Finite dimensional models inspired by the perturbative algebraic quantum field theory (pAQFT) framework
Lead Research Organisation:
University of York
Department Name: Mathematics
Abstract
The student will work on finite dimensional models inspired by the perturbative algebraic quantum field theory (pAQFT) framework, which is framework used to construct models of quantum field theories on Lorentzian manifolds. Instead of a Lorentzian manifold M one can consider a causal set S, i.e. a set with a partial order relation that models a causal structure (based on ideas of Rafael Sorkin). There are strong reasons to believe that pAQFT can work on such structures (possibly with some modifications) and this could be a good toy model for testing ideas that can then be applied in the infinite dimensional setting. Classical theory was the topic of an EPSRC funded summer student project (of Edmund Dable-Heath, summer 2016) and the results indicate that there is a natural way to construct the canonical bracket on S (i.e. construct the classical theory). The current PhD project will concern exploring the next steps: deformation quantization and renormalization.
Organisations
People |
ORCID iD |
| Katarzyna Anna Rejzner (Primary Supervisor) | |
| Christoph Minz (Student) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509802/1 | 01/10/2016 | 31/03/2022 | |||
| 1941147 | Studentship | EP/N509802/1 | 01/10/2017 | 31/03/2021 | Christoph Minz |
| Description | We investigated discrete spacetime models, known as causal sets (locally finite partially ordered sets), which are given by a set of points and a relation between those points as the causal structure. If any point B (with its space and time coordinate) can be influenced by an earlier (and possibly distant point) A in the set, then A is causally related to B. On the one hand, causal sets are discussed as a framework for a theory of quantum gravity (unification of gravitational and quantum physics). On the other hand, their discrete nature yields computable models to study quantum field theory (in elementary particle physics). In one part of the project, we established the mathematical basis for the sprinkling process in causal set theory, which is a random (Poisson) process to generate causal sets from a given spacetime. We then used this process by conducting numerical simulations and analyse a previously proposed structure that is necessary to describe the motion of scalar quantum fields (bosons) on a causal set. The simulations have been conducted using the high performance computing facilities of the University of York (the Viking Cluster) and we have published the results. In a second part of the project, we looked into the mathematical techniques that are necessary to establish an algebra of quantum observables (quantized, experimentally observable quantities like a particel position) over a given causal set. By applying known techniques to quantize / convert a classical, commutative algebra into a quantum, non-commutative algebra, we investigated a construction of a certain state. In general, a states gives measureable outcomes for observable quantities. The most common example of a state in causal set theory is the Sorkin-Johnston state - for which we showed a gave a natural construction using the techniques of quantization. |
| Exploitation Route | Academically, the research outcomes show directions how to continue investigations on the models of causal sets and (quantum) fields on them. The results have the potential to solve problems with renormalization and gravitational interactions in fundamental and high energy physics. These methodological problems in fundamental physics are caused by singularities (infinities) that appear in the calculations of elementary particle interactions and have to be counteracted. In the future, a more complete description of the fundamental forces and interactions in nature can be used to develop new communication technologies, next generations of (quantum) computers, and possibly new ways to harvest energy (from quantum interactions and from gravity). Our current standard model of elementary particle physics does not consider gravitational interactions due to their smaller energy scale. When a better understanding of the interaction between matter and the gravitational fields is achieved, a better understanding of scientific questions, for exmple, about the physics of black holes can be established. In the long run, the understanding of the fundamental aspects of gravitational and quantum physics will be applicable in new technologies. |
| Sectors | Aerospace, Defence and Marine,Chemicals,Digital/Communication/Information Technologies (including Software),Electronics,Energy,Manufacturing, including Industrial Biotechology,Other |
| Title | Local diamond structure of sprinkled causal sets (MATLAB) |
| Description | As part of my PhD research project, I investigated the statistics of sprinkled causal sets for which I developed an algorithm in MATLAB. The algorithm is an implementation of the following functionalities. Firstly, it can generate causal sets (finite spacetime models) by a sprinkling process (random Poisson process) on subsets of a flat spacetime manifold of various dimensions -- we generated causal sets on diamond shaped 1+1, 1+2 and 1+3 dimensional subsets. Secondly, the algorithm includes functions to convert aspects of the local structure for ensembles of generated causal sets into statistics (histograms) -- we compared such statistics in the publication, currently in publication. Thirdly, after running the algorithm (on a high performance cumputing cluster), a set of functions reformats the output data such that graphics can be plotted. |
