Formalism

Anxiang Ge, Johannes Halbinger, Seung‐Sup B. Lee +2 more

Abstract Conceptually, the Matsubara formalism (MF), using imaginary frequencies, and the Keldysh formalism (KF), formulated in real frequencies, give equivalent results for systems in thermal equilibrium. The MF has less complexity and is thus more convenient than the KF. However, computing dynamical observables in the MF requires the analytic continuation from imaginary to real frequencies. The analytic continuation is well‐known for two‐point correlation functions (having one frequency argument), but, for multipoint correlators, a straightforward recipe for deducing all Keldysh components from the MF correlator had not been formulated yet. Recently, a representation of MF and KF correlators in terms of formalism‐independent partial spectral functions and formalism‐specific kernels was introduced by Kugler, Lee, and von Delft [Phys. Rev. X 11, 041006 (2021)]. This representation is used to formally elucidate the connection between both formalisms. How a multipoint MF correlator can be analytically continued to recover all partial spectral functions and yield all Keldysh components of its KF counterpart is shown. The procedure is illustrated for various correlators of the Hubbard atom.

Kazuki Koshino

The measurement-modified decay rate is calculated in two distinct formalisms, i.e., the conventional formalism and the dynamical formalism. The relation between the two formalisms is clarified, by recasting the decay rates obtained by the two formalisms into a unified form. It is shown that the dynamical formalism reproduces the conventional results only under the condition that the apparatus detects the decayed states with an identical response time.

Robin de la Llata

Kurt Gottfried, Tung‐Mow Yan

Veronika Baumann, Stefan Wolf

One of the reasons for the heated debates around the interpretations of quantum theory is a simple confusion between the notions of formalism versus interpretation. In this note, we make a clear distinction between them and show that there are actually two inequivalent quantum formalisms, namely the relative-state formalism and the standard formalism with the Born and measurement-update rules. We further propose a different probability rule for the relative-state formalism and discuss how Wigner's-friend-type experiments could show the inequivalence with the standard formalism. The feasibility in principle of such experiments, however, remains an open question.