quantum algebraic topology topics

quantum algebraic topology topics

This is a contributed topics list on quantum

algebraic topology

.
Online resources are also included for selected areas of QAT.

1

Quantum Algebraic Topology (QAT)

Quantum algebraic topology

can be described as the area of mathematical physics and physical mathematics concerned with the application of algebraic topology

concepts

, procedures and results to

quantum theories

such as

quantum field theories

(QFT, AQFT, locally covariant relativististic quantum theories and

quantum gravity

(QG)). QAT has close

connections

to several other fundamental fields of mathematics, such as:

noncommutative geometry

(NCG), the theory of

categories

,

functors

and

natural transformations

(TCFN),

non-Abelian

algebraic topology (NAAT), and

higher dimensional algebra

(HDA).

Related references are available at the websites and documents in the following topics list.

1.1

QAT Topics : Online Resources

•

QAT:

http://planetmath.org/?op=getobj&from=lec&id=68

Quantum Algebraic Topology-preprint.

•

Axiomatic quantum field theory (AQFT)

•

AT:

http://www.bangor.ac.uk/ mas010/publicfull.htm

Algebraic Topology papers

•

NAAT:

http://www.bangor.ac.uk/ mas010/nonab-a-t.html

A first textbook on “Non-Abelian Algebraic Topology”

•

QA:

Quantum automata

and quantum supercomputers (

http://planetmath.org/QuantumAutomataAndQuantumComputation2

)

•

NAQAT:

http://www.bangor.ac.uk/ mas010/pdffiles/BBG-158-NAC0STQG.pdf

Non-Abelian QAT

•

NAAT-List:

http://www.informatics.bangor.ac.uk/public/mathematics/research/preprints/07/cathom07.html

Category Theory

,

Homotopy Theory

and AT Publications

•

SPE:

http://plato.stanford.edu/entries/category-theory/

Stanford Plato: Category Theory and Applications

•

Abc

References

1

Abstracts1:

http://www.springerlink.com/

content

/t08637r333403846/

Springer link

2

Abstracts2:

http://www.springerlink.com/content/92r13230n3381746/

Springer link

3

CERN Preprint Archives:

http://documents.cern.ch/cgi-bin/setlink?base=preprint&categ=ext&id=ext-2004-125

CERN Preprints-1

4

CERN Articles and Preprint Archives:

http://doc.cern.ch/archive/electronic/other/ext/ext-2004-125/Baianu_okCERNMyPreprintsJuly9k04.doc

CERN Preprints-2

.2

Additional items

1.

QAT1

2.

QAT2

3.

A3

Title

quantum algebraic topology topics

Canonical name

QuantumAlgebraicTopologyTopics

Date of creation

2013-03-22 18:13:31

Last modified on

2013-03-22 18:13:31

Owner

bci1 (20947)

Last modified by

bci1 (20947)

Numerical id

63

Author

bci1 (20947)

Entry type

Topic

Classification

msc 81Q60

Classification

msc 55-02

Classification

msc 81R50

Classification

msc 81R15

Synonym

non-Abelian Quantum Algebraic Topology

Synonym

NAQAT

Synonym

Quantum Operator Algebras

Synonym

Supersymmetry and symmetry breaking

Synonym

Algebraic Topology Foundations of Quantum theories

Related topic

CAlgebra3

Related topic

TopicEntryOnTheAlgebraicFoundationsOfQuantumAlgebraicTopology

Related topic

CategoryOfQuantumAutomata

Related topic

TheoremOnCWComplexApproximationOfQuantumStateSpacesInQAT

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