scholarly journals FERMION DYNAMICS BY INTERNAL AND SPACETIME SYMMETRIES

2009 ◽  
Vol 24 (06) ◽  
pp. 415-427 ◽  
Author(s):  
NAKIA CARLEVARO ◽  
ORCHIDEA MARIA LECIAN ◽  
GIOVANNI MONTANI
Keyword(s):  
Gauge Theory ◽  
Stationary Solutions ◽  
Gauge Fields ◽  
Spacetime Symmetries ◽  
Lorentz Transformations ◽  
Relativistic Limit ◽  
Spinor Structure ◽  
Flat Spacetime ◽  
Fermion Fields

This paper is devoted to introduce a gauge theory of the Lorentz group based on the ambiguity emerging in dealing with isometric diffeomorphism-induced Lorentz transformations. The behaviors under local transformations of fermion fields and spin connections (assumed to be ordinary world vectors) are analyzed in flat spacetime and the role of the torsion field, within the generalization to curved spacetime, is briefly discussed. The fermion dynamics is then analyzed including the new gauge fields and assuming time-gauge. Stationary solutions of the problem are also analyzed in the non-relativistic limit, to study the spinor structure of an hydrogen-like atom.

scholarly journals LORENTZ GAUGE THEORY AND SPINOR INTERACTION

2008 ◽  
Vol 23 (08) ◽  
pp. 1282-1285 ◽  
Author(s):  
NAKIA CARLEVARO ◽  
ORCHIDEA MARIA LECIAN ◽  
GIOVANNI MONTANI
Keyword(s):  
Gauge Theory ◽  
Gauge Field ◽  
Lorentz Group ◽  
Flat Space ◽  
Stationary Solutions ◽  
Space Time ◽  
Pauli Equation ◽  
Relativistic Limit ◽  
Curved Space

A gauge theory of the Lorentz group, based on the different behavior of spinors and vectors under local transformations, is formulated in a flat space-time and the role of the torsion field within the generalization to curved space-time is briefly discussed. The spinor interaction with the new gauge field is then analyzed assuming the time gauge and stationary solutions, in the non-relativistic limit, are treated to generalize the Pauli equation.

ZERO ENERGY GAUGE FIELDS AND THE PHASES OF A GAUGE THEORY

1990 ◽  
Vol 05 (14) ◽  
pp. 2783-2798 ◽  
Author(s):  
E.I. GUENDELMAN
Keyword(s):  
Gauge Theory ◽  
Gauge Fields ◽  
Zero Energy ◽  
Massless Particles ◽  
New Approach ◽  
Gauge Transformations ◽  
Definition Of ◽  
Higgs Fields ◽  
Invariant Gauge

A new approach to the definition of the phases of a Poincare invariant gauge theory is developed. It is based on the role of gauge transformations that change the asymptotic value of the gauge fields from zero to a constant. In the context of theories without Higgs fields, this symmetry can be spontaneously broken when the gauge fields are massless particles, explicitly broken when the gauge fields develop a mass. Finally, the vacuum can be invariant under this transformation, this last case can be achieved when the theory has a violent infrared behavior, which in some theories can be connected to a confinement mechanism.

scholarly journals Nilpotent symmetries as a mechanism for Grand Unification

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Lars Andersson ◽  
András László ◽  
Błażej Ruba
Keyword(s):  
Gauge Field ◽  
Scalar Product ◽  
Local Symmetry ◽  
Matter Field ◽  
Gauge Fields ◽  
Spacetime Symmetries ◽  
Invariant Scalar ◽  
Spacetime Manifold ◽  
Local Symmetries ◽  
Dilatation Group

Abstract In the classic Coleman-Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential. If one instead allows the scalar product to be positive semi-definite, this opens new possibilities for unification of gauge and spacetime symmetries. It follows from theorems on the structure of Lie algebras, that in the case of unified symmetries, the degenerate directions of the positive semi-definite invariant scalar product have to correspond to local symmetries with nilpotent generators. In this paper we construct a workable minimal toy model making use of this mechanism: it admits unified local symmetries having a compact (U(1)) component, a Lorentz (SL(2, ℂ)) component, and a nilpotent component gluing these together. The construction is such that the full unified symmetry group acts locally and faithfully on the matter field sector, whereas the gauge fields which would correspond to the nilpotent generators can be transformed out from the theory, leaving gauge fields only with compact charges. It is shown that already the ordinary Dirac equation admits an extremely simple prototype example for the above gauge field elimination mechanism: it has a local symmetry with corresponding eliminable gauge field, related to the dilatation group. The outlined symmetry unification mechanism can be used to by-pass the Coleman-Mandula and related no-go theorems in a way that is fundamentally different from supersymmetry. In particular, the mechanism avoids invocation of super-coordinates or extra dimensions for the underlying spacetime manifold.

scholarly journals ON THE KALUZA–KLEIN GEOMETRIZATION OF THE ELECTROWEAK MODEL WITHIN A GAUGE THEORY OF THE FIVE-DIMENSIONAL LORENTZ GROUP

2006 ◽  
Vol 15 (05) ◽  
pp. 717-736
Author(s):  
ORCHIDEA MARIA LECIAN ◽  
GIOVANNI MONTANI
Keyword(s):  
Gauge Theory ◽  
Lorentz Group ◽  
Lagrangian Density ◽  
Gauge Fields ◽  
Normalization Factor ◽  
Current Term ◽  
Electroweak Model ◽  
Kaluza Klein

