Utrecht University. Complex Transformations. and the. Cosmological Constant Problem. Gerard ’t Hooft Spinoza Institute Utrecht. One sees here an accelerated expansion . = density of matter at = spacelike curvature, usually assumed to vanish = cosmological constant.
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Gerard ’t Hooft
= spacelike curvature, usually assumed to vanish
= cosmological constant
The expanding Universe
on the cosmological cnstant term
but the subtraction term is crucial:
during inflation ???
Various theories claim such an effect,
but the physical forces for that
Can this happen ?
With S. Nobbenhuis,
There can exist only one state, , obeying boundary conditions
both at and
real or complex
Note: change of hermiticity properties
There is a condition that must be obeyed: translation invariance:
3. Harmonic oscillator:
Change hermiticity but not the algebra:
We get all negative energy states, but the vacuum is not invariant !
Definition of delta function:
x -space hermiticity conditions:
Then, the Hamiltonian becomes:
“ = 0 by contour integration ”
and then the vacuum is invariant !
The vacuum energy is forced to vanish because of the
x↔ ix symmetry
Particle masses and interactions appear to violate the symmetry:
Perhaps there is
a Higgs pair ?
but gauge fields ??
The image of the gauge group then becomes non-compact ...
scale of physics, Yang-Mills fields become emergent ...
questions: relation with supersymmetry ... ?
renormalization group ....