Supersymmetry on Lattice : An Introduction Wednesday, Jul 4 2007 

Last week, I gave a presentation titled “Supersymmetry on Lattice- An Introduction”[PDF] as a part of a course on Lattice Field theory.

It was an attempt at outlining the broad issues that arise when one tries to put Supersymmetry in Lattice. I have uploaded the presentation in the link above – Readers comments and criticisms are welcome.

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Links on Nuclear Supersymmetry Wednesday, Nov 8 2006 

susy.jpg

Explanation of the image : In the words of its designer,

It has an apple in front of a mirror and the reflection is an orange. The idea being that fermions and bosons are as different as proverbial apples and oranges, yet supersymmetry (the mirror) relates them.

So why does this image have two mirrors at right angles and a total of four objects (one real, and three images)? Because it actually depicts a specific kind of supersymmetry that arises in nuclear physics. The symmetry relates the spectra of of four nuclei that differ by one in their number of protons or neutrons. If you like, there are two superymmetries at work; one changes the number of protons by 1, the other changes the number of neutrons by 1. Hence two mirrors.

Two of the elements related in this way are platinum and gold, which is why the orange in the mirror on the left is silvery, and the apple at the rear is golden….For completeness, here’s the caption that went with the image:

PROVERBIAL APPLES AND ORANGES are as different as the types of quantum particles called fermions and bosons. Just as an ordinary mirror cannot make an apple look like an orange, no ordinary symmetry in physics can transform a fermion into a boson, or vice versa. To do that trick requires supersymmetry, an extraordinary class of symmetries that may hold the key to a deep understanding of the universe. Experimenters have detected a nuclear version of supersymmetry that connects two isotopes of gold and two of platinum.

Now to the actual post. Sometime ago, I was collecting links on nuclear supersymmetry(explanation below) for Adish and I came across some really good articles on the subject worth posting here.

Note that this supersymmetry is different from the one which can occur in particle physics. Whereas supersymmetry in particle physics is still just a hypothesis waiting to be confirmed/disproved , there are occurences of supersymmetry in nuclear physics which seem to have stronger evidences to its favour.

You can start off by looking at these two news articles(written at a popular level) which report evidences for nuclear supersymmetry

Supersymmetry stands the test
Evidence for supersymmetry found

These were inspired by the PRL paper- Evidence for the Existence of Supersymmetry in Atomic Nuclei by Metz.,et al (subscription required)

Another good article written at a popular level is an article from Scientific american titled Uncovering Supersymmetry. Just to nudge you into reading this, I’ll give some excerpts out of it

Supersymmetry is a remarkable symmetry. In elementary particle physics, it interchanges particles of completely dissimilar types—the kind called fermions (such as electrons, protons and neutrons), which make up the material world, and those called bosons (such as photons), which generate the forces of nature. Fermions are inherently the individualists and loners of the quantum particle world: no two fermions ever occupy the same quantum state. Their aversion to close company is strong enough to hold up a neutron star against collapse even when the crushing weight of gravity has overcome every other force of nature. Bosons, in contrast, are convivial copycats and readily gather in identical states. Every boson in a particular state encourages more of its species to emulate it. Under the right conditions, bosons form regimented armies of clones, such as the photons in a laser beam or the atoms in superfluid helium 4.

Yet somehow in the mirror of supersymmetry, standoffish fermions look magically like sociable bosons, and vice versa….

At least that’s the theory. Elementary particle theorists have studied
supersymmetry intensively since its invention in the 1970s, and many
believe it holds the key to the next major advance in our understanding
of the fundamental particles and forces. Experimenters, however, have
searched at their highest-energy colliders for particles predicted by
supersymmetry, so far to no avail.

In the 1980s nuclear theorists proposed that superviolent collisions were
not necessarily the only way to see supersymmetry; they predicted that
a different form of supersymmetry could exist in certain atomic nuclei.
Here, too, the symmetry relates what in physics are quite dissimilar objects: nuclei with even numbers of protons and neutrons and those with odd numbers.(This again involves fermions and bosons, because a composite particle made of an odd number of fermions is itself a fermion, whereas an even number produces a boson.)….

The atomic nucleus is a fascinating quantum system holding many secrets. Its study over the decades has been a continuous source of unexpected observations. Theorists must use many tools to understand all the facets of the very complicated physics of nuclei. The new result adds supersymmetry to the toolkit and it shows that supersymmetry is not just a mathematical curiosity but exists in the world.

Nuclear physics research also provides tools needed to understand other quantum systems that have general features similar to nuclei— the so-called finite many-body systems, containing anything from a few particles to hundreds of them. Experimental methods now allow the study of such objects built from small numbers of atoms or molecules. Supersymmetry might also be important to those fields of physics…

Do read the whole article !

