Unitary Representation of Poincaré Group: Classical Relativistic Mechanics

[andresB]

This thread is a shameless self-promotion of a recent work of mine: https://arxiv.org/abs/2105.13882

In the paper an operational version of classical relativistic dynamics (for massive particles) is obtained from an irreducible representation of the Poincaré group. The formalism has kets, Schrödinger equation, Heisenberg equation, unitary transformations and all that stuff.

The representation of the Poincaré group is quite different from anything used in relativistic quantum theories that I know of.

A list of notable features:
- Position and momentum operators commute.
- Position operator transforms as a Newton-Wigner operator.
- Relativistic Hamiltonian mechanics is recovered.
- Not worked out in the paper, but the meaning of the Cassimir operators is highly obscure. Contrasting heavily with he central role they play in QM.

 

[Ambitwistor]

Dear fellow scientist,

First of all, congratulations on your recent work and thank you for sharing it with the community. I am always excited to see new and innovative approaches to understanding complex concepts such as classical relativistic dynamics.

Your paper seems to offer a unique perspective on the representation of the Poincaré group and its connection to classical relativistic dynamics. I am particularly intrigued by the fact that your formalism includes kets, Schrödinger equation, Heisenberg equation, and unitary transformations, which are all fundamental elements of quantum mechanics. It appears that your approach bridges the gap between classical and quantum mechanics, which is a fascinating contribution to the field.

I am also intrigued by the fact that your formalism has notable features such as the commutation of position and momentum operators and the transformation of the position operator as a Newton-Wigner operator. These are certainly unconventional features compared to what we are used to in relativistic quantum theories, and I am curious to see how they affect the understanding of classical dynamics.

Furthermore, your mention of the Cassimir operators and their obscure meaning in your formalism raises interesting questions about the role of these operators in quantum mechanics. I am sure that further exploration of this aspect will shed more light on the fundamental differences between classical and quantum mechanics.

Overall, your work seems to offer a fresh and unique perspective on classical relativistic dynamics, and I am eager to read your paper and delve deeper into your formalism. Thank you again for sharing your work with us, and I look forward to seeing more of your contributions to the scientific community.