skip to main content

SciTech ConnectSciTech Connect

Title: 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 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. -- Highlights: •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.
Authors:
 [1] ;  [2] ;  [1]
  1. Department of Physics, National Cheng Kung University, Taiwan (China)
  2. Department of Physics, US Naval Academy, Annapolis, MD (United States)
Publication Date:
OSTI Identifier:
22314794
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 343; Journal Issue: Complete; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACTION INTEGRAL; ANNIHILATION OPERATORS; COSMOLOGICAL CONSTANT; EIGENSTATES; ENERGY DENSITY; FERMIONS; FOUR-DIMENSIONAL CALCULATIONS; GRAVITATION; HAMILTONIANS; HIGGS BOSONS; HIGGS MODEL; LIE GROUPS; QUANTIZATION; STANDARD MODEL; YANG-MILLS THEORY