Mathematical physics

Mathematical physics, including mathematics, is a research area where novel mathematical techniques are invented to tackle problems in physics, and where novel mathematical ideas find an elegant physical realization. Historically, it would have been impossible to distinguish between theoretical physics and pure mathematics. Often spectacular advances were seen with the concurrent development of new ideas and fields in both mathematics and physics. Here one might note Newton's invention of modern calculus to advance the understanding of mechanics and gravitation. In the twentieth century, quantum theory was developed almost simultaneously with a variety of mathematical fields, including linear algebra, the spectral theory of operators and functional analysis. This fruitful partnership continues today with, for example, the discovery of remarkable connections between gauge theories and string theories from physics and geometry and topology in mathematics.

Displaying 781 - 792 of 904

Non equilibrium thermodynamic of gravitational screens

Laurent Freidel Perimeter Institute for Theoretical Physics
February 19, 2014

PIRSA:14020144
Quantum Gravity

Mathematical physics
Fractional statistics in two-dimensions: Anyon there?

Smitha Vishveshwara University of Illinois Urbana-Champaign
November 06, 2013

PIRSA:13110062
Mathematical physics
Slippery Waves: Brilliance Brings Blind Spots

Leo Kadanoff
September 25, 2013

PIRSA:13090051
Mathematical physics
Conjugates, Correlation and the Jordan Structure of Finite-Dimensional Quantum Theory
May 30, 2013

PIRSA:13050070
Mathematical physics
Resources

Tobias Fritz Universität Innsbruck
May 15, 2013

PIRSA:13050019
Mathematical physics
TQFTs and Topological Phases of Matter

Zhenghan Wang Microsoft Corporation
May 06, 2013

PIRSA:13050022
Mathematical physics
Energy and the Environment - What Physicists Can Do

John Baez University of California, Riverside
April 17, 2013

PIRSA:13040030
Mathematical physics
Mathematica - Lecture 4

Pedro Vieira Perimeter Institute for Theoretical Physics
December 14, 2012

PIRSA:12120022
Mathematical physics
Mathematica - Lecture 3b

Pedro Vieira Perimeter Institute for Theoretical Physics
December 10, 2012

PIRSA:12120021
Mathematical physics
Mathematica - Lecture 3a

Pedro Vieira Perimeter Institute for Theoretical Physics
December 10, 2012

PIRSA:12120020
Mathematical physics
Geometric algebra techniques in flux compactifications

Calin Lazaroiu Horia Hulubei National Institute for R and D in Physics and Nuclear Engineering
November 09, 2012

PIRSA:12110058
Mathematical physics
Is spacetime fundamentally discrete?
- Bianca Dittrich Perimeter Institute for Theoretical Physics
- Seth Major Hamilton College
- Daniele Oriti Complutense University of Madrid
- Roberto Percacci SISSA International School for Advanced Studies
- Tobias Fritz Universität Innsbruck
October 24, 2012

PIRSA:12100100
Mathematical physics

Non equilibrium thermodynamic of gravitational screens

Laurent Freidel Perimeter Institute for Theoretical Physics
February 19, 2014

PIRSA:14020144
Quantum Gravity

Mathematical physics
In this talk I will review the evidence for a mysterious and deep relationship between gravitational dynamics and thermodynamics. I will show how we can extend this connection to non equilibrium thermodynamics. Using the fact that the gravitational equations are fundamentally holographic, we express them in a way that shows a deep connection between gravity and the dynamics of viscous bubbles. We will explore some aspects of this surprising correspondence.
Fractional statistics in two-dimensions: Anyon there?

Smitha Vishveshwara University of Illinois Urbana-Champaign
November 06, 2013

PIRSA:13110062
Mathematical physics
A fascinating aspect of the two dimensional world is the possible existence of anyons, particles which obey 'fractional' statistics different from fermionic and bosonic statistics. In this colloquium, following an introduction to fractional particles in the context of quantum Hall systems, some of the tantalizing experiments for detecting the fractional charge of these particles will be described. Probes of fractional statistics in these systems will be discussed, drawing from analogies with the bosonic behavior of light studied by Hanbury Brown and Twiss in the 1950's as well as in the more recent beam-splitter settings in quantum optics. Finally, the exciting prospect of detecting fractional statistics in the context of superconductors will be explored.
Slippery Waves: Brilliance Brings Blind Spots

