Mathematical Physics

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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
New Directions in Categorical Logic for Classical, Probabilistic and Quantum Physics

Tobias Fritz Universität Innsbruck
October 09, 2012

PIRSA:12100055
Mathematical Physics
AdS(3)/CFT(2) correspondence and integrability

Konstantin Zarembo Nordic Institute for Theoretical Physics
October 09, 2012

PIRSA:12100062
High Energy Physics

Mathematical Physics
Hamiltonian Theory of Fractional Chern Bands

Ramamurti Shankar Yale University
September 14, 2012

PIRSA:12090047
Mathematical Physics
Introduction to Mathematica - Lecture 2b

Pedro Vieira Perimeter Institute for Theoretical Physics
September 07, 2012

PIRSA:12090053
Mathematical Physics
Introduction to Mathematica - Lecture 2a

Pedro Vieira Perimeter Institute for Theoretical Physics
September 07, 2012

PIRSA:12090052
Mathematical Physics
Entropic uncertainty relations for quantum operations

Karol Zyczkowski Jagiellonian University
September 05, 2012

PIRSA:12090057
Mathematical Physics
Ising Model

John Berlinsky McMaster University
September 04, 2012

PIRSA:12090054
Mathematical Physics
Introduction to Mathematica - Lecture 1b

Pedro Vieira Perimeter Institute for Theoretical Physics
September 04, 2012

PIRSA:12090051
Mathematical Physics
Introduction to Mathematica - Lecture 1a

Pedro Vieira Perimeter Institute for Theoretical Physics
September 04, 2012

PIRSA:12090041
Mathematical Physics
Integral Transforms & Green's Functions - Lecture 4

David Kubiznak Charles University
August 30, 2012

PIRSA:12080031
Mathematical Physics
Integral Transforms & Green's Functions - Lecture 3

David Kubiznak Charles University
August 29, 2012

PIRSA:12080030
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
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.

______________________________

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.
New Directions in Categorical Logic for Classical, Probabilistic and Quantum Physics

Tobias Fritz Universität Innsbruck
October 09, 2012

PIRSA:12100055
Mathematical Physics
I will give an idea of what category theory is and how it can be successfully applied in mathematics and the mathematical sciences by means of example. The example is a notion from mathematical logic formalizing the intuitive concept of "property". The new category-theoretical definition of this notion can physically be interpreted as a measurement. Unraveling this definition in particular categories can be regarded as defining the concept of "property" in different context, e.g. in classical, probabilistic and quantum physics, and in each case this recovers familiar things.
Disclaimer: Up to some differences in the technical details, all of this is work of Bart Jacobs. (See arXiv:1205.3940)
AdS(3)/CFT(2) correspondence and integrability

Konstantin Zarembo Nordic Institute for Theoretical Physics
October 09, 2012

PIRSA:12100062
High Energy Physics

Mathematical Physics
Integrability has been successfully used to compute the non-perturbative spectrum, Wilson loops and scattering amplitudes in the AdS/CFT correspondence. Most of these results apply to N=4, D=4 SYM / strings on AdS(5)xS(5). Strings on AdS(3)xM, where M is either S(3)xT(4) or S(3)xS(3)xS(1), are also integrable and potentially solvable by the same methods (Bethe ansatz, Y-system, TBA etc). An interesting aspect of string theory on AdS(3) is a large number of parameters that preserve integrability. One parameters, in particular, interpolates between the integrable RR AdS(3) background and conformal NSNS background described by a non-compact WZW model. Another interesting aspect of string theory on AdS(3) is emergence of target-space Viraroso symmetry. I will review how integrability arises in the AdS(3)/CFT(2) correspondence, and will describe what is (not) know about the Bethe ansatz solution of the relevant sigma-models.
Hamiltonian Theory of Fractional Chern Bands

Ramamurti Shankar Yale University
September 14, 2012

PIRSA:12090047
Mathematical Physics
It has been known for some time that a system with a filled band will have an integer quantum Hall conductance equal to its Chern number, a toplogical index associated with the band. While this is true for a system in a magnetic field with filled Landau Levels, even a system in zero external field can exhibit the QHE if its band has a Chern number. I review this issue and discuss a more recent question of whether a partially filled Chern band can exhibit the Fractional QHE. I describe the work done with Ganpathy Murthy in which we show how composite fermions, which were so useful in explaining the usual FQHE, can be introduced here and with equal success by adapting our Hamiltonian Theory of CFs developed for the FQHE in the continuum.
Introduction to Mathematica - Lecture 2b

