Quaternionic Dirac free particle

2021 ◽  
Author(s):  
Sergio Giardino
Keyword(s):  
Field Theory ◽  
Dirac Equation ◽  
Real Hilbert Space ◽  
Free Particle ◽  
Massive Particle ◽  
Essential Element ◽  
Massless Particle ◽  
Quantum Field ◽  
Quaternionic Quantum Mechanics ◽  
Theory Formula

In this paper, we solve the quaternionic Dirac equation [Formula: see text] in the real Hilbert space, and we ascertain that their free particle solutions set comprises eight elements in the case of a massive particle, and a four elements solutions set in the case of a massless particle, a richer situation when compared to the four elements solutions set of the usual complex Dirac equation [Formula: see text]. These free particle solutions were unknown in the previous solutions of anti-Hermitian quaternionic quantum mechanics, and constitute an essential element in order to build a quaternionic quantum field theory [Formula: see text].

scholarly journals Colourful Poincaré symmetry, gravity and particle actions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Joaquim Gomis ◽  
Euihun Joung ◽  
Axel Kleinschmidt ◽  
Karapet Mkrtchyan
Keyword(s):  
Field Theory ◽  
Free Particle ◽  
Three Dimensional ◽  
Background Field ◽  
Quantum Field ◽  
Symmetry Factor ◽  
Starting Point ◽  
Poincaré Algebra ◽  
Poincaré Symmetry ◽  
Three Space

Abstract We construct a generalisation of the three-dimensional Poincaré algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincaré gravity in three space-time dimensions as well as to study generalisations of massive and massless free particle models. We present various such generalised particle models that differ in which orbits of the coloured Poincaré symmetry are described. Our approach can be seen as a stepping stone towards the description of particles interacting with a non-abelian background field or as a starting point for a worldline formulation of an associated quantum field theory.

scholarly journals Some differences between Dirac's hole theory and quantum field theory

2005 ◽  
Vol 83 (3) ◽  
pp. 257-271 ◽  
Author(s):  
Dan Solomon
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Exact Solution ◽  
Dirac Equation ◽  
Vacuum Energy ◽  
Time Dependent ◽  
Quantum Field ◽  
Hole Theory

Dirac's hole theory (HT) and quantum field theory (QFT) are generally considered equivalent. However, it was recently shown by several investigators that this is not necessarily the case because when the change in the vacuum energy was calculated for a time-independent perturbation, HT and QFT yielded different results. In this paper, we extend this discussion to include a time-dependent perturbation for which the exact solution to the Dirac equation is known. We show that for this case also, HT and QFT yield different results. In addition, we offer some discussion of the problem of anomalies in QFT. PACS Nos.: 03.65–w, 11.10–z

scholarly journals NETS OF SUBFACTORS

1995 ◽  
Vol 07 (04) ◽  
pp. 567-597 ◽  
Author(s):  
R. LONGO ◽  
K.-H. REHREN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Relative Position ◽  
Von Neumann Algebras ◽  
Space Time ◽  
Quantum Field ◽  
Von Neumann ◽  
Time Region ◽  
Theoretical Application ◽  
Theory Formula

A subtheory of a quantum field theory specifies von Neumann subalgebras [Formula: see text] (the ‘observables’ in the space-time region [Formula: see text]) of the von Neumann algebras [Formula: see text] (the 'field' localized in [Formula: see text]). Every local algebra being a (type III1) factor, the inclusion [Formula: see text] is a subfactor. The assignment of these local subfactors to the space-time regions is called a ‘net of subfactors’. The theory of subfactors is applied to such nets. In order to characterize the ‘relative position’ of the subtheory, and in particular to control the restriction and induction of superselection sectors, the canonical endomorphism is studied. The crucial observation is this: the canonical endomorphism of a single local subfactor extends to an endomorphism of the field net, which in turn restricts to a localized endomorphism of the observable net. The method allows one to characterize, and reconstruct, local extensions ℬ of a given theory [Formula: see text] in terms of the observables. Various non-trivial examples are given. Several results go beyond the quantum field theoretical application.

scholarly journals Hydrodynamic quantum field theory: the free particle

2020 ◽  
Vol 348 (6-7) ◽  
pp. 555-571
Author(s):  
Yuval Dagan ◽  
John W. M. Bush
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Free Particle ◽  
Quantum Field

scholarly journals The hypergeneralized Heun equation in quantum field theory in curved space-times

Open Physics ◽  
2010 ◽  
Vol 8 (3) ◽  
Author(s):  
Davide Batic ◽  
Manuel Sandoval
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Dirac Equation ◽  
Heun Equation ◽  
Quantum Field ◽  
Curved Space ◽  
First Time

AbstractWe show for the first time the role played by the hypergeneralized Heun equation (HHE) in the context of quantum field theory in curved space-times. More precisely, we find suitable transformations relating the separated radial and angular parts of a massive Dirac equation in the Kerr-Newman-deSitter metric to a HHE.

Notizen:Eichfeldtheorie zur U3-invarianten Pais-Gleichung/ Gauge Field Theory of an U3-invariant Pais Equation

1980 ◽  
Vol 35 (3) ◽  
pp. 355-357
Author(s):  
Fritz Bopp
Keyword(s):  
Field Theory ◽  
Dirac Equation ◽  
Gauge Field ◽  
Free Particle ◽  
Gauge Field Theory

AbstractWe are looking for the gauge field theory which corresponds to the U3-invariance of the recently obtained free particle Dirac equation generalized according to an idea of Pais.

scholarly journals DIRAC EQUATION FOR QUASI-PARTICLES IN GRAPHENE AND QUANTUM FIELD THEORY OF THEIR COULOMB INTERACTION

2012 ◽  
Vol 26 (21) ◽  
pp. 1242005 ◽  
Author(s):  
RIAZUDDIN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Dirac Equation ◽  
Coulomb Interaction ◽  
Group Analysis ◽  
Fermi Velocity ◽  
Quantum Field ◽  
Renormalization Group Analysis ◽  
Self Energy ◽  
Conserved Currents

There is evidence for existence of massless Dirac quasiparticles in graphene, which satisfy Dirac equation in (1+2) dimensions near the so called Dirac points which lie at the corners at the graphene's brilluoin zone. We revisit the derivation of Dirac equation in (1+2) dimensions obeyed by quasiparticles in graphene near the Dirac points. It is shown that parity operator in (1+2) dimensions play an interesting role and can be used for defining "conserved" currents resulting from the underlying Lagrangian for Dirac quasiparticles in graphene which is shown to have UA(1) × UB(1) symmetry. Further the quantum field theory (QFT) of Coulomb interaction of 2D graphene is developed and applied to vacuum polarization and electron self-energy and the renormalization of the effective coupling g of this interaction and Fermi velocity vf which has important implications in the renormalization group analysis of g and vf.

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