Thursday, July 31, 2014

[1312.2007] The Amplituhedron

[1312.2007] The Amplituhedron:



"Perturbative scattering amplitudes in gauge theories have remarkable simplicity and hidden infinite dimensional symmetries that are completely obscured in the conventional formulation of field theory using Feynman diagrams. This suggests the existence of a new understanding for scattering amplitudes where locality and unitarity do not play a central role but are derived consequences from a different starting point. In this note we provide such an understanding for N=4 SYM scattering amplitudes in the planar limit, which we identify as ``the volume" of a new mathematical object--the Amplituhedron--generalizing the positive Grassmannian. Locality and unitarity emerge hand-in-hand from positive geometry."



'via Blog this'

Why is Space 3D?

A friend got me thinking about this basic question, here I write ideas related to it.

There is a perception issue to begin with. If your rooms are not cubes, like most people's, from my city of birth, you may not know what 3D is. Then you have to go to a technical high school like I did, and then you learn everything about vectors, having fun with it, like I did. I still remember explaining to a friend, who was absent that day, these ideas. I was really excited. We had already studied Cartesian Geometry in a previous lesson. All the abstract frame, was in my head, by the time I was a teenager.

Now I am over sixty, and I still don't know, why it is so. I do not feel bad, because nobody does.

Now I know much more, I even  personally met one actor of this narrative. Let me start there:

Manoj Prasad, was a very young, and famous person, when I met him. He discovered, with his professor Michael Sommerfield, what we now call, the Bogomol'nyi-Prasad-Sommerfield monopole. Neat exact solution, to a Non-Abelian field. To this day nobody has seen one of these, in the real world, so far it only exists in our minds.

As it turns out, these exact solutions exist in 3D, and through the magic of the gauge field, involve time as well. We know we live in 3 huge spatial dimensions, and something inside, or prior to us, maybe the so-called strings, has been around during a huge time. To be exact 13.798±0.037 billion years, according to Wikipedia.

Why?

It gets curiouser and curiouser, as Alice in Wonderland says.

Enter Roger Penrose, unfortunately I have not met him personally, but two friends did. One was his contemporary, Jerzy Plebanski, and the other is younger than I, Gerardo Torres del Castillo.

Penrose loved complex variables, like I did. He was studying mathematics in England, and had the insight, that a set of two complex manifolds together, would make a neat mathematical representation, of the four dimensional macroscopic space, we were born in. This proposal goes by the name of Twistor Theory.

To finish this note, I link to the computer calculations done by a Japanese group, as reported a few years back.

You can read about it in Discover Magazine.


[1312.7878] Into the Amplituhedron

[1312.7878] Into the Amplituhedron:



"We initiate an exploration of the physics and geometry of the amplituhedron, starting with the simplest case of the integrand for four-particle scattering in planar N=4 SYM. We show how the textbook structure of the unitarity double-cut follows from the positive geometry. We also use the geometry to expose the behavior of the multicollinear limit, providing a direct motivation for studying the logarithm of the amplitude. In addition to computing the two and three-loop integrands, we explore various lower-dimensional faces of the amplituhedron, thereby computing non-trivial cuts of the integrand to all loop orders."



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[hep-th/9707009] BPS Monopoles

[hep-th/9707009] BPS Monopoles:



"We review classical BPS monopoles, their moduli spaces, twistor descriptions and dynamics. Particular emphasis is placed upon symmetric monopoles, where recent progress has been made. Some remarks on the role of monopoles in S-duality and Seiberg-Witten theory are also made."



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[1210.3382] Generalized BPS magnetic monopoles

[1210.3382] Generalized BPS magnetic monopoles:



"We show the existence of Bogomol'nyi-Prasad-Sommerfield (BPS) magnetic monopoles in a generalized Yang-Mills-Higgs model which is controlled by two positive functions. This effective model, in principle, would describe the dynamics of the nonabelian fields in a chromoelectric media. We check the consistency of our generalized construction by analyzing an explicit case ruled by a real parameter. We also use the well-known spherically symmetric Ansatz to attain the corresponding self-dual equations describing the topological solutions. The overall conclusion is that the new solutions behave around the canonical one, with smaller or greater characteristic length."



