with its quantum field theory bedrock and the great bulk of the mathematical treasures.”

this is most lovely….

 

 

 

 

 

 

[gview file=”http://www.billtoole.net/wordpress/wp-content/uploads/2016/05/Surreal_number_tree.svg”]

By Lukáš Lánský If you want to help me create some nicer or more accurate version of this image, see Python code that generates it. I welcome pull requests. – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=19134117

wikipedia entry

 

Childhood home of Srinivasa Ramanujan (1887-1920) : Kumbakonam, Tamil Nadu    |    birthplace of 21st century physics    |   [  see also this in Quanta on the Umbral Moonshine Conjecture ]

 

 

 

 

 

 

 

Thanu Padmanabhan, of the Inter-University Centre for Astronomy and Astrophysics in Pune, India : very nice – a reformulation of the geometry of GR space time using thermodynamics.

via  George Musser

George Musser’s book Spooky Action at a Distance is both erudite and a highly interesting and compelling historical birds eye view of non-locality.

 

Ramanujan’s manuscript. The representations of 1729 as the sum of two cubes appear in the bottom right corner. The equation expressing the near counter examples to Fermat’s last theorem appears further up: α3 + β3 = γ3 + (-1)n. Image courtesy Trinity College library.

see article

The animations above illustrate the typical four-dimensional structure of gluon-field configurations averaged over in describing the vacuum properties of QCD [ Quantum Chromodynamics ]. The volume of the box is 2.4 by 2.4 by 3.6 fm, big enough to hold a couple of protons. Contrary to the concept of an empty vacuum, QCD induces chromo-electric and chromo-magnetic fields throughout space-time in its lowest energy state. After a few sweeps of smoothing the gluon field (50 sweeps of APE smearing), a lumpy structure reminiscent of a lava lamp is revealed. This is the QCD Lava Lamp. The action density (left) and the topological charge density (right) are displayed. The former is similar to an energy density while the latter is a measure of the winding of the gluon field lines in the QCD vacuum.

The animation at left was featured in Prof. Frank Wilczek’s 2004 Nobel Prize Lecture.

Visualizations : Centre for the Subatomic Structure of Matter (CSSM) and Department of Physics, University of Adelaide, 5005 Australia    |    link

 
 
link to JPL

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Srinivasa Ramanujan’s final letter to G. H. Hardy in 1920, explaining his discovery of what he called “mock theta” functions [ image :  Ken Ono ].

see also Quanta magazine article on Umbral Moonshine Conjecture

 

Recent interviews with 5 physicists that give an undoubtedly incomplete [ but terrific nonetheless ] snapshot of where physics is late 2014.

Parameter	Meaning	Measured Value
g θW gs	Weak coupling constant at mZ Weinberg angle Strong coupling constant at mZ	0.6520 ± 0.0001 0.48290 ± 0.00005 1.221 ± 0.022
μ2 λ	Quadratic Higgs coefficient Quartic Higgs coefficient	~ −10−33 ~ 1 ?
Ge Gμ Gτ	Electron Yukawa coupling Muon Yukawa coupling Tauon Yukawa coupling	2.94 × 10−6 0.000607 0.0102156233
Gu Gd Gc Gs Gt Gb	Up quark Yukawa coupling Down quark Yukawa coupling Charm quark Yukawa coupling Strange quark Yukawa coupling Top quark Yukawa coupling Bottom quark Yukawa coupling	0.000016 ± 0.000007 0.00003 ± 0.00002 0.0072 ± 0.0006 0.0006 ± 0.0002 1.002 ± 0.029 0.026 ± 0.003
sin θ12 sin θ23 sin θ13 δ13	Quark CKM matrix angle Quark CKM matrix angle Quark CKM matrix angle Quark CKM matrix phase	0.2243 ± 0.0016 0.0413 ± 0.0015 0.0037 ± 0.0005 1.05 ± 0.24
θqcd	CP – violating QCD vacuum phase	< 10−9
Gνe Gνμ Gντ	Electron neutrino Yukawa coupling Muon neutrino Yukawa coupling Tau neutrino Yukawa coupling	< 1.7 × 10−11 < 1.1 × 10−6 < 0.10
sin θ′12 sin 2θ′23 sin θ′13 δ′13	Neutrino MNS matrix angle Neutrino MNS matrix angle Neutrino MNS matrix angle Neutrino MNS matrix phase	0.55 ± 0.06 ≥ 0.94 ≤ 0.22 ?
ρΛ ξb ξc ξν Q ns	Dark energy density Baryon mass per photon ρb / nγ Cold dark matter mass per photon ρc / nγ Neutrino mass per photon ρν / nγ  =  3⁄11 Σ mνi Scalar fluctuation amplitude δH on horizon Scalar spectral index	(1.25 ± 0.25) × 10−123 (0.50 ± 0.03) × 10−28 (2.5 ± 0.2) × 10−28 < 0.9 × 10−28 (2.0 ± 0.2) × 10−5 0.98 ± 0.02

 

from Dimensionless constants, cosmology and other dark matters : Max Tegmark, Anthony Aguirre, Martin J. Rees & Frank Wilczek

“Every fundamental property of nature ever measured can be computed from the 32 numbers in this table – at least in principle.” Max Tegmark in Our Mathematical Universe