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

the programme

In our framework, we consider the full phase space, with coordinates defined as


1

α = 2

⎪⎨

⎪⎩

ln

1

δab

3 Σ d3

xqab

πα = 2e2α

δab Σ d3xπab T (0)

=

Σ d3

xT

=

and

In this coordinates we:

p (0)

T

Σ d3 xpT


δqab(x) = qab(x) − e

⎪⎨

⎪⎩

2αδab δπab (x) = πab (x) − πα

6 e−2αδab δT(x) = T(x) − T (0)

δpT(x) = pT(x) − p (0)

T

δφ(x) = φ(x)

δπφ(x) = πφ(x)

1 solve the full constraints of the theory

2 reduce to the constraint surface ΓC

3 study the gauge transformations generated by the constraints and restrict to ΓP

4 construct the algebra of basic Dirac observables

5 study the 1-dimensional group of automorphisms on it parametrized by T (0)

6 find the physical Hamiltonian (generator of such group)

7 go home and find a real job

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