# Dirac and Faddeev–Jackiw quantization of a five-dimensional Stüeckelberg theory with a compact dimension

## Abstract

A detailed Hamiltonian analysis for a five-dimensional Stüeckelberg theory with a compact dimension is performed. First, we develop a pure Dirac’s analysis of the theory; we show that after performing the compactification, the theory is reduced to four-dimensional Stüeckelberg theory plus a tower of Kaluza–Klein modes. We develop a complete analysis of the constraints, we fix the gauge and we show that there are present pseudo-Goldstone bosons. Then we quantize the theory by constructing the Dirac brackets. As complementary work, we perform the Faddeev–Jackiw quantization for the theory under study, and we calculate the generalized Faddeev–Jackiw brackets, we show that both the Faddeev–Jackiw and Dirac’s brackets are the same. Finally we discuss some remarks and prospects. - Highlights: • Dirac’s method for 5D Stueckelberg theory with a compact dimension is performed. • By fixing the gauge in the effective theory we find present pseudo-Goldstone bosons. • Dirac’s brackets are constructed for the zero-modes and the kk-excitations. • The Faddeev–Jackiw quantization is performed. • The equivalence between generalized Faddeev–Jackiw and Dirac’s brackets is shown.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22447590

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 353; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FOUR-DIMENSIONAL CALCULATIONS; GOLDSTONE BOSONS; HAMILTONIANS; KALUZA-KLEIN THEORY; MANY-DIMENSIONAL CALCULATIONS; QUANTIZATION

### Citation Formats

```
Escalante, Alberto, E-mail: aescalan@ifuap.buap.mx, and Zarate, Moises, E-mail: mzarate@ifuap.buap.mx.
```*Dirac and Faddeev–Jackiw quantization of a five-dimensional Stüeckelberg theory with a compact dimension*. United States: N. p., 2015.
Web. doi:10.1016/J.AOP.2014.11.007.

```
Escalante, Alberto, E-mail: aescalan@ifuap.buap.mx, & Zarate, Moises, E-mail: mzarate@ifuap.buap.mx.
```*Dirac and Faddeev–Jackiw quantization of a five-dimensional Stüeckelberg theory with a compact dimension*. United States. doi:10.1016/J.AOP.2014.11.007.

```
Escalante, Alberto, E-mail: aescalan@ifuap.buap.mx, and Zarate, Moises, E-mail: mzarate@ifuap.buap.mx. Sun .
"Dirac and Faddeev–Jackiw quantization of a five-dimensional Stüeckelberg theory with a compact dimension". United States.
doi:10.1016/J.AOP.2014.11.007.
```

```
@article{osti_22447590,
```

title = {Dirac and Faddeev–Jackiw quantization of a five-dimensional Stüeckelberg theory with a compact dimension},

author = {Escalante, Alberto, E-mail: aescalan@ifuap.buap.mx and Zarate, Moises, E-mail: mzarate@ifuap.buap.mx},

abstractNote = {A detailed Hamiltonian analysis for a five-dimensional Stüeckelberg theory with a compact dimension is performed. First, we develop a pure Dirac’s analysis of the theory; we show that after performing the compactification, the theory is reduced to four-dimensional Stüeckelberg theory plus a tower of Kaluza–Klein modes. We develop a complete analysis of the constraints, we fix the gauge and we show that there are present pseudo-Goldstone bosons. Then we quantize the theory by constructing the Dirac brackets. As complementary work, we perform the Faddeev–Jackiw quantization for the theory under study, and we calculate the generalized Faddeev–Jackiw brackets, we show that both the Faddeev–Jackiw and Dirac’s brackets are the same. Finally we discuss some remarks and prospects. - Highlights: • Dirac’s method for 5D Stueckelberg theory with a compact dimension is performed. • By fixing the gauge in the effective theory we find present pseudo-Goldstone bosons. • Dirac’s brackets are constructed for the zero-modes and the kk-excitations. • The Faddeev–Jackiw quantization is performed. • The equivalence between generalized Faddeev–Jackiw and Dirac’s brackets is shown.},

doi = {10.1016/J.AOP.2014.11.007},

journal = {Annals of Physics},

number = ,

volume = 353,

place = {United States},

year = {Sun Feb 15 00:00:00 EST 2015},

month = {Sun Feb 15 00:00:00 EST 2015}

}