Homepage of Robert Oeckl
Quantum gravity is the search for a theory that may
unify general relativity with quantum mechanics and
ultimately with the standard model of elementary particle physics.
A key obstacle to this unification program lies in the problem that the two theories in question
are built on very different and a priori incompatible conceptual foundations. Concrete
approaches to quantum gravity (such as loop quantum gravity or string theory)
often ignore or postpone the solution of this problem, which thus sheds doubt on their physical
interpretation. This motivates my interest in this problem and more generally in the
foundations of quantum theory.
In particular, I am working on an extension of the standard formulation of quantum mechanics, precisely
to make it compatible with general relativistic concepts and hence overcome the obstacle described.
It turns out that this is best
done directly in the context of quantum field theory rather than nonrelativistic
quantum mechanics. This program is called the general boundary
formulation of quantum theory.
I am also working on more direct
approaches to quantum gravity which are both nonperturbative and backgroundindependent
(in contrast e.g. to string theory).
Surprisingly many approaches have converged on spin foam models, for example
the canonical quantization known as loop quantum gravity as well as covariant
path integral quantizations. Spin foams can be thought of
as encoding quantum spacetime. Remarkably, they exhibit a fundamental discrete
structure.
Current problems include the proper
interpretation as a generally covariant quantum theory (including the problem
of time) and understanding the summation over
spacetimes or histories. The further goal is to
recover classical general relativity and fixedbackground quantum field theory as
limiting cases.
Quantum groups emerged as generalized symmetries in the study of integrable systems.
Ever since, they are of increasing importance in both physics and mathematics.
They play a role in topological quantum field theory and knot invariants, in
quantum gravity, noncommutative geometry, conformal field theory, systems with
anyonic particles, supersymmetry, the renormalization of quantum field theory
as well as other areas. I am interested in many of these connections as they lead
to new and often surprizing links between the different fields.
Furthermore, it appears now that they form a key ingredient in many approaches
at understanding the structure of spacetime at the Planckscale (loop quantum
gravity, noncommutative spacetime models, phenomenological models).
I am also interested in the purely mathematical development of quantum groups
and their role as symmetry objects in noncommutative geometry.
Selected Talks
 Handson with the positive formalism [video], 7 December 2021, Seminar (virtual), Okinawa Institute of Science and Technology, Japan.
 Categorías y la teoría cuántica de campos (español) [video], 10 Anniversary of the Centro de Ciencias Matemáticas, Morelia, Mexico.
 alphaKähler quantization [video], 9 July 2021, Working Seminar “Mathematical Physics” (virtual), Universität Regensburg, Germany.
 What is quantum theory? [video], 16 July 2020, QISS Virtual Seminar.
 Quantization on timelike hypersurfaces in curved spacetime [video], 2 August 2019, Timelike Boundaries in General Relativistic Evolution Problems, Casa Matemática Oaxaca, Oaxaca, Mexico.
 A universal framework for quantum theory from qubits to quantum gravity [slides (PDF)], 23 November 2018, Gravity in Qubits, Smolenice, Slovakia.
 Local quantum operations and causality [various formats], 30 July 2018, Foundations of Quantum Mechanics, Perimeter Institute, Waterloo, Canada.
 Predictions in quantum gravity [slides (PDF)], 16 November 2017, MexiLazos 2017, Instituto de Ciencias Nucleares, UNAM, Mexico City, Mexico.
 Functorial quantization of linear field theory [video], 8 June 2017, Field Theories and Higher Structures in Mathematics and Physics, Casa Matemática Oaxaca, Oaxaca, Mexico.
 Abstract quantum theory [various formats], 20 April 2017, Perimeter Institute, Waterloo, Canada.
 Fermionic coherent states in infinite dimensions [slides (PDF)], 18 November 2016, Coherent States and their Applications: A Contemporary Panorama, CIRM, Marseille, France.
 Positive TQFT [video], 16 August 2016, Modular Categories  Their Representations, Classification, and Applications, Casa Matemática Oaxaca, Oaxaca, Mexico.
 Towards new foundations of quantum theory from first principles and from quantum field theory [various formats], 15 May 2015, Information Theoretic Foundations for Physics, Perimeter Institute, Waterloo, Canada.
 From locality and operationalism to classical and quantum theory? [various formats], 25 November 2014, Perimeter Institute, Waterloo, Canada.
 Quantum Gravity and the Foundations of Quantum Theory [slides (PDF)], 26 April 2014, LQP 34, Erlangen, Germany.
 Encoding local dynamics without time [slides (PDF)], 11 February 2014, Second EFI winter conference on Quantum Gravity, Tux, Austria.
 Recent results in the general boundary formulation and their implications for quantum gravity (first talk in session) [various formats], 26 July 2013, Loops 13, Perimeter Institute, Waterloo, Canada.
 A positive and local formalism for quantum theory [various formats], 5 February 2013, Perimeter Institute, Waterloo, Canada.
 Quantum gravity via spin foams in the general boundary formulation [slides (PDF)], 10 November 2012, Mexi Lazos 2012, CCM, Morelia, Mexico.
 General covariance and the foundations of quantum theory [slides (PDF)], 12 June 2012, Quantum Theory: Reconsideration of Foundations  6, Linnéuniversitetet, Växjö, Sweden.
 Holomorphic quantization in backgroundindependent quantum field theory [slides (PDF)], 19 August 2011, New Trends in Analysis, Geometry and Physics, Cinvestav, Querétaro, Mexico.
 Introduction to the general boundary formulation of quantum theory [slides (PDF)], 29 September 2010, Quantum Field Theory and Gravity, Universität Regensburg, Regensburg, Germany.
 Against Commutators [various formats], 20 January 2009, Perimeter Institute, Waterloo, Canada.
 Quantum gravity, probabilities and general boundaries
[slides (PDF)], 17 October 2006,
International Loop Quantum Gravity Seminar.

The General Boundary Formulation of Quantum Theory
[slides (PDF)], 25 August 2006,
Quantum Gravity in the Americas III,
IGPG, Pennsylvania State University, State College, PA, USA.

Renormalization without Background
[slides (PDF)], 24 August 2006,
Quantum Gravity in the Americas III,
IGPG, Pennsylvania State University, State College, PA, USA.

The general boundary formulation of quantum mechanics: Motivations and elementary examples
[various formats], 2 November 2004, Perimeter Institute, Waterloo, Canada.

General Boundaries and Transition Amplitudes in Quantum Gravity
[various formats], 29 October 2004, Workshop
on Quantum Gravity in the Americas: Status and future directions,
Perimeter Institute, Waterloo, Canada.

Renormalization for Spin Foam Models of Quantum Gravity
[slides (PDF)], 12 June 2003,
Gravitation: A Decennial Perspective,
CGPG, Pennsylvania State University, State College, PA, USA.
Other resources

PhD thesis: Quantum Geometry and Quantum Field Theory, Cambridge,
September 2000. [(PS),
(PDF)]
Last updated 12 January 2022.