# Effect of the variational symmetries of the Lagrangian on the propagator and associated conserved operators

## TL;DR

This paper investigates how variational symmetries of a Lagrangian influence the quantum propagator and conserved operators, establishing relations between propagators of related Lagrangians through point transformations.

## Contribution

It introduces a method to connect propagators of different Lagrangians via point transformations and explores the impact of variational symmetries on the propagator.

## Key findings

- Variational symmetries affect the form of the propagator.
- Point transformations relate propagators of different Lagrangians.
- Conserved operators are linked to these symmetries.

## Abstract

Making use of the expression for the propagator in terms of path integrals, we study the effect of certain variational symmetries of a Lagrangian on the corresponding propagator. We also show that by considering a point transformation that relates two different Lagrangians one can obtain a relation between the corresponding propagators.