7 research outputs found
Spontaneously Generated Gauge Invariance
We argue that the non-observability of the spontaneous breakdown of Lorentz
symmetry (SBLS) caused by the vacuum expectation values of vector fields could
provide the origin of all internal symmetries observed. Remarkably, the
application of this principle to the most general relativistically invariant
Lagrangian, with arbitrary couplings for all the fields involved, leads by
itself to the appearance of a symmetry and, what is more, to the massless
vector field(s) gauging this symmetry. A simple model for the SBLS based on
massive vector and real scalar field interactions is considered; it is found
that spontaneously broken gauge symmetries could also appear, when SBLS happens
and is required to be physically unobservable.Comment: 20 page LaTeX file, expanded conclusion and other minor addition
Lorentz Invariance and Origin of Symmetries
In this letter we reconsider the role of Lorentz invariance in the dynamical
generation of the observed internal symmetries. We argue that, generally,
Lorentz invariance can only be imposed in the sense that all Lorentz
non-invariant effects caused by the spontaneous breakdown of Lorentz symmetry
are physically unobservable. Remarkably, the application of this principle to
the most general relativistically invariant Lagrangian, with arbitrary
couplings for all the fields involved, leads by itself to the appearance of a
symmetry and, what is more, to the massless vector fields gauging this symmetry
in both Abelian and non-Abelian cases. In contrast, purely global symmetries
are only generated as accidental consequences of the gauge symmetry.Comment: 10 page LaTeX fil
Constrained Gauge Fields from Spontaneous Lorentz Violation
Spontaneous Lorentz violation realized through a nonlinear vector field
constraint of the type ( is the proposed scale for
Lorentz violation) is shown to generate massless vector Goldstone bosons,
gauging the starting global internal symmetries in arbitrary relativistically
invariant theories. The gauge invariance appears in essence as a necessary
condition for these bosons not to be superfluously restricted in degrees of
freedom, apart from the constraint due to which the true vacuum in a theory is
chosen by the Lorentz violation. In the Abelian symmetry case the only possible
theory proves to be QED with a massless vector Goldstone boson naturally
associated with the photon, while the non-Abelian symmetry case results in a
conventional Yang-Mills theory. These theories, both Abelian and non-Abelian,
look essentially nonlinear and contain particular Lorentz (and ) violating
couplings when expressed in terms of the pure Goldstone vector modes. However,
they do not lead to physical Lorentz violation due to the simultaneously
generated gauge invariance.Comment: 15 pages, minor corrections, version to be published in Nucl. Phys.
Spontaneous Lorentz Violation: Non-Abelian Gauge Fields as Pseudo-Goldstone Vector Bosons
We argue that non-Abelian gauge fields can be treated as the pseudo-Goldstone
vector bosons caused by spontaneous Lorentz invariance violation (SLIV). To
this end, the SLIV which evolves in a general Yang-Mills type theory with the
nonlinear vector field constraint Tr(% \boldsymbol{A}_{\mu
}\boldsymbol{A}^{\mu})=\pm M^{2} ( is a proposed SLIV scale) imposed is
considered in detail. With an internal symmetry group having generators
not only the pure Lorentz symmetry SO(1,3), but the larger accidental symmetry
of the SLIV constraint in itself appears to be spontaneously broken
as well. As a result, while the pure Lorentz violation still generates only one
genuine Goldstone vector boson, the accompanying pseudo-Goldstone vector bosons
related to the breaking also come into play in the final arrangement
of the entire Goldstone vector field multiplet. Remarkably, they remain
strictly massless, being protected by gauge invariance of the Yang-Mills theory
involved. We show that, although this theory contains a plethora of Lorentz and
violating couplings, they do not lead to physical SLIV effects which turn
out to be strictly cancelled in all the lowest order processes considered.
However, the physical Lorentz violation could appear if the internal gauge
invariance were slightly broken at very small distances influenced by gravity.
For the SLIV scale comparable with the Planck one the Lorentz violation could
become directly observable at low energies.Comment: Invited talk given at Caucasian-German School and Workshop in Hadron
Physics (4-7 September 2006, Tbilisi, Georgia
Spontaneous Lorentz Violation via QED with Non-Exact Gauge Invariance
We reconsider an alternative theory of the QED with the photon as a massless
vector Nambu-Goldstone boson and show that the underlying spontaneous Lorentz
violation caused by the vector field vacuum expectation value, while being
superficial in gauge invariant theory, becomes physically significant in the
QED with a tiny gauge non-invariance. This leads, through special dispersion
relations appearing for charged fermions, to a new class of phenomena which
could be of distinctive observational interest in particle physics and
astrophysics. They include a significant change in the GZK cutoff for UHE
cosmic-ray nucleons, stability of high-energy pions and W bosons, modification
of nucleon beta decays, and some others.Comment: 15 pages, to appear in Eur.Phys.J.
Standard Model with Partial Gauge Invariance
We argue that an exact gauge invariance may disable some generic features of
the Standard Model which could otherwise manifest themselves at high energies.
One of them might be related to the spontaneous Lorentz invariance violation
(SLIV) which could provide an alternative dynamical approach to QED and
Yang-Mills theories with photon and non-Abelian gauge fields appearing as
massless Nambu-Goldstone bosons. To see some key features of the new physics
expected we propose partial rather than exact gauge invariance in an extended
SM framework. This principle applied, in some minimal form, to the weak
hypercharge gauge field B_{mu} and its interactions leads to SLIV with B field
components appearing as the massless Nambu-Goldstone modes, and provides a
number of distinctive Lorentz beaking effects. Being naturally suppressed at
low energies they may become detectable in high energy physics and
astrophysics. Some of the most interesting SLIV processes are considered in
significant detail.Comment: 32 pages, extended version, to appear in Eur.Phys.J.