# Angular momentum on the lattice: The case of nonzero linear momentum

## Abstract

The irreducible representations (IRs) of the double cover of the Euclidean group with parity in three dimensions are subduced to the corresponding cubic space group. The reduction of these representations gives the mapping of continuum angular momentum states to the lattice in the case of nonzero linear momentum. The continuous states correspond to lattice states with the same momentum and continuum rotational quantum numbers decompose into those of the IRs of the little group of the momentum vector on the lattice. The inverse mapping indicates degeneracies that will appear between levels of different lattice IRs in the continuum limit, recovering the continuum angular momentum multiplets. An example of this inverse mapping is given for the case of the 'moving' isotropic harmonic oscillator.

- Authors:

- Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520 (United States)

- Publication Date:

- OSTI Identifier:
- 20774616

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevD.73.014504; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANGULAR MOMENTUM; EUCLIDEAN SPACE; HARMONIC OSCILLATORS; IRREDUCIBLE REPRESENTATIONS; LATTICE FIELD THEORY; LINEAR MOMENTUM; MULTIPLETS; PARITY; QUANTUM NUMBERS; SPACE GROUPS; VECTORS

### Citation Formats

```
Moore, David C., and Fleming, George T..
```*Angular momentum on the lattice: The case of nonzero linear momentum*. United States: N. p., 2006.
Web. doi:10.1103/PhysRevD.73.014504.

```
Moore, David C., & Fleming, George T..
```*Angular momentum on the lattice: The case of nonzero linear momentum*. United States. doi:10.1103/PhysRevD.73.014504.

```
Moore, David C., and Fleming, George T.. Sun .
"Angular momentum on the lattice: The case of nonzero linear momentum". United States.
doi:10.1103/PhysRevD.73.014504.
```

```
@article{osti_20774616,
```

title = {Angular momentum on the lattice: The case of nonzero linear momentum},

author = {Moore, David C. and Fleming, George T.},

abstractNote = {The irreducible representations (IRs) of the double cover of the Euclidean group with parity in three dimensions are subduced to the corresponding cubic space group. The reduction of these representations gives the mapping of continuum angular momentum states to the lattice in the case of nonzero linear momentum. The continuous states correspond to lattice states with the same momentum and continuum rotational quantum numbers decompose into those of the IRs of the little group of the momentum vector on the lattice. The inverse mapping indicates degeneracies that will appear between levels of different lattice IRs in the continuum limit, recovering the continuum angular momentum multiplets. An example of this inverse mapping is given for the case of the 'moving' isotropic harmonic oscillator.},

doi = {10.1103/PhysRevD.73.014504},

journal = {Physical Review. D, Particles Fields},

number = 1,

volume = 73,

place = {United States},

year = {Sun Jan 01 00:00:00 EST 2006},

month = {Sun Jan 01 00:00:00 EST 2006}

}