On equations of motion, invariance of the action integral and symmetry transformations \\ \\

Ysla Adans; Abdul Qadeer Rehan; Abdul Qadeer Rehan

On equations of motion, invariance of the action integral and symmetry transformations \\ \\

ORAL

Abstract

\\ \\As it is well known, group theory has a wide application in Classical Physics and Quantum Theory, both in relativistic and non-relativistic formulation. On this subject, one of the themes of interest is the formulation of methods capable of determining the symmetry group of a given physical system. In this work, we aim to show the application of two methods: one explores the system's equation of motion and the other uses the invariance of the system's action. In the first, starting from the equation of motion and general expressions of the generators, the Lie algebra of the symmetry group is determined; in the second starting from the action integral, conditions are obtained that characterize the symmetry group that leaves the Lagrangian invariant, the invariant action and the invariant motion equation. We apply these methods to the simple harmonic oscillator and to the damped harmonic oscillator. In both cases we obtain as a result a group with eight parameters that preserves the equation of motion and a subgroup with five parameters that preserves the action named in the literature by the group of Noether symmetries. Constants of the motion for each system are also determined and explored.

Jan. 24, 2021, 12:40 PM – Jan. 24, 2021, 12:50 PM

Authors

Ysla Adans

Federal University of Bahia
Abdul Qadeer Rehan

University of Tennessee, University of York, Old Dominion University, Massachusetts Institute of Technology, Old Dominion University, Massachusetts Institute of Technology, Lawrence Berkeley National Laboratory, University of California, Berkeley, Institute of Physics - University of Sao Paulo, Naval Research Laboratory, St. Cloud State University, University of Illinois at Urbana-Champaign, Space Sciences Laboratory, Virginia Polytechnic Institute and State University, Space Sciences Laboratory, University of California Berkeley, University of Maryland - Baltimore County, Sandia National Laboratories, Pacific Northwest National Laboratory, Federal University of Bahia; University of Brasília, Federal University of Bahia, Department of Applied Physics, Yale University & Department of Physics, Yale University, Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Department of Physics, University of Illinois at Urbana-Champaign & Current affiliation: Seagate Research Group, Seagate Technology, Department of Physics and Astronomy, Wayne State University, Department of Physics, University of Illinois at Urbana-Champaign, Department of Applied Physics, Yale University, Swarthmore College, Western Washington University, Departments of Chemistry and Physics and The Baruch 60 Center for Biochemical Solar Energy Research at Rensselaer Polytechnic Institute, University of Florida, Wayne State University, Vanderbilt University, University of Maryland, College Park, NASA GSFC, CfA, California Institute of Technology, Skidmore College, Durham University, University of Alberta, University of Michigan, Curtin University, Michigan State University, University of Nevada, University of Chicago, Duke University, Cornell, Pennsylvania State University, New York University Abu Dhabi, NASA Ames Research Center, Kenyon Coll, Kenyon College, University of Texas at Austin, Flatiron Institute, University of California, Los Angeles, Ohio State University, University of Pennsylvania, HERA, HERA, Rochester Institute of Technology, Howard Community College, Carleton College, California State University at Long Beach, Bishop Ireton High School, Fayetteville State University, Univ of Oklahoma, University of Massachusetts Amherst, Carnegie Observatories, San Diego State University, Associate of the National Institute of Standards and Technology, National Institute of Standards and Technology, NTT Basic Research Laboratories and NTT Research Center for Theoretical Quantum Physics, JILA, University of Colorado, 440 UCB, Boulder, CO, Department of Physics, 390 UCB University of Colorado, University of Washington, James Franck Institute, Enrico Fermi Institute, University of Chicago Department of Physics, Princeton University, Department of Physics, Arizona State University, Indiana Univ - Bloomington, National Autonomous University of Mexico, Harvard University, Nagoya University, Toyota Technological Institute, University of Tokyo, Zhejiang University, Clark University, Natl Univ of Singapore, University of Richmond
Abdul Qadeer Rehan

University of Tennessee, University of York, Old Dominion University, Massachusetts Institute of Technology, Old Dominion University, Massachusetts Institute of Technology, Lawrence Berkeley National Laboratory, University of California, Berkeley, Institute of Physics - University of Sao Paulo, Naval Research Laboratory, St. Cloud State University, University of Illinois at Urbana-Champaign, Space Sciences Laboratory, Virginia Polytechnic Institute and State University, Space Sciences Laboratory, University of California Berkeley, University of Maryland - Baltimore County, Sandia National Laboratories, Pacific Northwest National Laboratory, Federal University of Bahia; University of Brasília, Federal University of Bahia, Department of Applied Physics, Yale University & Department of Physics, Yale University, Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Department of Physics, University of Illinois at Urbana-Champaign & Current affiliation: Seagate Research Group, Seagate Technology, Department of Physics and Astronomy, Wayne State University, Department of Physics, University of Illinois at Urbana-Champaign, Department of Applied Physics, Yale University, Swarthmore College, Western Washington University, Departments of Chemistry and Physics and The Baruch 60 Center for Biochemical Solar Energy Research at Rensselaer Polytechnic Institute, University of Florida, Wayne State University, Vanderbilt University, University of Maryland, College Park, NASA GSFC, CfA, California Institute of Technology, Skidmore College, Durham University, University of Alberta, University of Michigan, Curtin University, Michigan State University, University of Nevada, University of Chicago, Duke University, Cornell, Pennsylvania State University, New York University Abu Dhabi, NASA Ames Research Center, Kenyon Coll, Kenyon College, University of Texas at Austin, Flatiron Institute, University of California, Los Angeles, Ohio State University, University of Pennsylvania, HERA, HERA, Rochester Institute of Technology, Howard Community College, Carleton College, California State University at Long Beach, Bishop Ireton High School, Fayetteville State University, Univ of Oklahoma, University of Massachusetts Amherst, Carnegie Observatories, San Diego State University, Associate of the National Institute of Standards and Technology, National Institute of Standards and Technology, NTT Basic Research Laboratories and NTT Research Center for Theoretical Quantum Physics, JILA, University of Colorado, 440 UCB, Boulder, CO, Department of Physics, 390 UCB University of Colorado, University of Washington, James Franck Institute, Enrico Fermi Institute, University of Chicago Department of Physics, Princeton University, Department of Physics, Arizona State University, Indiana Univ - Bloomington, National Autonomous University of Mexico, Harvard University, Nagoya University, Toyota Technological Institute, University of Tokyo, Zhejiang University, Clark University, Natl Univ of Singapore, University of Richmond