Endnote : For people who are not satisfied with popular articles, I will provide below some more technical articles that I came across. Note that I’ven’t read/understood any of these completely 🙂


An Introduction to Nuclear Supersymmetry: a Unification Scheme for Nuclei

Dynamic symmetries and supersymmetries in nuclear physics(RMP article – subscription required)

Dynamical symmetries in the structure of nuclei

A good (but, unfortunately old) review on interacting boson model – The interacting boson model of nuclear structure

Supersymmetry series at TowardsTengen Friday, Jul 7 2006 

Background: Nothing more than basic Quantum Mechanics, actually. Knowing a bit of QFT would be useful, but not essential.

I’m trying to write up a bit about what I’ve been doing, the first (badly written) installment is up here.  In case you check it out, let me know if there are any errors or mistakes.
Link: http://towardstengen.wordpress.com/2006/07/07/susy/

Enjoy Physics …

Anderson’s article Saturday, May 6 2006 

anderson_philip.jpg

Background: I guess quantum mechanics would do. Since, as usual, high-energy physics is dominating the posts here, it’s time for some condensed matter stuff. Let us start with what is arguably the most famous article in CMP.

Link : P. W. Anderson, “More is different”, Science 177, 393 (1972)
(via the blog http://nanoscale.blogspot.com/ which is one of the very few blogs dealing with condensed matter physics.)

This article outlines what I call the “Anderson philosophy behind CMP” 🙂 In case you didn’t know, P.W.Anderson(Physics Nobel Laureate(1977) – is arguably among the most famous physicists in condensed matter physics. You can find his website at Princeton here and here.

And people who are into condensed matter physics would find this link to Journal Club for Condensed Matter Physics from Bell-labs interesting ….

Posted by : Loganayagam.R.

Time Reversal Invariance Saturday, Apr 8 2006 

There is something about the time reversal principle that I dont completely understand.

Consider an isolated gas of molecules that has undergone expansion in volume. Now, we know that Newtonian dynamics obeys time reversal symmetry, ie if I reverse the velocities of all particles in the system at some instant, the evolution from then on would be backward. In other words the system would retrace its path. Atleast , this definitely holds when there are no velocity dependent interactions, which we can assume here for the sake of simplicity.
However, we also know for sure (from both second law of thermodynamics and common experience) that isolated gas molecules would never contract (statistically speaking) and decrease in overall volume.

How then does one account for this apparent contradiction?

Posted By :Venkateshan

Symmetry breaking Saturday, Apr 1 2006 

Necessary Background: Not much as the article starts out at a sort of popular science level, but those of us doing Particle Physics now, may appreciate this a bit more.

Link: http://cosmicvariance.com/2005/10/24/hidden-symmetries/

Comment: This blog is quite interesting by the way, with a lot of interesting discussions by a few High energy and Astrophysics people, so check it out when you have the time at http://www.cosmicvariance.com/ or http://cosmicvariance.com/category/science/

Posted by: Shanth

Identical Particles Saturday, Apr 1 2006 

This came up during a Particle Physics discussion :

Here is a proof that the wavefunction of n identical particles has to be either completely symmetric or anti-symmetric.

Wavefunction ψ=ψ(a1,a2,……..,an)

Let Pij be the operator which flips particles i and j

Now indistinguishability requires

Pijψ=c ψ

Since flipping twice results in the same wavefunction

Pij Pij ψ = ψ

Implies c=1 or -1

Now consider this relation

Pij=Pik Pkj Pki

One can easily veryify that this true by looking at the action of Pij on the ordrerd set (i,j,k).

Since Pik Pik=1

Pij=Pkj

Extending this simlarly one gets

Pij = Pik = Pkl for any k,l

Thus Pfg = c for all f,g

Thus the wavefunction has to be completely symmetric or antisymmetric.

Venkateshan

PS: I took the liberty of tidying up the notation, hope I didn't make any mistake/ change your argument. –Shanth

How to Talk to a Physicist: Groups, Symmetry, and Topology Saturday, Apr 1 2006 

Necessary Background : Mathematical Physics, Quantum mechanics, probably quantum field theory/Particle Physics for the later parts. But, more than anything else, interest in symmetry groups and topology as they enter into physics.
Link : from http://physics.harvard.edu/~dtlarson/tutorial05/

Groups, Symmetry, and Topology

Comment : This is a collection lecture notes written in a kind of no-nonsense approach. Contains a short intro to Lie Algebra, its representations and stuff. Do look at the list of books provided at the site linked above !

Posted By : Loganayagam.R.(Tom)