ELFT HÍRADÓ

[somogyi <somogyi.gabor AT wigner.hu>]

Wigner FK RMI Elméleti Osztály Szemináriuma
Tisztelettel meghívjuk


                  László András
                  (Wigner FK)


"On generally covariant mathematical formulation of Feynman integral in 
Lorentz signature"


     címmel tartandó szemináriumára.


Kivonat:



Feynman integral is one of the most promising methodologies for defining 
a generally covariant formulation of nonperturbative interacting quantum 
field theories (QFTs) without a fixed prearranged causal background. 
Recent literature indicates that in such scenario, one needs to consider 
the problematics in the original Lorentz signature. Lorentz signature 
Feynman integrals are known, however, to be mathematically ill-defined. 
The Feynman integral formulation has, however, a differential 
reformulation: the master Dyson-Schwinger (MDS) equation for field 
correlators. In this talk we show that with the right choice of 
variables, the MDS equation is mathematically well defined: the involved 
function spaces and operators can be defined and their properties can be 
established. Therefore, MDS equation can serve as a substitute for the 
Feynman integral, in a mathematically sound formulation of constructive 
QFT, in arbitrary signature, without a fixed background causal 
structure. It is also shown that the Wilsonian regularization of the MDS 
equation can be canonically defined. Our main result is a necessary and 
sufficient condition for the regularized MDS solution space to be 
nonempty, which also provides a convergent iterative approximation for 
the solution. The talk is based on the paper: Class. Quant. Grav. 39 
(2022) 185004.



Helye: Wigner FK RMI III. ép. Tanácsterem
Ideje: 2022 október 7 péntek  d.u. 14 óra

Szívesen látunk minden érdeklődőt.


                             Somogyi Gábor