scholarly journals Large 𝑁 quantum field theory and matrix models

1996 ◽  
pp. 21-40 ◽  
Author(s):  
Michael Douglas
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Matrix Models ◽  
Quantum Field

Combinatorial Physics

2021 ◽  
Author(s):  
Adrian Tanasa
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Matrix Models ◽  
High Energy ◽  
Polynomial Systems ◽  
Algebraic Combinatorics ◽  
Tensor Model ◽  
Quantum Field ◽  
Analytic Combinatorics ◽  
Tensor Models

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 concepts of quantum field theory (QFT), the book shows how algebraic combinatorics can be used to deal with perturbative renormalisation (both in commutative and non-commutative quantum field theory), how analytic combinatorics can be used for QFT issues (again, for both commutative and non-commutative QFT), how Grassmann integrals (frequently used in QFT) can be used to proCve new combinatorial identities (generalizing the Lindström–Gessel–Viennot formula), how combinatorial QFT can bring a new insight on the celebrated Jacobian conjecture (which concerns global invertibility of polynomial systems) and so on. In the second part of the book, matrix models, and tensor models are presented to the reader as QFT models. Several tensor model results (such as the implementation of the large N limit and of the double-scaling limit for various such tensor models, N being here the size of the tensor) are then exposed. These results are natural generalizations of results extensively used by theoretical physicists in the study of matrix models and they are obtained through intensive use of combinatorial techniques (this time mainly enumerative techniques). The last part of the book is dedicated to the recently discovered relation between tensor models and the holographic Sachdev–Ye–Kitaev model, model which has been extensively studied in the last years by condensed matter and by high-energy physicists.

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

Some remarks on a deformed quantum field theory

2002 ◽  
Author(s):  
Marco Aurelio Do Rego Monteiro ◽  
V. B. Bezerra ◽  
E. M.F. Curado
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field

Quantum mechanics

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Transition Amplitude ◽  
External Source ◽  
Quantum Field ◽  
Damping Term ◽  
Relativistic Quantum Theory ◽  
Generating Functional

After a brief review of the operator approach to quantum mechanics, Feynmans path integral, which expresses a transition amplitude as a sum over all paths, is derived. Adding a linear coupling to an external source J and a damping term to the Lagrangian, the ground-state persistence amplitude is obtained. This quantity serves as the generating functional Z[J] for n-point Green functions which are the main target when studying quantum field theory. Then the harmonic oscillator as an example for a one-dimensional quantum field theory is discussed and the reason why a relativistic quantum theory should be based on quantum fields is explained.

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