| Type Of Material | Computer model/algorithm |
| Year Produced | 2021 |
| Provided To Others? | Yes |
| Impact | The data generated with the algorithm via the University of York High Performance Computing service (Viking Cluster) was analysed and the results published in a research article ( https://arxiv.org/abs/2011.02965 ). There are two repositories available, one to use the simulation model ( https://github.com/c-minz/diamondsprinkling ) and one to analyse the results ( https://github.com/c-minz/diamondresults ). Our corresponding publication is available in Physical Review D (APS Journal) at: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.103.086020. |
| URL | https://github.com/c-minz/diamondsprinkling |
| Description | "Diamonds and Local Structure in Sprinkled Causal Sets" at Quantum Gravity 2020 |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | As a PhD student I participated in a poster presentation session. Since the conference was held virtually, I prepared a poster video ( https://www.youtube.com/watch?v=EF1Wb3d0BJI&feature=youtu.be ). My poster won the poster prize and I got the opportunity to give a short talk about our research results. Our research sparked interest among the other researchers and we got a few suggestions to extend our analysis. These suggestions eventually improved our results (currently in publication with the journal Physical Review D) and we received new ideas for further research. |
| Year(s) Of Engagement Activity | 2020 |
| URL | https://www2.perimeterinstitute.ca/conferences/quantum-gravity-2020 |
| Description | "Sprinklings in Causal Set Theory and Local Structures to Discretize Field Propagators" at NBMPS59 |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Professional Practitioners |
| Results and Impact | I gave a talk at the 59th North British Mathematical Physics Seminar with the aim to present our research findings at a regional one day conference. It was a good opportunity to promote our research results and gain experiences in giving scientific presentations (also as practice for a larger international conferences). |
| Year(s) Of Engagement Activity | 2020 |
| URL | https://www-users.york.ac.uk/~bv557/NBMPS59.html |
| Description | "The Sprinkling Process, Diamonds and Local Structures in Causal Set Theory" at The Virtual Causet |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | A few month after the Quantum Gravity 2020 conference, the conference "The Virtual Causet" was held to which I was invited as a speaker. I presented our research results, we received questions and an inspiring discussion. |
| Year(s) Of Engagement Activity | 2020 |
| Description | 12-16 October, Quantum Spacetime and the Renormalization group, CP3-Origins (online workshop), panelist in discussion Future of Asymptotically Safe Gravity, chairing discussion Lorentzian signature. |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | I took part in/chaired discussions, where I had a chance to talk about the results of my research and to discuss future directions. |
| Year(s) Of Engagement Activity | 2020 |
| Description | 13-14 January, Directions in quantum gravity, on-line conference hosted by the Centre for Cosmology and Particle Physics Phenomenology at the University of Southern Denmark (SDU) in Odense, |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | I gave a talk with the title "Algebraic QFT on causal sets." The talk was well received and was followed by a discussion. |
| Year(s) Of Engagement Activity | 2021 |
| Description | 13-17 July, Quantum Gravity 2020, Perimeter institute (on-line conference), chaired a discussion Lorentzian vs. Euclidean Quantum Gravit and co-chaired a panel discussion Time in Quantum Gravity. |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | I chaired two discussions on topics related to my research. This was also an opportunity to present the results of my research and discuss about possible directions for further research. |
| Year(s) Of Engagement Activity | 2020 |
| Description | 18 January, "Non-local observables in quantum gravity from the algebraic QFT perspective", on-line seminar: Quantum Gravity Across Approaches |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | I presented a talk with the title "Non-local observables in quantum gravity from the algebraic QFT perspective", where I reported on some of my findings related to the award. The talk provoked some interesting discussions and was well received. The participants of this on-line seminar series are mainly physicists and mathematical physicists working on quantum gravity. It was important for the dissemination of my results to reach out to that community. |
| Year(s) Of Engagement Activity | 2021 |
| Description | Quantum Spacetime and the Renormalization group, CP3-Origins (online workshop), 12-16 October, 2020 |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | I gave a talk with the title "Algebraic quantum field theory on causal sets: what have we learnt?" The talk was well received and was followed by a discussion. |
| Year(s) Of Engagement Activity | 2020 |