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Hopf Algebras—Variant Notions and Reconstruction Theorems

Joost Vercruysse

in Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199646296
eISBN:
9780191747847
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199646296.003.0005
Subject:
Mathematics, Applied Mathematics

Hopf algebras are closely related to monoidal categories. More precisely, k-Hopf algebras can be characterized as those algebras whose category of finite-dimensional representations is an autonomous ... More


Algebraic combinatorics and QFT

Adrian Tanasa

in Combinatorial Physics: Combinatorics, Quantum Field Theory, and Quantum Gravity Models

Published in print:
2021
Published Online:
May 2021
ISBN:
9780192895493
eISBN:
9780191914973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192895493.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

We have seen in the previous chapter some of the non-trivial interplay between analytic combinatorics and QFT. In this chapter, we illustrate how yet another branch of combinatorics, algebraic ... More


Epilogue: Miscellaneous Topics and Possible Extensions

Gerald W. Johnson, Michel L. Lapidus, and Lance Nielsen

in Feynman's Operational Calculus and Beyond: Noncommutativity and Time-Ordering

Published in print:
2015
Published Online:
September 2015
ISBN:
9780198702498
eISBN:
9780191772160
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198702498.003.0011
Subject:
Mathematics, Mathematical Physics, Numerical Analysis

A brief discussion is given of possible extensions to the theory developed in this book, and suggestions for the direction of future research in this general area are given. This is done via a ... More


Complementarity

Chris Heunen and Jamie Vicary

in Categories for Quantum Theory: An Introduction

Published in print:
2019
Published Online:
January 2020
ISBN:
9780198739623
eISBN:
9780191802584
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198739623.003.0006
Subject:
Mathematics, Mathematical Physics, Applied Mathematics

Complementarity is a property of a pair of observables being ‘maximally distinct’ from each other and, in this chapter, we analyse this property in categorical terms as a pair of interacting ... More


Categories for Quantum Theory: An Introduction

Chris Heunen and Jamie Vicary

Published in print:
2019
Published Online:
January 2020
ISBN:
9780198739623
eISBN:
9780191802584
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198739623.001.0001
Subject:
Mathematics, Mathematical Physics, Applied Mathematics

Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition and a conceptual way to ... More


Quantum gravity, group field theory (GFT), and combinatorics

Adrian Tanasa

in Combinatorial Physics: Combinatorics, Quantum Field Theory, and Quantum Gravity Models

Published in print:
2021
Published Online:
May 2021
ISBN:
9780192895493
eISBN:
9780191914973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192895493.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter is the first chapter of the book dedicated to the study of the combinatorics of various quantum gravity approaches. After a brief introductory section to quantum gravity, we shortly ... More


QFT on the non-commutative Moyal space and combinatorics

Adrian Tanasa

in Combinatorial Physics: Combinatorics, Quantum Field Theory, and Quantum Gravity Models

Published in print:
2021
Published Online:
May 2021
ISBN:
9780192895493
eISBN:
9780191914973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192895493.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In this chapter we present the Phi? QFT model on the non-commutative Moyal space and the UV/IR mixing issue, which prevents it from being renormalizable. We then present the Grosse–Wulkenhaar Phi? ... More


Introduction

Adrian Tanasa

in Combinatorial Physics: Combinatorics, Quantum Field Theory, and Quantum Gravity Models

Published in print:
2021
Published Online:
May 2021
ISBN:
9780192895493
eISBN:
9780191914973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192895493.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The chapter explains the interplay between Combinatorisc and Physics and the emerging of the domain of Combinatorial Physics. The content of the book is then made explicit, chapter-by-chapter. The ... More


Combinatorial Physics: Combinatorics, Quantum Field Theory, and Quantum Gravity Models

Adrian Tanasa

Published in print:
2021
Published Online:
May 2021
ISBN:
9780192895493
eISBN:
9780191914973
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192895493.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

After briefly presenting (for the physicist) some notions frequently used in combinatorics (such as graphs or combinatorial maps) and after briefly presenting (for the combinatorialist) the main ... More


The Secondary Characteristic Classes

Ercüment H. Ortaçgil

in An Alternative Approach to Lie Groups and Geometric Structures

Published in print:
2018
Published Online:
September 2018
ISBN:
9780198821656
eISBN:
9780191860959
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198821656.003.0013
Subject:
Mathematics, Pure Mathematics

Changing the representation bundle from T to T ⊗ T∗ gives a sequence where both torsion and curvature live. Vanishing of the curvature gives rise to some closed forms.


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