scholarly journals An Approach to Classical Quantum Field Theory Based on the Geometry of Locally Conformally Flat Space-Time

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
John Mashford
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vector Bundles ◽  
Principal Bundle ◽  
Adjoint Action ◽  
Flat Space ◽  
Quantum Field ◽  
Euclidean Topology ◽  
Fermion Fields ◽  
Classical Quantum

This paper gives an introduction to certain classical physical theories described in the context of locally Minkowskian causal structures (LMCSs). For simplicity of exposition we consider LMCSs which have locally Euclidean topology (i.e., are manifolds) and hence are Möbius structures. We describe natural principal bundle structures associated with Möbius structures. Fermion fields are associated with sections of vector bundles associated with the principal bundles while interaction fields (bosons) are associated with endomorphisms of the space of fermion fields. Classical quantum field theory (the Dirac equation and Maxwell’s equations) is obtained by considering representations of the structure group K⊂SU(2,2) of a principal bundle associated with a given Möbius structure where K, while being a subset of SU(2,2), is also isomorphic to SL2,C×U(1). The analysis requires the use of an intertwining operator between the action of K on R4 and the adjoint action of K on su⁡(2,2) and it is shown that the Feynman slash operator, in the chiral representation for the Dirac gamma matrices, has this intertwining property.

scholarly journals Quantum Field Theory of Open Spin Networks and New Spin Foam Models

2003 ◽  
Vol 18 (supp02) ◽  
pp. 83-96 ◽  
Author(s):  
A. Miković
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vector Bundles ◽  
Tensor Category ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Spin Networks ◽  
Spin Foam Models ◽  
Topological Quantum ◽  
Spin Foam

We describe how a spin-foam state sum model can be reformulated as a quantum field theory of spin networks, such that the Feynman diagrams of that field theory are the spin-foam amplitudes. In the case of open spin networks, we obtain a new type of state-sum models, which we call the matter spin foam models. In this type of state-sum models, one labels both the faces and the edges of the dual two-complex for a manifold triangulation with the simple objects from a tensor category. In the case of Lie groups, such a model corresponds to a quantization of a theory whose fields are the principal bundle connection and the sections of the associated vector bundles. We briefly discuss the relevance of the matter spin foam models for quantum gravity and for topological quantum field theories.

scholarly journals Introduction to “Quantum Light Theory” (QLT)

2021 ◽  
Author(s):  
Wim Vegt
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Electromagnetic Field ◽  
Fundamental Question ◽  
Quantum Mechanical ◽  
Quantum Field ◽  
Fundamental Interaction ◽  
Electromagnetic Equation ◽  
Classical Quantum ◽  
Light Theory

Quantum Light Theory (QLT) is the development in Quantum Field Theory (QFT). In Quantum Field Theory, the fundamental interaction fields are replacing the concept of elementary particles in Classical Quantum Mechanics. In Quantum Light Theory the fundamental interaction fields are being replaced by One Single Field. The Electromagnetic Field, generally well known as Light. To realize this theoretical concept, the fundamental theory has to go back in time 300 years, the time of Isaac Newton to follow a different path in development. Nowadays experiments question more and more the fundamental concepts in Quantum Field Theory and Classical Quantum Mechanics. The publication “Operational Resource Theory of Imaginarity“ in “Physical Review Letters” in 2021 (Ref. [2]) presenting the first experimental evidence for the measurability of “Quantum Mechanical Imaginarity” directly leads to the fundamental question in this experiment: How is it possible to measure the imaginary part of “Quantum Physical Probability Waves”? This publication provides an unambiguously answer to this fundamental question in Physics, based on the fundamental “Gravitational Electromagnetic Interaction” force densities. The “Quantum Light Theory” presents a new “Gravitational-Electromagnetic Equation” describing Electromagnetic Field Configurations which are simultaneously the Mathematical Solutions for the Quantum Mechanical “Schrodinger Wave Equation” and more exactly the Mathematical Solutions for the “Relativistic Quantum Mechanical Dirac Equation”. The Mathematical Solutions for the “Gravitational-Electromagnetic Equation” carry Mass, Electric Charge and Magnetic Spin at discrete values.

scholarly journals Charged quantum fields in AdS$_2$

2019 ◽  
Vol 7 (4) ◽  
Author(s):  
Dionysios Anninos ◽  
Diego Hofman ◽  
Jorrit Kruthoff
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Kerr Black Hole ◽  
Principal Series ◽  
Flat Space ◽  
Quantum Field ◽  
Quantum Fields ◽  
Electrically Charged ◽  
Large Charge

