Asymptotics of the evolution semigroup associated with a scalar field in the presence of a non-linear electromagnetic field

Albeverio, Sergio; Tamura, Hiroshi

doi:10.1063/1.4996880

Asymptotics of the evolution semigroup associated with a scalar field in the presence of a non-linear electromagnetic field

Sergio Albeverio
(
- Bonn U. and
- Bielefeld U. and
- CERFIM, Locarno
)
,
Hiroshi Tamura
(
- Kanazawa U.
)

Apr 5, 2018

Published in:

J.Math.Phys. 59 (2018) 4, 042301

Published: Apr 5, 2018

DOI:

10.1063/1.4996880

View in:

AMS MathSciNet

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Abstract: (AIP)

We consider a model describing the coupling of a vector-valued and a scalar homogeneous Markovian random field over R4, interpreted as expressing the interaction between a charged scalar quantum field coupled with a nonlinear quantized electromagnetic field. Expectations of functionals of the random fields are expressed by Brownian bridges. Using this, together with Feynman-Kac-Itô type formulae and estimates on the small time and large time behaviour of Brownian functionals, we prove asymptotic upper and lower bounds on the kernel of the transition semigroup for our model. The upper bound gives faster than exponential decay for large distances of the corresponding resolvent (propagator).

electromagnetic field: nonlinear
field theory: scalar
electromagnetic field: quantization
field theory: coupling
quantization: nonlinear
random field
propagator

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