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MICZ-Kepler System

C stands for the Mexican physicist Arturo Cisneros Stoianoswki

[0711.1037] Generalizations of MICZ-Kepler system

[0711.1037] Generalizations of MICZ-Kepler system:



"We discuss the generalizations of the MICZ-Kepler system (the system describing the motion of the charged particle in the field of Dirac dyon), to the curved spaces, arbitrary potentials and to the multi-dyon background."



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[1004.4579] Generalized MICZ-Kepler system, duality, polynomial and deformed oscillator algebras

[1004.4579] Generalized MICZ-Kepler system, duality, polynomial and deformed oscillator algebras:



"We present the quadratic algebra of the generalized MICZ-Kepler system in three-dimensional Euclidean space E3 and its dual the four dimensional singular oscillator in four-dimensional Euclidean space E4. We present their realization in terms of a deformed oscillator algebra using the Daskaloyannis construction. The structure constants are in these cases function not only of the Hamiltonian but also of other integrals commuting with all generators of the quadratic algebra. We also present a new algebraic derivation of the energy spectrum of the MICZ-Kepler system on the three sphere S3 using a quadratic algebra. These results point out also that results and explicit formula for structure functions obtained for quadratic, cubic and higher order polynomial algebras in context of two-dimensional superintegrable systems may be applied to superintegrable systems in higher dimensions with and without monopoles."



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[1312.5415] A renormalization group method for studying the early universe in the Lorentzian IIB matrix model

[1312.5415] A renormalization group method for studying the early universe in the Lorentzian IIB matrix model:



"We propose a new method for studying the early universe in the Lorentzian version of the IIB matrix model, which is considered to be a nonperturbative formulation of superstring theory. This method is based on the idea of renormalization group, and it enables us to study the time-evolution of the universe for much longer time than in the previous work, which showed that the SO(9) rotational symmetry is spontaneously broken down to SO(3) after a "critical time". We demonstrate how this method works in a simplified model, which is expected to capture the behaviors of the original model when the space is not so large. In particular, we present clear evidence that the three-dimensional space expands exponentially after the critical time in this simplified model."



'via Blog this'

Wednesday, July 30, 2014

U.S. Economy Grew at 4% Rate in Second Quarter, Beating Expectations - NYTimes.com

U.S. Economy Grew at 4% Rate in Second Quarter, Beating Expectations - NYTimes.com:



 "The United States economy rebounded heartily in the spring after a dismal winter, the Commerce Department reported on Wednesday, growing at an annual rate of 4 percent from April through June and surpassing economists’ expectations."



'via Blog this'

Tuesday, July 29, 2014

Why Can’t the Banking Industry Solve Its Ethics Problems? - NYTimes.com

Why Can’t the Banking Industry Solve Its Ethics Problems? - NYTimes.com:



 "The financial crisis that nearly brought down the global economy was triggered in no small part by the aggressive culture and spotty ethics within the world’s biggest banks. But after six years and countless efforts to reform finance, the banking scandals never seem to end."



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Monday, July 28, 2014

Ultra-high-energy cosmic ray - Wikipedia, the free encyclopedia

Ultra-high-energy cosmic ray - Wikipedia, the free encyclopedia:



"In astroparticle physics, an ultra-high-energy cosmic ray (UHECR) is a cosmic ray particle with a kinetic energy greater than 1018 eV, far beyond both its rest mass and energies typical of other cosmic ray particles."



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U.S. and Europe Agree to Escalate Sanctions on Russia - NYTimes.com

U.S. and Europe Agree to Escalate Sanctions on Russia - NYTimes.com:



 "FRANKFURT — The United States and Europe put aside their differences and agreed on Monday to sharply escalate economic sanctions against Russia in a set of coordinated actions driven by the conclusion that Moscow has taken a more direct role in the war in Ukraine."



