Scalar gauge fields Authors Eduardo I. Guendelman Physics Department Ben Gurion University of the Negev Department of Physics California State University Douglas Singleton Department of Physics California State University Open Access Article

First Online: 22 May 2014 Received: 11 March 2014 Accepted: 27 April 2014 DOI :
10.1007/JHEP05(2014)096

Cite this article as: Guendelman, E.I. & Singleton, D. J. High Energ. Phys. (2014) 2014: 96. doi:10.1007/JHEP05(2014)096
Abstract In this paper we give a variation of the gauge procedure which employs a scalar gauge field, B (x ), in addition to the usual vector gauge field, A _{μ} (x ). We study this variant of the usual gauge procedure in the context of a complex scalar, matter field ϕ (x ) with a U(1) symmetry. We will focus most on the case when ϕ develops a vacuum expectation value via spontaneous symmetry breaking. We find that under these conditions the scalar gauge field mixes with the Goldstone boson that arises from the breaking of a global symmetry. Some other interesting features of this scalar gauge model are: (i) The new gauge procedure gives rise to terms which violate C and CP symmetries. This may have have applications in cosmology or for CP violation in particle physics; (ii) the existence of mass terms in the Lagrangian which respect the new extended gauge symmetry. Thus one can have gauge field mass terms even in the absence of the usual Higgs mechanism; (iii) the emergence of a sine-Gordon potential for the scalar gauge field; (iv) a natural, axion-like suppression of the interaction strength of the scalar gauge boson.

Keywords Gauge Symmetry Spontaneous Symmetry Breaking Download to read the full article text

References [1]

E.C.G. Stueckelberg,

Interaction energy in electrodynamics and in the field theory of nuclear forces ,

Helv. Phys. Acta
11 (1938) 225 [

INSPIRE ].

MATH [2]

H. Ruegg and M. Ruiz-Altaba,

The Stueckelberg field ,

Int. J. Mod. Phys.
A 19 (2004) 3265 [

hep-th/0304245 ] [

INSPIRE ].

ADS CrossRef MathSciNet [3]

E. Guendelman,

Gauge invariance and mass without spontaneous symmetry breaking ,

Phys. Rev. Lett.
43 (1979) 543 [

INSPIRE ].

ADS CrossRef [4]

A. Kato and D. Singleton,

Gauging dual symmetry ,

Int. J. Theor. Phys.
41 (2002) 1563 [

hep-th/0106277 ] [

INSPIRE ].

CrossRef MATH MathSciNet [5]

J.D. Jackson, Classical Electrodynamics , 3rd edition, section 6.11, John Wiley & Sons Inc., 1999.

[6]

A. Saa,

Local electromagnetic duality and gauge invariance ,

Class. Quant. Grav.
28 (2011) 127002 [

arXiv:1101.3927 ] [

INSPIRE ].

ADS CrossRef MathSciNet [7]

M. Chaves and H. Morales,

Unification of SU(2) × U(1)

using a generalized covariant derivative and U(3) ,

Mod. Phys. Lett.
A 13 (1998) 2021 [

hep-th/9801088 ] [

INSPIRE ].

ADS CrossRef [8]

M. Chaves and H. Morales,

Grand unification using a generalized Yang-Mills theory ,

Mod. Phys. Lett.
A 15 (2000) 197 [

hep-th/9911162 ] [

INSPIRE ].

ADS CrossRef [9]

D. Singleton, A. Kato and A. Yoshida,

Gauge procedure with gauge fields of various ranks ,

Phys. Lett.
A 330 (2004) 326 [

hep-th/0408031 ] [

INSPIRE ].

ADS CrossRef MathSciNet [10]

E. Guendelman,

Coupling Electromagnetism to Global Charge ,

Int. J. Mod. Phys.
A 28 (2013) 1350169 [

arXiv:1307.6913 ] [

INSPIRE ].

ADS CrossRef MathSciNet [11]

E.I. Guendelman and R. Steiner,

Confining Boundary conditions from dynamical Coupling Constants ,

arXiv:1311.2536 [

INSPIRE ].

[12]

J.M. Cornwall,

Dynamical Mass Generation in Continuum QCD ,

Phys. Rev.
D 26 (1982) 1453 [

INSPIRE ].

ADS [13]

Ta-Pei Cheng and Ling-Fong Li, Gauge Theory of elementary Particle Physics , Oxford Science Publications, Clarendon Press, Oxford, Oxford University Press, New York, 1988.

[14]

F.L. Bezrukov and M. Shaposhnikov,

The Standard Model Higgs boson as the inflaton ,

Phys. Lett.
B 659 (2008) 703 [

arXiv:0710.3755 ] [

INSPIRE ].

ADS CrossRef [15]

F. Bezrukov,

The Higgs field as an inflaton ,

Class. Quant. Grav.
30 (2013) 214001 [

arXiv:1307.0708 ] [

INSPIRE ].

ADS CrossRef MathSciNet [16]

R. Rajaraman, Solitons and Instantons: an Introduction to Solitons and Instantons in Quantum Field Theory , pg. 34, North-Holland, 1989.

[17]

J.E. Kim and G. Carosi,

Axions and the Strong CP Problem ,

Rev. Mod. Phys.
82 (2010) 557 [

arXiv:0807.3125 ] [

INSPIRE ].

ADS CrossRef [18]

E. Leader and C. Lorce,

The angular momentum controversy: What ’

s it all about and does it matter? ,

Phys. Rept. (2013) [

arXiv:1309.4235 ] [

INSPIRE ].

[19]

D. Singleton, ‘

Electromagnetic ’

answer to the nucleon spin puzzle ,

Phys. Lett.
B 427 (1998) 155 [

hep-ph/9710201 ] [

INSPIRE ].

ADS CrossRef [20]

D. Singleton and V.D. Dzhunushaliev,

Orbital angular momentum in the nucleon spin ,

Found. Phys.
30 (2000) 1093 [

hep-ph/9807239 ] [

INSPIRE ].

CrossRef