Algebraic Conformal Quantum Field Theory in Perspective

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".Â Â

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Quantum field theory

Physics Subject Headings (PhySH) ◽

10.29172/ee82ad04-6c47-46a4-a70d-c9a7d7989f6a ◽

2018 ◽

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Quantum Field

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Some remarks on a deformed quantum field theory

10.22323/1.008.0031 ◽

2002 ◽

Author(s):

Marco Aurelio Do Rego Monteiro ◽

V. B. Bezerra ◽

E. M.F. Curado

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Quantum Field

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Quantum mechanics

10.1093/oso/9780198802877.003.0002 ◽

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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QLB for Quantum Many-Body and Quantum Field Theory

10.1093/oso/9780199592357.003.0033 ◽

2018 ◽

Author(s):

Sauro Succi

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Quantum Mechanics ◽

Quantum Computing ◽

Single Particle ◽

Body Problem ◽

Three Dimensions ◽

Quantum Field ◽

Many Body ◽

Quantum Particles

Chapter 32 expounded the basic theory of quantum LB for the case of relativistic and non-relativistic wavefunctions, namely single-particle quantum mechanics. This chapter goes on to cover extensions of the quantum LB formalism to the overly challenging arena of quantum many-body problems and quantum field theory, along with an appraisal of prospective quantum computing implementations. Solving the single particle Schrodinger, or Dirac, equation in three dimensions is a computationally demanding task. This task, however, pales in front of the ordeal of solving the Schrodinger equation for the quantum many-body problem, namely a collection of many quantum particles, typically nuclei and electrons in a given atom or molecule.

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