1,655 research outputs found
Critical angular velocity for vortex lines formation
For helium II inside a rotating cylinder, it is proposed that the formation
of vortex lines of the frictionless superfluid component of the liquid is
caused by the presence of the rotating quasi-particles gas. By minimising the
free energy of the system, the critical value Omega_0 of the angular velocity
for the formation of the first vortex line is determined. This value
nontrivially depends on the temperature, and numerical estimations of its
temperature behaviour are produced. It is shown that the latent heat for a
vortex formation and the associated discontinuous change in the angular
momentum of the quasi-particles gas determine the slope of Omega_0 (T) via some
kind of Clapeyron equation.Comment: 16 page
Schwinger-Dyson functional in Chern-Simons theory
In perturbative SU(N) Chern-Simons gauge theory, it is shown that the
Schwinger-Dyson equations assume a quite simplified form. The generating
functional of the correlation functions of the curvature is considered; it is
demonstrated that the renormalized Schwinger-Dyson functional is related with
the generating functional of the correlation functions of the gauge connections
by some kind of duality transformation.Comment: 11 page
Quasi-particles, thermodynamic consistency and the gap equation
The thermodynamic properties of superconducting electrons are usually studied
by means of the quasi-particles distribution; but in this approach, the ground
state energy and the dependence of the chemical potential on the electron
density cannot be determined. In order to solve these problems, the
thermodynamic potentials are derived by means of the Bogoliubov-Valatin
formalism. The thermodynamic potentials can be obtained by computing the free
energy of a gas of quasi-particles, whose energy spectrum is conditional on the
gap function. However, the nontrivial dependence of the gap on the temperature
jeopardises the validity of the standard thermodynamic relations. In this
article it is shown how the thermodynamic consistency (i.e. the validity of the
Maxwell relations) is recovered, and the correction terms to the
quasi-particles potentials are computed. It is shown that the
Bogoliubov-Valatin transformation avoids the problem of the thermodynamic
consistency of the quasi-particle approach; in facts, the correct
identification of the variables, which are associated with the quasi-particles,
leads to a precise calculation of the quasi-particles vacuum energy and of the
dependence of the chemical potential on the electron density. The stationarity
condition for the grand potential coincides with the gap equation, which
guarantees the thermodynamic consistency. The expressions of various
thermodynamic potentials, as functions of the (T,V,N) variables, are produced
in the low temperature limit; as a final check, a rederivation of the
condensation energy is presented.Comment: 16 page
Functional integration and abelian link invariants
The functional integral computation of the various topological invariants,
which are associated with the Chern-Simons field theory, is considered. The
standard perturbative setting in quantum field theory is rewieved and new
developments in the path-integral approach, based on the Deligne-Beilinson
cohomology, are described in the case of the abelian U(1) Chern-Simons field
theory formulated in S^1 x S^2.Comment: 20 pages, 4 figures, Contribution to the Proceedings of the workshop
"Chern-Simons Gauge theory: 20 years after", Bonn, August 200
Representations for creation and annihilation operators
A new representation -which is similar to the Bargmann representation- of the
creation and annihilation operators is introduced, in which the operators act
like "multiplication with" and like "derivation with respect to" a single real
variable. The Hilbert space structure of the corresponding states space is
produced and the relations with the Schroedinger representation are derived.
Possible connections of this new representation with the asymptotic wave
functions of the gauge-fixed quantum Chern-Simons field theory and (2+1)
gravity are pointed out. It is shown that the representation of the fields
operator algebra of the Chern-Simons theory in the Landau gauge is not a
*-representation; the consequences on the evolution of the states in the
semiclassical approximation are discussed.Comment: 15 page
Three-manifold invariants and their relation with the fundamental group
We consider the 3-manifold invariant I(M) which is defined by means of the
Chern-Simons quantum field theory and which coincides with the
Reshetikhin-Turaev invariant. We present some arguments and numerical results
supporting the conjecture that, for nonvanishing I(M), the absolute value |
I(M) | only depends on the fundamental group \pi_1 (M) of the manifold M. For
lens spaces, the conjecture is proved when the gauge group is SU(2). In the
case in which the gauge group is SU(3), we present numerical computations
confirming the conjecture.Comment: 22 pages, Latex document, two eps figure
Gravitational helicity interaction
For gravitational deflections of massless particles of given helicity from a
classical rotating body, we describe the general relativity corrections to the
geometric optics approximation. We compute the corresponding scattering cross
sections for neutrinos, photons and gravitons to lowest order in the
gravitational coupling constant. We find that the helicity coupling to
spacetime geometry modifies the ray deflection formula of the geometric optics,
so that rays of different helicity are deflected by different amounts. We also
discuss the validity range of the Born approximation.Comment: 16 pages, 1 figure, to be published in Nuclear Physics
Chern-Simons Theory in the Temporal Gauge and Knot Invariants through the Universal Quantum R-Matrix
In temporal gauge A_{0}=0 the 3d Chern-Simons theory acquires quadratic
action and an ultralocal propagator. This directly implies a 2d R-matrix
representation for the correlators of Wilson lines (knot invariants), where
only the crossing points of the contours projection on the xy plane contribute.
Though the theory is quadratic, P-exponents remain non-trivial operators and
R-factors are easier to guess then derive. We show that the topological
invariants arise if additional flag structure (xy plane and an y line in it) is
introduced, R is the universal quantum R-matrix and turning points contribute
the "enhancement" factors q^{\rho}.Comment: 27 pages, 17 figure
Path-integral invariants in abelian Chern-Simons theory
We consider the Chern-Simons gauge theory defined in a general closed
oriented 3-manifold ; the functional integration is used to compute the
normalized partition function and the expectation values of the link
holonomies. The nonperturbative path-integral is defined in the space of the
gauge orbits of the connections which belong to the various inequivalent
principal bundles over ; the different sectors of the configuration space
are labelled by the elements of the first homology group of and are
characterized by appropriate background connections. The gauge orbits of flat
connections, whose classification is also based on the homology group, control
the extent of the nonperturbative contributions to the mean values. The
functional integration is achieved in any 3-manifold , and the corresponding
path-integral invariants turn out to be strictly related with the abelian
Reshetikhin-Turaev surgery invariants
An analytical expression for the third coefficient of the Jones Polynomial
An analytical expression for the third coefficient of the Jones Polynomial
P_J[\gamma,\, {\em e}^q] in the variable is reported. Applications of the
result in Quantum Gravity are considered.Comment: 9 page
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