Numerical methods for studying anharmonic oscillator approximations to the φ24 quantum field theory

1980 ◽  
Vol 18 (2) ◽  
pp. 341-349 ◽  
Author(s):  
D. Isaacson ◽  
D. Marchesin ◽  
P.J. Paes-Leme
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Numerical Methods ◽  
Anharmonic Oscillator ◽  
Quantum Field

THE UNCERTAINTY OF THE GAUSSIAN EFFECTIVE POTENTIAL

1988 ◽  
Vol 03 (09) ◽  
pp. 2143-2163 ◽  
Author(s):  
R. MUÑOZ-TAPIA ◽  
J. TARON ◽  
R. TARRACH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Effective Potential ◽  
Anharmonic Oscillator ◽  
Liouville Theory ◽  
Quantum Field ◽  
First Case ◽  
Gaussian Effective Potential

An uncertainty is introduced for the Gaussian Effective Potential. The definition is quite straightforward for quantum mechanics but fairly subtle for quantum field theory. The uncertainty provides a good estimation of the error in the first case, but renormalization seems to spoil its usefulness in the second case. The examples considered are the anharmonic oscillator, λϕ4 in 3+1 dimensions and the Liouville theory in 1+1 dimensions.

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".  

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