QFT on quantum spacetime: a compatible classical framework (Tux ...

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QFT on quantum spacetime: a compatible classical framework (Tux ...

ong>QFTong> on

quantum

spacetime

AD, JL, JP

motivation

full theory,

full reduction

again full

constraints to

1st order

physical

phase space

Action:


S =

where κ = 8πG. Three sectors:

full theory

d 4 x √

1 1

−g R −

2κ 2 gµν∂µT∂νT − 1

2 gµν

∂µφ∂νφ

• the geometric (G) sector, associated to the metric gµν

• the time (T) sector, a K-G ”clock field” T

• the matter (M) sector, a K-G ”matter field” φ

Hamiltonian analysis (ADM): kinematical phase space Γ = ΓG × ΓT × ΓM with

{qab(x), π cd (y)} = δ (c

a δ d)

b δ(3) (x, y), {T(x), pT(y)} = δ (3) (x, y), {φ(x), πφ(y)} = δ (3) (x, y)

and constraints


C =

⎪⎨




q

πabπ ab − 1

+ 1

2 √ q p2 T +

2 (qabπab ) 2


q


2κ R(3) +


q

2 qab∂aT∂bT + 1

2 √ q π2 φ +

⎪⎩

Ca = −2qac∇bπbc + pT∂aT + πφ∂aφ

√ q

2 qab ∂aφ∂bφ

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