# Diffeomorphism Group Representations in Relativistic Quantum Field Theory

## Abstract

We explore the role played by the di eomorphism group and its unitary representations in relativistic quantum eld theory. From the quantum kinematics of particles described by representations of the di eomorphism group of a space-like surface in an inertial reference frame, we reconstruct the local relativistic neutral scalar eld in the Fock representation. An explicit expression for the free Hamiltonian is obtained in terms of the Lie algebra generators (mass and momentum densities). We suggest that this approach can be generalized to elds whose quanta are spatially extended objects.

- Authors:

- Rutgers Univ., Piscataway, NJ (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1415360

- Report Number(s):
- LA-UR-17-31393

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 97 MATHEMATICS AND COMPUTING; Atomic and Nuclear Physics; Mathematics

### Citation Formats

```
Goldin, Gerald A., and Sharp, David H.
```*Diffeomorphism Group Representations in Relativistic Quantum Field Theory*. United States: N. p., 2017.
Web. doi:10.2172/1415360.

```
Goldin, Gerald A., & Sharp, David H.
```*Diffeomorphism Group Representations in Relativistic Quantum Field Theory*. United States. doi:10.2172/1415360.

```
Goldin, Gerald A., and Sharp, David H. Wed .
"Diffeomorphism Group Representations in Relativistic Quantum Field Theory". United States.
doi:10.2172/1415360. https://www.osti.gov/servlets/purl/1415360.
```

```
@article{osti_1415360,
```

title = {Diffeomorphism Group Representations in Relativistic Quantum Field Theory},

author = {Goldin, Gerald A. and Sharp, David H.},

abstractNote = {We explore the role played by the di eomorphism group and its unitary representations in relativistic quantum eld theory. From the quantum kinematics of particles described by representations of the di eomorphism group of a space-like surface in an inertial reference frame, we reconstruct the local relativistic neutral scalar eld in the Fock representation. An explicit expression for the free Hamiltonian is obtained in terms of the Lie algebra generators (mass and momentum densities). We suggest that this approach can be generalized to elds whose quanta are spatially extended objects.},

doi = {10.2172/1415360},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Wed Dec 20 00:00:00 EST 2017},

month = {Wed Dec 20 00:00:00 EST 2017}

}

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