A study of Schrödinger’s equation in quantum field theory

The goal of prof. dr hab Zbigniew Haba’s paper titled Functional Formulation of Quantum Theory of a Scalar Field in a Metric with Lorentzian and Euclidean Signatures, published in the Entropy journal, was to present the quantum field theory through stochastic processes. This formulation is known for continuation to imaginary time.

‘My formulation is in real physical time’, says prof. Haba. ‘An advantage of such formalism is the possibility of computer simulation of quantum processes using classical stochastic processes.’

The work shows that the method of continuation to real time is particularly useful together with spatial signature inversion. We then have evolution in real time but in the Euclidean metric. This allows to solve some of the singularity problems in quantum field theory.

‘In my work I study the inversion of spatial signature for a metric which is the solution of Einstein’s equations in the radiation field. It is a dynamic effect resulting from extending in time the known solution,’ prof. Haba continues. ‘I study the consequences of such extension for quantum theory of a scalar field. I indicate that the difficulties of quantum field theory on small subdivisions can be solved by quantum gravity as a result of a change in the signature of the metric.’