4,908 research outputs found
Non-commutative Complex Projective Spaces and the Standard Model
The standard model fermion spectrum, including a right handed neutrino, can
be obtained as a zero-mode of the Dirac operator on a space which is the
product of complex projective spaces of complex dimension two and three. The
construction requires the introduction of topologically non-trivial background
gauge fields. By borrowing from ideas in Connes' non-commutative geometry and
making the complex spaces `fuzzy' a matrix approximation to the fuzzy space
allows for three generations to emerge. The generations are associated with
three copies of space-time. Higgs' fields and Yukawa couplings can be
accommodated in the usual way.Comment: Contribution to conference in honour of A.P. Balachandran's 65th
birthday: "Space-time and Fundamental Interactions: Quantum Aspects", Vietri
sul Mare, Italy, 25th-31st May, 2003, 10 pages, typset in LaTe
The Information Geometry of the Ising Model on Planar Random Graphs
It has been suggested that an information geometric view of statistical
mechanics in which a metric is introduced onto the space of parameters provides
an interesting alternative characterisation of the phase structure,
particularly in the case where there are two such parameters -- such as the
Ising model with inverse temperature and external field .
In various two parameter calculable models the scalar curvature of
the information metric has been found to diverge at the phase transition point
and a plausible scaling relation postulated: . For spin models the necessity of calculating in
non-zero field has limited analytic consideration to 1D, mean-field and Bethe
lattice Ising models. In this letter we use the solution in field of the Ising
model on an ensemble of planar random graphs (where ) to evaluate the scaling behaviour of the scalar curvature, and find
. The apparent discrepancy is traced
back to the effect of a negative .Comment: Version accepted for publication in PRE, revtex
On the Role of Chaos in the AdS/CFT Connection
The question of how infalling matter in a pure state forms a Schwarzschild
black hole that appears to be at non-zero temperature is discussed in the
context of the AdS/CFT connection. It is argued that the phenomenon of
self-thermalization in non-linear (chaotic) systems can be invoked to explain
how the boundary theory, initially at zero temperature self thermalizes and
acquires a finite temperature. Yang-Mills theory is known to be chaotic
(classically) and the imaginary part of the gluon self-energy (damping rate of
the gluon plasma) is expected to give the Lyapunov exponent. We explain how the
imaginary part would arise in the corresponding supergravity calculation due to
absorption at the horizon of the black hole.Comment: 18 pages. Latex file. Minor changes. Final version to appear in
Modern Physics Letters
Effective Action of Spontaneously Broken Gauge Theories
The effective action of a Higgs theory should be gauge-invariant. However,
the quantum and/or thermal contributions to the effective potential seem to be
gauge-dependent, posing a problem for its physical interpretation. In this
paper, we identify the source of the problem and argue that in a Higgs theory,
perturbative contributions should be evaluated with the Higgs fields in the
polar basis, not in the Cartesian basis. Formally, this observation can be made
from the derivation of the Higgs theorem, which we provide. We show explicitly
that, properly defined, the effective action for the Abelian Higgs theory is
gauge invariant to all orders in perturbation expansion when evaluated in the
covariant gauge in the polar basis. In particular, the effective potential is
gauge invariant. We also show the equivalence between the calculations in the
covariant gauge in the polar basis and the unitary gauge. These points are
illustrated explicitly with the one-loop calculations of the effective action.
With a field redefinition, we obtain the physical effective potential. The
SU(2) non-Abelian case is also discussed.Comment: Expanded version, 32 pages, figures produced by LaTeX, plain LaTe
Scalar Field Theory on Fuzzy S^4
Scalar fields are studied on fuzzy and a solution is found for the
elimination of the unwanted degrees of freedom that occur in the model. The
resulting theory can be interpreted as a Kaluza-Klein reduction of CP^3 to S^4
in the fuzzy context.Comment: 16 pages, LaTe
Path integrals and degrees of freedom in many-body systems and relativistic field theories
The identification of physical degrees of freedom is sometimes obscured in
the path integral formalism, and this makes it difficult to impose some
constraints or to do some approximations. I review a number of cases where the
difficulty is overcame by deriving the path integral from the operator form of
the partition function after such identification has been made.Comment: 15 pages, volume in honor of prof.Yu.A.Simono
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