Pedro Vieira Perimeter Institute for Theoretical Physics
September 07, 2012

PIRSA:12090053
Mathematical Physics
Introduction to Mathematica - Lecture 2a

Pedro Vieira Perimeter Institute for Theoretical Physics
September 07, 2012

PIRSA:12090052
Mathematical Physics
Entropic uncertainty relations for quantum operations

Karol Zyczkowski Jagiellonian University
September 05, 2012

PIRSA:12090057
Mathematical Physics
Ising Model

John Berlinsky McMaster University
September 04, 2012

PIRSA:12090054
Mathematical Physics
Introduction to Mathematica - Lecture 1b

Pedro Vieira Perimeter Institute for Theoretical Physics
September 04, 2012

PIRSA:12090051
Mathematical Physics
Introduction to Mathematica - Lecture 1a

Pedro Vieira Perimeter Institute for Theoretical Physics
September 04, 2012

PIRSA:12090041
Mathematical Physics
Integral Transforms & Green's Functions - Lecture 4

David Kubiznak Charles University
August 30, 2012

PIRSA:12080031
Mathematical Physics
Integral Transforms & Green's Functions - Lecture 3

David Kubiznak Charles University
August 29, 2012

PIRSA:12080030
Mathematical Physics

Title	Speaker(s)	Date	Talk Type	Info link
Is spacetime fundamentally discrete?	Bianca Dittrich, Seth Major, Daniele Oriti, Roberto Percacci, Tobias Fritz	2012-10-24	Conference	View details
New Directions in Categorical Logic for Classical, Probabilistic and Quantum Physics	Tobias Fritz	2012-10-09	Scientific Series	View details
AdS(3)/CFT(2) correspondence and integrability	Konstantin Zarembo	2012-10-09	Scientific Series	View details
Hamiltonian Theory of Fractional Chern Bands	Ramamurti Shankar	2012-09-14	Scientific Series	View details
Introduction to Mathematica - Lecture 2b	Pedro Vieira	2012-09-07	Course	View details
Introduction to Mathematica - Lecture 2a	Pedro Vieira	2012-09-07	Course	View details
Entropic uncertainty relations for quantum operations	Karol Zyczkowski	2012-09-05	Scientific Series	View details
Ising Model	John Berlinsky	2012-09-04	Course	View details
Introduction to Mathematica - Lecture 1b	Pedro Vieira	2012-09-04	Course	View details
Introduction to Mathematica - Lecture 1a	Pedro Vieira	2012-09-04	Course	View details
Integral Transforms & Green's Functions - Lecture 4	David Kubiznak	2012-08-30	Course	View details
Integral Transforms & Green's Functions - Lecture 3	David Kubiznak	2012-08-29	Course	View details

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Mathematical Physics

Format results

Is spacetime fundamentally discrete?

New Directions in Categorical Logic for Classical, Probabilistic and Quantum Physics

AdS(3)/CFT(2) correspondence and integrability

Hamiltonian Theory of Fractional Chern Bands

Introduction to Mathematica - Lecture 2b

Introduction to Mathematica - Lecture 2a

Entropic uncertainty relations for quantum operations

Ising Model

Introduction to Mathematica - Lecture 1b

Introduction to Mathematica - Lecture 1a

Integral Transforms & Green's Functions - Lecture 4

Integral Transforms & Green's Functions - Lecture 3

Is spacetime fundamentally discrete?

New Directions in Categorical Logic for Classical, Probabilistic and Quantum Physics

AdS(3)/CFT(2) correspondence and integrability

Hamiltonian Theory of Fractional Chern Bands

Introduction to Mathematica - Lecture 2b

Introduction to Mathematica - Lecture 2a

Entropic uncertainty relations for quantum operations

Ising Model

Introduction to Mathematica - Lecture 1b

Introduction to Mathematica - Lecture 1a

Integral Transforms & Green's Functions - Lecture 4

Integral Transforms & Green's Functions - Lecture 3