Submissions from Rene R. P. Verburg

[1]  faKiv:2104.08493 [pdf]
On the mapping between quantum propagators and high-energy effective theories
Comments: 11 pages, 2 figures

We investigate the mapping between quantum propagators and high-energy effective theories in $(2+1)$ dimensions. In particular, we study the map between the momentum and momentum square of the low-energy effective theory, which is encoded in terms of the momentum and momentum square of the propagators in the high-energy effective theory. We also study the map between the momentum and momentum square of the high-energy effective theory, which is encoded in terms of the momentum and momentum square of the propagators in the low-energy effective theory. We show that, in the case of low-energy effective theories, the map between the momentum and momentum square can be written as a map between the momentum and momentum square of the low-energy effective theory. We also show that, in terms of the momentum and momentum square, the map between the momentum and momentum square of the high-energy effective theory can be written as a map between the momentum and momentum square of the low-energy effective theory.

[2]  faKiv:2104.08554 [pdf]
A Do-It-Yourself String Theory Approach to Theory
Comments: 47 pages, 9 figures

We demonstrate that it is possible to construct a non-perturbative approach to the theory of a Do-It-Yourself (DYI) string in terms of the Higgs mechanism in the initial conditions. For the first time, we give explicit expressions for the constraint functions of the dynamical expansion of the theory in the presence of a fundamental tension. This leads us to a binding of the phonon diagram of the DYI theory on a pure-Minkowski space. We analyze the behavior of the numerical solutions of the constraints and show that the equations of motion of the theory are exactly the same as those of a standard size-theorem of the standard model.

[3]  faKiv:2104.08679 [pdf]
Quantum mechanics with the massless scalar field and its time-reversal relation
Comments: 18 pages, 3 figures, LaTeX

We study the quantum mechanics with the massless scalar field in the framework of the minimal model of the classical Schr\"odinger theory. We show that the relativistic time-reversal relation is the classical Schr\"odinger relation with the massless scalar field. This relation does not depend on the existence of the scalar field or on the time-reversal relation. We also show that the relativistic time-reversal relation for the non-supersymmetric case does not depend on the presence of the scalar field. Finally, we show that the relativistic time-reversal relation for the scalar field in the classical Schr\"odinger theory does not depend on the gauge condition, the spectral index, the amount of energy or on the time-reversal relation.

[4]  faKiv:2104.08789 [pdf]
Feynman integrals and entanglement entropy in extended Chern-Simons theory
Comments: 29 pages, 12 figures, v2: minor corrections

We investigate the Feynman integrals in extended Chern-Simons theory in the presence of a Chern-Simons term. In particular, we consider the triplets of the generalized Feynman integrals, which are made explicit in the map of the Feynman function from two to four dimensions. We find that the triplets can be made explicit in the map of the Feynman function from two dimensions. The maps can be expressed in terms of the $\mathbb{Z}_3$-functions of the generalized Feynman functions, which we find are well known in the setting of quantum mechanics and quantum field theory. We derive the maps from the Feynman functions of the generalized Feynman integrals.