We consider quantum field theory near the horizon of an extreme Kerr black hole. In this limit, the dynamics is well approximated by a tower of electrically charged fields propagating in an SL(2,\mathbb{R})SL(2,ℝ) invariant AdS_22 geometry endowed with a constant, symmetry preserving background electric field. At large charge the fields oscillate near the AdS_22 boundary and no longer admit a standard Dirichlet treatment. From the Kerr black hole perspective, this phenomenon is related to the presence of an ergosphere. We discuss a definition for the quantum field theory whereby we ‘UV’ complete AdS_22 by appending an asymptotically two dimensional Minkowski region. This allows the construction of a novel observable for the flux-carrying modes that resembles the standard flat space SS-matrix. We relate various features displayed by the highly charged particles to the principal series representations of SL(2,\mathbb{R})SL(2,ℝ). These representations are unitary and also appear for massive quantum fields in dS_22.

scholarly journals Hamiltonian models of interacting fermion fields in quantum field theory

2019 ◽  
Vol 109 (11) ◽  
pp. 2403-2437
Author(s):  
Benjamin Alvarez ◽  
Jérémy Faupin ◽  
Jean-Claude Guillot
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Hamiltonian Models ◽  
Fermion Fields

scholarly journals INFINITE QUANTUM GROUP SYMMETRY OF FIELDS IN MASSIVE 2D QUANTUM FIELD THEORY

1992 ◽  
Vol 07 (13) ◽  
pp. 2997-3022 ◽  
Author(s):  
ANDRÉ LECLAIR ◽  
F. A. SMIRNOV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Group ◽  
Form Factors ◽  
Adjoint Action ◽  
Momentum Tensor ◽  
Group Symmetry ◽  
Quantum Field ◽  
Infinite Dimensional ◽  
Symmetry Generators

Starting from a given S-matrix of an integrable quantum field theory in 1 + 1 dimensions, and knowledge of its on-shell quantum group symmetries, we describe how to extend the symmetry to the space of fields. This is accomplished by introducing an adjoint action of the symmetry generators on fields, and specifying the form factors of descendents. The braiding relations of quantum field multiplets is shown to be given by the universal ℛ-matrix. We develop in some detail the case of infinite-dimensional Yangian symmetry. We show that the quantum double of the Yangian is a Hopf algebra deformation of a level zero Kac–Moody algebra that preserves its finite-dimensional Lie subalgebra. The fields form infinite-dimensional Verma module representations; in particular, the energy–momentum tensor and isotopic current are in the same multiplet.

scholarly journals Revisiting Coleman-de Luccia transitions in the AdS regime using holography

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Jewel K. Ghosh ◽  
Elias Kiritsis ◽  
Francesco Nitti ◽  
Lukas T. Witkowski
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Flat Space ◽  
Field Theories ◽  
Quantum Field ◽  
De Sitter ◽  
Thin Walled ◽  
Scalar Theories ◽  
Scalar Potentials

Abstract Coleman-de Luccia processes for AdS to AdS decays in Einstein-scalar theories are studied. Such tunnelling processes are interpreted as vev-driven holographic RG flows of a quantum field theory on de Sitter space-time. These flows do not exist for generic scalar potentials, which is the holographic formulation of the fact that gravity can act to stabilise false AdS vacua. The existence of Coleman-de Luccia tunnelling solutions in a potential with a false AdS vacuum is found to be tied to the existence of exotic RG flows in the same potential. Such flows are solutions where the flow skips possible fixed points or reverses direction in the coupling. This connection is employed to construct explicit potentials that admit Coleman-de Luccia instantons in AdS and to study the associated tunnelling solutions. Thin-walled instantons are observed to correspond to dual field theories with a parametrically large value of the dimension ∆ for the operator dual to the scalar field, casting doubt on the attainability of this regime in holography. From the boundary perspective, maximally symmetric instantons describe the probability of symmetry breaking of the dual QFT in de Sitter. It is argued that, even when such instantons exist, they do not imply an instability of the same theory on flat space or on R × S3.

Can a Nonsymmetric Metric mimic NCQFT in e+e- → γγ?

2007 ◽  
Vol 22 (07n10) ◽  
pp. 699-709
Author(s):  
Nick Kersting ◽  
Yong-Liang Ma
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Flat Space ◽  
Gravitational Theory ◽  
Quantum Field ◽  
Noncommutative Quantum Field Theory ◽  
Pair Annihilation ◽  
Nonsymmetric Metric ◽  
Noncommutative Quantum ◽  
Gravitational Background

In the nonsymmetric gravitational theory (NGT) the space-time metric gμν departs from the flat-space Minkowski form ημν such that it is no longer symmetric, i.e.gμν ≠ gνμ. We find that in the most conservative such scenario coupled to quantum field theory, which we call Minimally Nonsymmetric Quantum Field Theory (MNQFT), there are experimentally measurable consequences similar to those from noncommutative quantum field theory (NCQFT). This can be expected from the Seiberg-Witten map which has recently been interpreted as equating gauge theories on noncommutative spacetimes with those in a field dependent gravitational background. In particular, in scattering processes such as the pair annihilation e+e- → γγ, both theories make the same striking prediction that the azimuthal cross section oscillates in ϕ. However the predicted number of oscillations differs in the two theories: MNQFT predicts between one and four, whereas NCQFT has no such restriction.

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