Affine group formulation of the Standard Model coupled to gravity

In this work we apply the affine group formalism for four dimensional gravity of Lorentzian signature, which is based on Klauder’s affine algebraic program, to the formulation of the Hamiltonian constraint of the interaction of matter and all forces, including gravity with non-vanishing cosmological...

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Bibliographic Details
Published in:Annals of physics 2014-04, Vol.343 (Complete), p.153-163
Main Authors: Chou, Ching-Yi, Ita, Eyo, Soo, Chopin
Format: Article
Language:English
Subjects:
ACTION INTEGRAL
Affine group formulation
Affine transformations
Algebra
ANNIHILATION OPERATORS
Commutation relation
COSMOLOGICAL CONSTANT
Density
EIGENSTATES
ENERGY DENSITY
FERMIONS
Formalism
FOUR-DIMENSIONAL CALCULATIONS
GRAVITATION
Hamiltonian constraint
HAMILTONIANS
HIGGS BOSONS
HIGGS MODEL
LIE GROUPS
Mathematical models
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTIZATION
STANDARD MODEL
YANG-MILLS THEORY
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Summary:In this work we apply the affine group formalism for four dimensional gravity of Lorentzian signature, which is based on Klauder’s affine algebraic program, to the formulation of the Hamiltonian constraint of the interaction of matter and all forces, including gravity with non-vanishing cosmological constant Λ, as an affine Lie algebra. We use the hermitian action of fermions coupled to gravitation and Yang–Mills theory to find the density weight one fermionic super-Hamiltonian constraint. This term, combined with the Yang–Mills and Higgs energy densities, are composed with York’s integrated time functional. The result, when combined with the imaginary part of the Chern–Simons functional Q, forms the affine commutation relation with the volume element V(x). Affine algebraic quantization of gravitation and matter on equal footing implies a fundamental uncertainty relation which is predicated upon a non-vanishing cosmological constant. •Wheeler–DeWitt equation (WDW) quantized as affine algebra, realizing Klauder’s program.•WDW formulated for interaction of matter and all forces, including gravity, as affine algebra.•WDW features Hermitian generators in spite of fermionic content: Standard Model addressed.•Constructed a family of physical states for the full, coupled theory via affine coherent states.•Fundamental uncertainty relation, predicated on non-vanishing cosmological constant.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2014.01.017