On-shell gauge invariant three-point fermion and boson amplitudes

2020 ◽  
Vol 35 (18) ◽  
pp. 2050085
Author(s):  
Hui Xu
Keyword(s):  
First Principles ◽  
Dimensional Space ◽  
Space Time ◽  
Polynomial Basis ◽  
Gauge Invariant ◽  
Higher Spin ◽  
Dimensional Space Time ◽  
Lagrangian Construction ◽  
Massless Fermions

A polynomial basis for parity-even three-point amplitudes of higher-spin massless fermions and bosons are derived in four-dimensional space–time from first principles. This basis can be used to construct three-point amplitudes of polarizations of any rank. The results are presented using polarization tensors and tensor-spinors, which is convenient when they are applied to Lagrangian construction.

EXACT SOLUTIONS FOR SELF-DUAL SU(2) GAUGE THEORY WITH AXIAL SYMMETRY

2001 ◽  
Vol 16 (11) ◽  
pp. 685-692 ◽  
Author(s):  
G. ZET ◽  
V. MANTA ◽  
C. BANDAC
Keyword(s):  
Gauge Theory ◽  
Axial Symmetry ◽  
Dimensional Space ◽  
Space Time ◽  
Field Equations ◽  
Metric Tensor ◽  
Gauge Invariant ◽  
Local Gauge ◽  
Dimensional Space Time ◽  
Strength Tensor

A model of SU(2) gauge theory is constructed in terms of local gauge-invariant variables defined over a four-dimensional space–time endowed with axial symmetry. A metric tensor gμν is defined starting with the components [Formula: see text] of the strength tensor and its dual [Formula: see text]. The components gμν are interpreted as new local gauge-invariant variables. Imposing the condition that the new metric coincides with the initial metric we obtain the field equations for the considered ansatz. We obtain the same field equations using the condition of self-duality. It is concluded that the self-dual variables are compatible with the axial symmetry of the space–time. A family of analytical solutions of the gauge field equations is also obtained. The solutions have the confining properties. All the calculations are performed using the GRTensorII computer algebra package, running on the MapleV platform.

A GAUGE THEORY OF SPIN-1/2 FIELD

1992 ◽  
Vol 07 (33) ◽  
pp. 3053-3057 ◽  
Author(s):  
KAZUNARI SHIMA
Keyword(s):  
Gauge Theory ◽  
Dimensional Space ◽  
Gravitational Interaction ◽  
Space Time ◽  
Dirac Field ◽  
Gauge Invariant ◽  
Dimensional Space Time

A gauge theory of spin-1/2 Dirac field in four-dimensional space-time is presented. The gauge invariant gravitational interaction is also investigated.

Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Dimensional Space ◽  
Space Time ◽  
Elementary Particles ◽  
Hierarchy Problem ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
New Formula

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

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