178 research outputs found
Effective Actions for the SU(2) Confinement-Deconfinement Phase Transition
We compare different Polyakov loop actions yielding effective descriptions of
finite-temperature SU(2) Yang-Mills theory on the lattice. The actions are
motivated by a simultaneous strong-coupling and character expansion obeying
center symmetry and include both Ising and Ginzburg-Landau type models. To keep
things simple we limit ourselves to nearest-neighbor interactions. Some
truncations involving the most relevant characters are studied within a novel
mean-field approximation. Using inverse Monte-Carlo techniques based on exact
geometrical Schwinger-Dyson equations we determine the effective couplings of
the Polyakov loop actions. Monte-Carlo simulations of these actions reveal that
the mean-field analysis is a fairly good guide to the physics involved. Our
Polyakov loop actions reproduce standard Yang-Mills observables well up to
limitations due to the nearest-neighbor approximation.Comment: 14 pages, 10 figures, v2: typos correcte
Discrete Dynamics: Gauge Invariance and Quantization
Gauge invariance in discrete dynamical systems and its connection with
quantization are considered. For a complete description of gauge symmetries of
a system we construct explicitly a class of groups unifying in a natural way
the space and internal symmetries. We describe the main features of the gauge
principle relevant to the discrete and finite background. Assuming that
continuous phenomena are approximations of more fundamental discrete processes,
we discuss -- with the help of a simple illustration -- relations between such
processes and their continuous approximations. We propose an approach to
introduce quantum structures in discrete systems, based on finite gauge groups.
In this approach quantization can be interpreted as introduction of gauge
connection of a special kind. We illustrate our approach to quantization by a
simple model and suggest generalization of this model. One of the main tools
for our study is a program written in C.Comment: 15 pages; CASC 2009, Kobe, Japan, September 13-17, 200
CP violation conditions in N-Higgs-doublet potentials
Conditions for CP violation in the scalar potential sector of general
N-Higgs-doublet models (NHDMs) are analyzed from a group theoretical
perspective. For the simplest two-Higgs-doublet model (2HDM) potential, a
minimum set of conditions for explicit and spontaneous CP violation is
presented. The conditions can be given a clear geometrical interpretation in
terms of quantities in the adjoint representation of the basis transformation
group for the two doublets. Such conditions depend on CP-odd pseudoscalar
invariants. When the potential is CP invariant, the explicit procedure to reach
the real CP-basis and the explicit CP transformation can also be obtained. The
procedure to find the real basis and the conditions for CP violation are then
extended to general NHDM potentials. The analysis becomes more involved and
only a formal procedure to reach the real basis is found. Necessary conditions
for CP invariance can still be formulated in terms of group invariants: the
CP-odd generalized pseudoscalars. The problem can be completely solved for
three Higgs-doublets.Comment: RevTeX4 used. Minor modifications, in particular, the parameter
counting of . v3: Eqs.(28)-(31) correcte
Symmetries of Discontinuous Flows and the Dual Rankine-Hugoniot Conditions in Fluid Dynamics
It has recently been shown that the maximal kinematical invariance group of
polytropic fluids, for smooth subsonic flows, is the semidirect product of
SL(2,R) and the static Galilei group G. This result purports to offer a
theoretical explanation for an intriguing similarity, that was recently
observed, between a supernova explosion and a plasma implosion. In this paper
we extend this result to discuss the symmetries of discontinuous flows, which
further validates the explanation by taking into account shock waves, which are
the driving force behind both the explosion and implosion. This is accomplished
by constructing a new set of Rankine-Hugoniot conditions, which follow from
Noether's conservation laws. The new set is dual to the standard
Rankine-Hugoniot conditions and is related to them through the SL(2,R)
transformations. The entropy condition, that the shock needs to satisfy for
physical reasons, is also seen to remain invariant under the transformations.Comment: 14 pages, 1 figur
The Central Correlations of Hypercharge, Isospin, Colour and Chirality in the Standard Model
The correlation of the fractionally represented hypercharge group with the
isospin and colour group in the standard model determines as faithfully
represented internal group the quotient group
{\U(1)\x\SU(2)\x\SU(3)\over\Z_2\x\Z_3}. The discrete cyclic central
abelian-nonabelian internal correlation involved is considered with respect to
its consequences for the representations by the standard model fields, the
electroweak mixing angle and the symmetry breakdown. There exists a further
discrete -correlation between chirality and Lorentz properties and also a
continuous \U(1)-external-internal one between hyperisospin and chirality.Comment: 18 pages, latex, macros include
Quantum Extremism: Effective Potential and Extremal Paths
The reality and convexity of the effective potential in quantum field
theories has been studied extensively in the context of Euclidean space-time.
It has been shown that canonical and path-integral approaches may yield
different results, thus resolving the `convexity problem'. We discuss the
transferral of these treatments to Minkowskian space-time, which also
necessitates a careful discussion of precisely which field configurations give
the dominant contributions to the path integral. In particular, we study the
effective potential for the N=1 linear sigma model.Comment: 11 pages, 4 figure
Infrared properties of propagators in Landau-gauge pure Yang-Mills theory at finite temperature
The finite-temperature behavior of gluon and of Faddeev-Popov-ghost
propagators is investigated for pure SU(2) Yang-Mills theory in Landau gauge.
We present nonperturbative results, obtained using lattice simulations and
Dyson-Schwinger equations. Possible limitations of these two approaches, such
as finite-volume effects and truncation artifacts, are extensively discussed.
Both methods suggest a very different temperature dependence for the magnetic
sector when compared to the electric one. In particular, a clear thermodynamic
transition seems to affect only the electric sector. These results imply in
particular the confinement of transverse gluons at all temperatures and they
can be understood inside the framework of the so-called Gribov-Zwanziger
scenario of confinement.Comment: 25 pages, 14 figures, 2 tables, minor changes of typographical and
design character, some minor errors corrected, version to appear in PR
The Path-Integral Approach to the N=2 Linear Sigma Model
In QFT the effective potential is an important tool to study symmetry
breaking phenomena. It is known that, in some theories, the canonical approach
and the path-integral approach yield different effective potentials. In this
paper we investigate this for the Euclidean N=2 linear sigma model. Both the
Green's functions and the effective potential will be computed in three
different ways. The relative merits of the various approaches are discussed.Comment: 2 figure
Supersymmetry and Lorentz Violation
Supersymmetric field theories can be constructed that violate Lorentz and CPT
symmetry. We illustrate this with some simple examples related to the original
Wess-Zumino model.Comment: 4 page
Conformal Symmetry of Relativistic and Nonrelativistic Systems and AdS/CFT Correspondence
The nonlinear realization of conformal so(2,d) symmetry for relativistic
systems and the dynamical conformal so(2,1) symmetry of nonrelativistic systems
are investigated in the context of AdS/CFT correspondence. We show that the
massless particle in d-dimensional Minkowski space can be treated as the system
confined to the border of the AdS_{d+1} of infinite radius, while various
nonrelativistic systems may be canonically related to a relativistic (massless,
massive, or tachyon) particle on the AdS_2 X S^{d-1}. The list of
nonrelativistic systems "unified" by such a correspondence comprises the
conformal mechanics model, the planar charge-vortex and 3-dimensional
charge-monopole systems, the particle in a planar gravitational field of a
point massive source, and the conformal model associated with the charged
particle propagating near the horizon of the extreme Reissner-Nordstrom black
hole.Comment: 21 pages, typos corrected, refs and note adde
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