Leo Kadanoff
September 25, 2013

PIRSA:13090051
Mathematical physics
Superfluidity and superconductivity are two remarkable phenomena in which, at low temperatures, materials abruptly gain the ability to flow without friction. Microscopic quantum theories of these phases of matter were constructed in blockbuster papers of Lev Landau (1940) and John Bardeen, Leon Cooper, and J. Robert Schrieffer (1957). The actual explanation of the flow, however, is rooted in a Einstein paper of 1924 that introduces a condensate, a quantum configuration describing a finite fraction of the particles in the system. Superfluidity can then be understood in terms of the wave function for this configuration, which necessarily extends over a finite fraction of the system. Neither blockbuster paper mentions Einstein or the crucial idea of a condensate wave function. The reasons for this omission are mooted.
Conjugates, Correlation and the Jordan Structure of Finite-Dimensional Quantum Theory
May 30, 2013

PIRSA:13050070
Mathematical physics
The last few years have seen a spate of operational or information-theoretic
derivations (or \reconstructions") of nite-dimensional quantum mechanics [1]. These rest of some strong assumptions. In particular, most assume the state of a composite system is entirely determined by the joint probabilities it assigns to the outcomes of measurements on the component systems. This condition, often called local tomography, is satis ed by neither real nor quaternionic quantum theory. If we are interested in the possibilities for theories more general than orthodox quantum mechanics, we might wish to relax this constraint.
In this talk I will discuss a weaker system of assumptions, involving correla-
tions between a probabilistic system and an isomorphic conjugate system, that leads to a representation of such systems in terms of euclidean Jordan algebras [2]. These have a well-known classi cation as direct sums of real, complex or quaternionic quantum systems, possibly the exceptional Jordan algebra, and spin factors. The last are a form of \bit", characterized by a family of two-valued observables, parametrized by antipodal vectors in a sphere of arbitrary dimension. Orthodox quantum mechanics can be singled out by imposing local tomography, plus the existence of a qubit as additional axioms [3]. However, there is a natural way to form non-signaling, but generally non-locally tomo-graphic, composites of systems based on special euclidean Jordan algebras (that is, excluding the exceptional one). This yields a probabilistic theory strictly, but not wildly, more general than orthodox nite-dimensional QM; one that elegantly uni es real, complex and quaternionic quantum theory, has a simple operational basis, and allows for a spectrum of bits more general than permitted in orthodox quantum theory. Parts of this talk reflect ongoing joint work with Howard Barnum, Matthew Graydon and Cozmin Ududec.
References:
[1] G. Chiribella, M. D'Ariano and P. Perinotti, Phys. Rev. A 84, (2011), 012311-
012350; B. Dakic and C. Brukner, in H. Halvorson (ed.), Deep Beauty, Cambridge,
2011; P. Goyal, Phys. Rev. A 78 (2008), 052120-052146; L. Hardy, arXiv:quant-
ph/0101012 (2001); L. Masanes and M. Mueller, New J. Phys. 13 (2011) ; J. Rau,
Annals of Physics 324 (2009) 2622{2637;
[2] A. Wilce, Conjugates, correlation and quantum mechanics, arXiv:1206.2897 (2012)
[3] H. Barnum and A. Wilce, Local tomography and the Jordan structure of quantum
theory, arXiv:1202.4513, (2012)
Resources

Tobias Fritz Universität Innsbruck
May 15, 2013

PIRSA:13050019
Mathematical physics
One of the main challenges that we face both as individual persons and as a species concerns the distribution and use of resources, such as water, time, capital, computing power or negatively valued
resources like nuclear waste. Also within theoretical physics, one frequently deals with resources like free energy or quantum entanglement. I will describe a mathematical theory of resources which makes quantitative predictions about how many resources are required for producing a certain commodity and outline some applications to information theory.
Joint work with Bob Coecke and Rob Spekkens.
TQFTs and Topological Phases of Matter

Zhenghan Wang Microsoft Corporation
May 06, 2013

PIRSA:13050022
Mathematical physics
In two spatial dimensions, there is a good correspondence between TQFTs and topological phases of matter for spin systems. I will discuss this correspondence in one and three spatial dimensions for spin systems. If time permits, I will also discuss the situation for fermion systems.
Energy and the Environment - What Physicists Can Do

John Baez University of California, Riverside
April 17, 2013

PIRSA:13040030
Mathematical physics
The global warming crisis is part of a bigger transformation in which humanity realizes that the Earth is a finite system and that our population, energy usage, and the like cannot continue to grow exponentially. While politics and economics pose the biggest challenges, physicists are in a good position to help make this transition a bit easier. After a quick review of the problems, we discuss a few ways physicists can help.
Mathematica - Lecture 4

