scholarly journals The Snyder Model and Quantum Field Theory

2019 ◽  
Vol 64 (11) ◽  
pp. 991 ◽  
Author(s):  
S. Mignemi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Finite Theory ◽  
Standard Formalism

We review the main features of the relativistic Snyder model and its generalizations. We discuss the quantum field theory on this background using the standard formalism of noncommutative QFT and discuss the possibility of obtaining a finite theory.

scholarly journals BOGOLUBOV'S RECURSION AND INTEGRABILITY OF EFFECTIVE ACTIONS

2001 ◽  
Vol 16 (09) ◽  
pp. 1531-1558 ◽  
Author(s):  
A. GERASIMOV ◽  
A. MOROZOV ◽  
K. SELIVANOV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hopf Algebra ◽  
Moduli Space ◽  
Feynman Diagrams ◽  
Coupling Constants ◽  
Quantum Field ◽  
Integrable Structure ◽  
Standard Formalism

The Hopf algebra of Feynman diagrams, analyzed by A. Connes and D. Kreimer, is considered from the perspective of the theory of effective actions and generalized τ-functions, which describes the action of diffeomorphism and shift groups in the moduli space of coupling constants. These considerations provide additional evidence of the hidden group (integrable) structure behind the standard formalism of quantum field theory.

A twistor approach to the regularization of divergences

1985 ◽  
Vol 397 (1813) ◽  
pp. 341-374 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Infrared Divergence ◽  
Standard Theory ◽  
Quantum Field ◽  
New Formalism ◽  
First Order ◽  
Finite Theory ◽  
Finite Quantity ◽  
Modified Theory

One object of the twistor programme, as developed principally by R. Penrose, is the production of a manifestly finite theory of scattering in quantum field theory. Earlier work has shown that progress towards this goal is obstructed even at the first-order level, by the appearance of an infrared divergence in the standard theory. New studies in many-dimensional contour integration now suggest a simple but very powerful modification to this branch of twistor theory, in which the full (as opposed to the projective) twistor space plays an essential role. In this modified theory there arise natural contour-integral expressions with the effect of eliminating the infrared divergence previously noted, and replacing it by a finite quantity. This regularization can be specified by using a formalism of ‘inhomogeneous twistor diagrams’. The interpretation of this new formalism is not yet wholly clear, but the inhomogeneity can be seen as a means of relinquishing the concept of space-time point, while preserving light-cone structure. It therefore suggests a quite fresh approach to the divergences of quantum field theory.

Quantum Gravity as a Resource

2020 ◽  
pp. 193-214
Author(s):  
Dean Rickles
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Gravity ◽  
Gravitational Collapse ◽  
Maximum Energy ◽  
Minimal Length ◽  
Quantum Field ◽  
Small Scales ◽  
Finite Theory ◽  
Primary Problem

This chapter focuses on the central motivation for much of what can be labeled ‘quantum gravity’ in the earliest phases of research, namely that it provides a potentially abundant resource for curing problems in quantum field theory. While it was rare to have fully worked out examples along these lines, it provided a much needed impetus to the study of quantum gravity at a time when there were few other reasons to bother with it. The primary problem was the ubiquitous divergences, which proved extremely stubborn and worrying to field theorists. Not all of the approaches were looked at involved gravitation directly, however, and focused more on ways of generating a discrete structure (with a minimal length or maximum energy) that would provide a physical cutoff, thus grounding a finite theory. These filtered through into gravitational research only later than our timeframe, in a variety of ways, including the small scales necessarily reached in gravitational collapse.

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.

Sign in / Sign up

Export Citation Format

Share Document