The geometrization of the Electroweak Model is achieved in a five-dimensional Riemann–Cartan framework. Matter spinorial fields are extended to 5 dimensions by the choice of a proper dependence on the extracoordinate and of a normalization factor. U (1) weak hypercharge gauge fields are obtained from a Kaluza–Klein scheme, while the tetradic projections of the extradimensional contortion fields are interpreted as SU (2) weak isospin gauge fields. SU (2) generators are derived by the identification of the weak isospin current to the extradimensional current term in the Lagrangian density of the local Lorentz group. The geometrized U (1) and SU (2) groups will provide the proper transformation laws for bosonic and spinorial fields. Spin connections will be found to be purely Riemannian.

scholarly journals Role of charged gauge fields in generating magnetic seed fields in bubble collisions during the cosmological electroweak phase transition

2008 ◽  
Vol 77 (2) ◽  
Author(s):  
Trevor Stevens ◽  
Mikkel B. Johnson ◽  
Leonard S. Kisslinger ◽  
Ernest M. Henley ◽  
W.-Y Pauchy Hwang ◽  
...  
Keyword(s):  
Phase Transition ◽  
Gauge Fields ◽  
Electroweak Phase Transition

scholarly journals On radial stationary solutions to a model of non-equilibrium growth

2013 ◽  
Vol 24 (3) ◽  
pp. 437-453 ◽  
Author(s):  
CARLOS ESCUDERO ◽  
ROBERT HAKL ◽  
IRENEO PERAL ◽  
PEDRO J. TORRES
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Stationary Solutions ◽  
Parabolic Partial Differential Equation ◽  
Radial Solutions ◽  
Variational Techniques ◽  
Existence And Multiplicity ◽  
Equilibrium Growth ◽  
Non Equilibrium

We present the formal geometric derivation of a non-equilibrium growth model that takes the form of a parabolic partial differential equation. Subsequently, we study its stationary radial solutions by means of variational techniques. Our results depend on the size of a parameter that plays the role of the strength of forcing. For small forcing we prove the existence and multiplicity of solutions to the elliptic problem. We discuss our results in the context of non-equilibrium statistical mechanics.

Non-Abelian gauge theory from the Poisson bracket

2018 ◽  
Vol 33 (30) ◽  
pp. 1850182
Author(s):  
Mu Yi Chen ◽  
Su-Long Nyeo
Keyword(s):  
Gauge Theory ◽  
Poisson Bracket ◽  
Commutation Relation ◽  
Maxwell Equations ◽  
Dynamical Variable ◽  
Gauge Fields ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Generalized Poisson ◽  
Lie Algebraic Structure

The Hamiltonian of a nonrelativistic particle coupled to non-Abelian gauge fields is defined to construct a non-Abelian gauge theory. The Hamiltonian which includes isospin as a dynamical variable dictates the dynamics of the particle and isospin according to the Poisson bracket that incorporates the Lie algebraic structure of isospin. The generalized Poisson bracket allows us to derive Wong’s equations, which describe the dynamics of isospin, and the homogeneous (sourceless) equations for non-Abelian gauge fields by following Feynman’s proof of the homogeneous Maxwell equations.It is shown that the derivation of the homogeneous equations for non-Abelian gauge fields using the generalized Poisson bracket does not require that Wong’s equations be defined in the time-axial gauge, which was used with the commutation relation. The homogeneous equations derived by using the commutation relation are not Galilean and Lorentz invariant. However, by using the generalized Poisson bracket, it can be shown that the homogeneous equations are not only Galilean and Lorentz invariant but also gauge independent. In addition, the quantum ordering ambiguity that arises from using the commutation relation can be avoided when using the Poisson bracket.From the homogeneous equations, which define the “electric field” and “magnetic field” in terms of non-Abelian gauge fields, we construct the gauge and Lorentz invariant Lagrangian density and derive the inhomogeneous equations that describe the interaction of non-Abelian gauge fields with a particle.

scholarly journals Emergent fields from hidden sectors

2021 ◽  
Vol 2105 (1) ◽  
pp. 012002
Author(s):  
Pascal Anastasopoulos
Keyword(s):  
String Theory ◽  
Particle Physics ◽  
Field Theories ◽  
Gauge Fields ◽  
Quantum Field Theories ◽  
Quantum Field

Abstract The present research proceeding aims at investigating/exploring/sharpening the phenomenological consequences of string theory and holography in particle physics and cosmology. We rely on and elaborate on the recently proposed framework whereby four-dimensional quantum field theories describe all interactions in Nature, and gravity is an emergent and not a fundamental force. New gauge fields, axions, and fermions, which can play the role of right-handed neutrinos, can also emerge in this framework. Preprint: UWThPh 2021-8

FERMI-BOSE TRANSMUTATIONS INDUCED BY GAUGE FIELDS

1988 ◽  
Vol 01 (11n12) ◽  
pp. 455-455 ◽  
Author(s):  
A.M. POLYAKOV
Keyword(s):  
Gauge Theory ◽  
Charged Particles ◽  
Gauge Fields ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Chern Simons

We show that in (2+1) -dimensional abelian gauge theory with the Chern-Simons term in the action, charged particles reverse their statistics.

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