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Sunday, July 27, 2014

Tax Avoidance du Jour: Inversion - NYTimes.com

Tax Avoidance du Jour: Inversion - NYTimes.com:



 "In recent decisions, the conservative majority on the Supreme Court has made clear its view that corporations are people, with all the attendant rights. They are entitled to free speech, which in their case means spending lots of money to bend the political process to their ends. They are entitled to religious beliefs, including those that mean denying benefits to their workers. Up next, the right to bear arms?"



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After Rejecting a Cease-Fire, Hamas Proposes a New One - NYTimes.com

After Rejecting a Cease-Fire, Hamas Proposes a New One - NYTimes.com:



 "JERUSALEM — Israel and Hamas went back and forth on Sunday over proposals for a humanitarian lull in the fighting in Gaza, underscoring the external and internal pressures on both sides."



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Eight hundred dead Palestinians. But Israel has impunity - Comment - Voices - The Independent

Eight hundred dead Palestinians. But Israel has impunity - Comment - Voices - The Independent:



"Impunity is the word that comes to mind. Eight hundred dead Palestinians. Eight hundred. That’s infinitely more than twice the total dead of flight MH17 over Ukraine. And if you refer only to the “innocent” dead – ie no Hamas fighters, young sympathisers or corrupt Hamas officials, with whom the Israelis will, in due course, have to talk – then the women and children and elderly who have been slaughtered in Gaza are still well over the total number of MH17 victims."



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3D Moebius



Saturday, July 26, 2014

What Is News? - NYTimes.com

What Is News? - NYTimes.com:



"FORT-DAUPHIN, Madagascar — WITH the world going crazy, I tried running away from the news. It didn’t work."



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Why the Border Crisis Is a Myth - NYTimes.com

Why the Border Crisis Is a Myth - NYTimes.com:



 "EL PASO — TO hear the national news media tell the story, you would think my city, El Paso, and others along the Texas-Mexico border were being overrun by children — tens of thousands of them, some with their mothers, arriving from Central America in recent months, exploiting an immigration loophole to avoid deportation and putting a fatal strain on border state resources."



'via Blog this'

Militants Resume Firing Rockets Into Israel From Gaza - NYTimes.com

Militants Resume Firing Rockets Into Israel From Gaza - NYTimes.com:



"GAZA — Militants resumed firing rockets into Israel from Gaza around two hours after the end of a 12-hour ceasefire, the armed wing of Islamist group Hamas said."



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A Brief Cease-Fire Gives Gazans and Israelis a Chance to Take Stock - NYTimes.com

A Brief Cease-Fire Gives Gazans and Israelis a Chance to Take Stock - NYTimes.com:



"BEIT HANOUN, Gaza Strip — Families across the Gaza Strip emerged from shelters and returned to their homes during a 12-hour cease-fire on Saturday to survey the damage to their neighborhoods, collect belongings and help dig bodies from the rubble, as Secretary of State John Kerry met in Paris with Arab and European diplomats to urge that the humanitarian truce be extended for at least another 12 hours."



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Friday, July 25, 2014

Death in the Peace Corps: A Trail of Medical Missteps - NYTimes.com

Death in the Peace Corps: A Trail of Medical Missteps - NYTimes.com:



"BRENTWOOD, Calif. — Nick Castle had just graduated from the University of California, Berkeley, when he loaded up his backpack with Mandarin-language books and set off for rural China to teach in the Peace Corps. Seven months later, in January 2013, a 2 a.m. telephone call jolted his parents awake."



'via Blog this'

As Ukraine Forces Make Headway, Russia Is Said to Step Up Role - NYTimes.com

As Ukraine Forces Make Headway, Russia Is Said to Step Up Role - NYTimes.com:



 "KIEV, Ukraine — Russia has stepped up its direct involvement in fighting between the Ukranian military and separatist insurgents, unleashing artillery attacks from Russian territory and massing heavy weapons along the border, Ukrainian and American officials say."



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