# Goldstone bosons in presence of charge density

## Abstract

We investigate spontaneous symmetry breaking in Lorentz-noninvariant theories. Our general discussion includes relativistic systems at finite density as well as intrinsically nonrelativistic systems. The main result of the paper is a direct proof that nonzero density of a non-Abelian charge in the ground state implies the existence of a Goldstone boson with nonlinear (typically, quadratic) dispersion law. We show that the Goldstone boson dispersion relation may in general be extracted from the current transition amplitude and demonstrate on examples from recent literature, how the calculation of the dispersion relation is utilized by this method. After then, we use the general results to analyze the nonrelativistic degenerate Fermi gas of four fermion species. Because of its internal SU(4) symmetry, this system provides an analog to relativistic two-color quantum chromodynamics with two quark flavors. In the end, we extend our results to pseudo-Goldstone bosons of an explicitly broken symmetry.

- Authors:

- Department of Theoretical Physics, Nuclear Physics Institute ASCR, 25068 Rez (Czech Republic)

- Publication Date:

- OSTI Identifier:
- 20933302

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.75.105014; (c) 2007 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; CHARGE DENSITY; COLOR MODEL; DISPERSION RELATIONS; FERMI GAS; FLAVOR MODEL; GOLDSTONE BOSONS; GROUND STATES; NONLINEAR PROBLEMS; QUANTUM CHROMODYNAMICS; QUARKS; RELATIVISTIC RANGE; SU-4 GROUPS; SYMMETRY BREAKING; TRANSITION AMPLITUDES

### Citation Formats

```
Brauner, Tomas.
```*Goldstone bosons in presence of charge density*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.105014.

```
Brauner, Tomas.
```*Goldstone bosons in presence of charge density*. United States. doi:10.1103/PHYSREVD.75.105014.

```
Brauner, Tomas. Tue .
"Goldstone bosons in presence of charge density". United States.
doi:10.1103/PHYSREVD.75.105014.
```

```
@article{osti_20933302,
```

title = {Goldstone bosons in presence of charge density},

author = {Brauner, Tomas},

abstractNote = {We investigate spontaneous symmetry breaking in Lorentz-noninvariant theories. Our general discussion includes relativistic systems at finite density as well as intrinsically nonrelativistic systems. The main result of the paper is a direct proof that nonzero density of a non-Abelian charge in the ground state implies the existence of a Goldstone boson with nonlinear (typically, quadratic) dispersion law. We show that the Goldstone boson dispersion relation may in general be extracted from the current transition amplitude and demonstrate on examples from recent literature, how the calculation of the dispersion relation is utilized by this method. After then, we use the general results to analyze the nonrelativistic degenerate Fermi gas of four fermion species. Because of its internal SU(4) symmetry, this system provides an analog to relativistic two-color quantum chromodynamics with two quark flavors. In the end, we extend our results to pseudo-Goldstone bosons of an explicitly broken symmetry.},

doi = {10.1103/PHYSREVD.75.105014},

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

number = 10,

volume = 75,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}