Unbounded representations of symmetry groups in gauge quantum field theory. II. Integration

1986 ◽  
Vol 27 (4) ◽  
pp. 1113-1127 ◽  
Author(s):  
A. H. Völkel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Symmetry Groups ◽  
Quantum Field ◽  
Unbounded Representations

INTRODUCTION TO BRAIDED QUANTUM FIELD THEORY

2000 ◽  
Vol 14 (22n23) ◽  
pp. 2461-2466 ◽  
Author(s):  
ROBERT OECKL
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Group ◽  
Noncommutative Geometry ◽  
Quantum Groups ◽  
Symmetry Groups ◽  
Quantum Field ◽  
Noncommutative Spaces ◽  
Small Scales ◽  
Group Symmetries

Indications from various areas of physics point to the possibility that space-time at small scales might not have the structure of a manifold. Noncommutative geometry provides an attractive framework for a perhaps more accurate description of nature. It encompasses the generalisation of spaces to noncommutative spaces and of symmetry groups to quantum groups. This motivates efforts to extend quantum field theory to noncommutative spaces and quantum group symmetries. One also expects that divergences of conventional theories might be regularised in this way.

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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