761 research outputs found
Functional Mellin Transforms
Conventional functional/path integrals used in physics often can be defined
as infinite-dimensional analogs of Fourier transforms. It turns out that the
infinite-dimensional analog of the Mellin transform similarly defines a class
of functional integrals. The associated functional integrals, called functional
Mellin transforms, are useful tools for probing non-commutative function spaces
in general and -algebras in particular: Functional Mellin transforms
can be used to define functional traces, logarithms, and determinants. Several
interesting aspects are explored.Comment: This is the second of two papers representing an expanded version of
arXiv:1308.106
A Non-standard Standard Model
This paper examines the Standard Model under the strong-electroweak gauge
group subject to the condition . Physically, the condition ensures that all electroweak
gauge bosons interact with each other prior to symmetry breaking --- as one
might expect from invariance. This represents a crucial shift in the
notion of physical gauge bosons: Unlike the Standard Model which posits a
change of Lie algebra basis induced by spontaneous symmetry breaking, here the
basis is unaltered and represent (modulo gauge
transformations) the physical bosons both \emph{before} and after spontaneous
symmetry breaking.
Our choice of basis requires some modification of the matter
field sector of the Standard Model. Careful attention to the product group
structure calls for strong-electroweak degrees of freedom in the
and the of
that possess integer electric charge just like
leptons. These degrees of freedom play the role of quarks, and they lead to a
modified Lagrangian that nevertheless reproduces transition rates and cross
sections equivalent to the Standard Model.
The close resemblance between quark and lepton electroweak doublets in this
picture suggests a mechanism for a phase transition between quarks and leptons
that stems from the product structure of the gauge group. Our hypothesis is
that the strong and electroweak bosons see each other as a source of
decoherence. In effect, leptons get identified with the -trace of
quark representations. This mechanism allows for possible extensions of the
Standard Model that don't require large inclusive multiplets of matter fields.
As an example, we propose and investigate a model that turns out to have some
promising cosmological implications.Comment: Added to discussion of dark energy. This is an extended version of
arXiv:hep-ph/0408266 and arXiv:hep-ph/040830
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