scholarly journals (3+1)-dimensional topological quantum field theory from a tight-binding model of interacting spinless fermions

2014 ◽  
Vol 90 (8) ◽  
Author(s):  
Mauro Cirio ◽  
Giandomenico Palumbo ◽  
Jiannis K. Pachos
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Tight Binding ◽  
Topological Quantum Field Theory ◽  
Quantum Field ◽  
Tight Binding Model ◽  
Binding Model ◽  
Topological Quantum

scholarly journals QUANTUM FIELD THEORY IN GRAPHENE

2012 ◽  
Vol 27 (15) ◽  
pp. 1260007 ◽  
Author(s):  
I. V. FIALKOVSKY ◽  
D. V. VASSILEVICH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Hall Effect ◽  
Faraday Effect ◽  
Quantum Hall ◽  
Tight Binding ◽  
Polarization Operator ◽  
Quantum Field ◽  
Tight Binding Model ◽  
Binding Model

This is a short nontechnical introduction to applications of the Quantum Field Theory methods to graphene. We derive the Dirac model from the tight binding model and describe calculations of the polarization operator (conductivity). Later on, we use this quantity to describe the Quantum Hall Effect, light absorption by graphene, the Faraday effect, and the Casimir interaction.

scholarly journals QUANTUM FIELD THEORY IN GRAPHENE

2012 ◽  
Vol 14 ◽  
pp. 88-99 ◽  
Author(s):  
I. V. FIALKOVSKY ◽  
D. V. VASSILEVICH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Hall Effect ◽  
Faraday Effect ◽  
Quantum Hall ◽  
Tight Binding ◽  
Polarization Operator ◽  
Quantum Field ◽  
Tight Binding Model ◽  
Binding Model

This is a short non-technical introduction to applications of the Quantum Field Theory methods to graphene. We derive the Dirac model from the tight binding model and describe calculations of the polarization operator (conductivity). Later on, we use this quantity to describe the Quantum Hall Effect, light absorption by graphene, the Faraday effect, and the Casimir interaction.

QFT and unification of knot theories

2014 ◽  
Vol 29 (24) ◽  
pp. 1430025
Author(s):  
Alexey Sleptsov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Knot Theory ◽  
Topological Quantum Field Theory ◽  
Quantum Field ◽  
Knot Invariants ◽  
Topological Quantum

We discuss relation between knot theory and topological quantum field theory. Also it is considered a theory of superpolynomial invariants of knots which generalizes all other known theories of knot invariants. We discuss a possible generalization of topological quantum field theory with the help of superpolynomial invariants.

TOWARDS A QUANTUM ALGORITHM FOR THE PERMANENT

2007 ◽  
Vol 05 (01n02) ◽  
pp. 223-228 ◽  
Author(s):  
ANNALISA MARZUOLI ◽  
MARIO RASETTI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Computation ◽  
Quantum Computer ◽  
Quantum Algorithm ◽  
Topological Quantum Field Theory ◽  
Quantum Field ◽  
Topological Quantum

We resort to considerations based on topological quantum field theory to outline the development of a possible quantum algorithm for the evaluation of the permanent of a 0 - 1 matrix. Such an algorithm might represent a breakthrough for quantum computation, since computing the permanent is considered a "universal problem", namely, one among the hardest problems that a quantum computer can efficiently handle.

scholarly journals ON ALGEBRAIC STRUCTURES IMPLICIT IN TOPOLOGICAL QUANTUM FIELD THEORIES

1999 ◽  
Vol 08 (02) ◽  
pp. 125-163 ◽  
Author(s):  
Louis Crane ◽  
David Yetter
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hopf Algebra ◽  
Tensor Category ◽  
Topological Quantum Field Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Topological Quantum ◽  
Natural Way

We show that any 3D topological quantum field theory satisfying physically reasonable factorizability conditions has associated to it in a natural way a Hopf algebra object in a suitable tensor category. We also show that all objects in the tensor category have the structure of left-left crossed bimodules over the Hopf algebra object. For 4D factorizable topological quantum filed theories, we provide by analogous methods a construction of a Hopf algebra category.

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