Pedro Vieira Perimeter Institute for Theoretical Physics
December 14, 2012

PIRSA:12120022
Mathematical physics
Mathematica - Lecture 3b

Pedro Vieira Perimeter Institute for Theoretical Physics
December 10, 2012

PIRSA:12120021
Mathematical physics
Mathematica - Lecture 3a

Pedro Vieira Perimeter Institute for Theoretical Physics
December 10, 2012

PIRSA:12120020
Mathematical physics
Geometric algebra techniques in flux compactifications

Calin Lazaroiu Horia Hulubei National Institute for R and D in Physics and Nuclear Engineering
November 09, 2012

PIRSA:12110058
Mathematical physics
Using techniques originating in a certain approach to Clifford bundles known as "geometric algebra", I discuss a geometric reformulation of constrained generalized Killing spinor equations which proves to be particularly effective in the study and classification of supersymmetric flux compactifications of string and M-theory. As an application, I discuss the most general N=2 compactifications of M-theory to three dimensions, which were never studied in full generality before. I also touch upon the connection of such techniques with a certain variant of the quantization of spin systems.
Is spacetime fundamentally discrete?
- Bianca Dittrich Perimeter Institute for Theoretical Physics
- Seth Major Hamilton College
- Daniele Oriti Complutense University of Madrid
- Roberto Percacci SISSA International School for Advanced Studies
- Tobias Fritz Universität Innsbruck
October 24, 2012

PIRSA:12100100
Mathematical physics
Modelling continuum dynamics on discrete space time
We will discuss perfect discretizations which aim at mirroring exactly continuum physics on a given lattice. Such discretizations avoid typical artifacts like Lorentz violation, energy dissipation, particle doubling and in particular breaking of diffeomorphism symmetry. Thus the question arises how to distinguish such lattice dynamics from continuum physics.

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Turning Weyl’s tile argument into a mathematically rigorous no-go theorem
Weyl's tile argument notes that if space was fundamentally discrete then the set of allowed velocities of a classical particle would not be isotropic. I will generalize Weyl's heuristic argument to a no-go theorem applying to any discrete periodic structure. Since this theorem does not take quantum mechanics into account it should only be regarded as the first step of a program of understanding the phenomenology of discrete spacetimes in a mathematically rigorous way.See arXiv:1109.1963

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On the Observability of Discrete Spatial Geometry
If quantum geometry is an accurate model of microscopic spatial geometry then two related questions arise, one observational and one theoretical: How and at what scale is the discreteness manifest? And, how is the general relativistic limit achieved? These questions will be discussed in the context of studies of a single atom of geometry. It will be shown that the effective scale of the discreteness could be much larger than the Planck scale. Before this scale can be predicted, the relations between discrete geometry, coherent states, and the semiclassical limit need to be clarified. Work towards this goal, using coherent states in spin foams and the spin geometry theorem of Penrose and Moussouris will be described.

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Asymptotic safety and minimal length
Since asymptotic safety - if true - would make a quantum field theory of gavity consistent "up to arbitrarily high energy", it would seem that this notion is incompatible with the existence of a minimal length. I will argue that this is not necessarily the case, due to ambiguity in the notion of minimal length.

Title	Speaker(s)	Date	Talk Type	Info link
Non equilibrium thermodynamic of gravitational screens	Laurent Freidel	2014-02-19	Scientific Series	View details
Fractional statistics in two-dimensions: Anyon there?	Smitha Vishveshwara	2013-11-06	Scientific Series	View details
Slippery Waves: Brilliance Brings Blind Spots	Leo Kadanoff	2013-09-25	Scientific Series	View details
Conjugates, Correlation and the Jordan Structure of Finite-Dimensional Quantum Theory		2013-05-30	Conference	View details
Resources	Tobias Fritz	2013-05-15	Scientific Series	View details
TQFTs and Topological Phases of Matter	Zhenghan Wang	2013-05-06	Conference	View details
Energy and the Environment - What Physicists Can Do	John Baez	2013-04-17	Scientific Series	View details
Mathematica - Lecture 4	Pedro Vieira	2012-12-14	Course	View details
Mathematica - Lecture 3b	Pedro Vieira	2012-12-10	Course	View details
Mathematica - Lecture 3a	Pedro Vieira	2012-12-10	Course	View details
Geometric algebra techniques in flux compactifications	Calin Lazaroiu	2012-11-09	Scientific Series	View details
Is spacetime fundamentally discrete?	Bianca Dittrich, Seth Major, Daniele Oriti, Roberto Percacci, Tobias Fritz	2012-10-24	Conference	View details

Mathematical physics

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