Hyperfunction quantum field theory: Analytic structure, modular aspects, and local observable algebras

2001 ◽  
Vol 42 (1) ◽  
pp. 99-129 ◽  
Author(s):  
S. Nagamachi ◽  
E. Brüning
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Analytic Structure ◽  
Local Observable ◽  
Quantum Field

scholarly journals The locality axiom in quantum field theory and tensor products of C*-algebras

2014 ◽  
Vol 26 (06) ◽  
pp. 1450010 ◽  
Author(s):  
Romeo Brunetti ◽  
Klaus Fredenhagen ◽  
Paniz Imani ◽  
Katarzyna Rejzner
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Local Observable ◽  
Quantum Field ◽  
Covariant Quantum ◽  
C Algebras ◽  
Local Algebras ◽  
Globally Hyperbolic Spacetimes ◽  
Split Property ◽  
Hyperbolic Spacetimes

The prototypes of mutually independent systems are systems which are localized in spacelike separated regions. In the framework of locally covariant quantum field theory, we show that the commutativity of observables in spacelike separated regions can be encoded in the tensorial structure of the functor which associates unital C*-algebras (the local observable algebras) to globally hyperbolic spacetimes. This holds under the assumption that the local algebras satisfy the split property and involves the minimal tensor product of C*-algebras.

Relativistic Invariance and Mass Renormalization in Quantum Field Theory

2014 ◽  
Vol 59 (11) ◽  
pp. 1060-1064
Author(s):  
P.A. Frolov ◽  
◽  
A.V. Shebeko ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Relativistic Invariance ◽  
Mass Renormalization

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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