188 research outputs found
The thermal operator representation for Matsubara sums
We prove in full generality the thermal operator representation for Matsubara
sums in a relativistic field theory of scalar and fermionic particles. It
states that the full result of performing the Matsubara sum associated to any
given Feynman graph, in the imaginary-time formalism of finite-temperature
field theory, can be directly obtained from its corresponding zero-temperature
energy integral, by means of a simple linear operator, which is independent of
the external Euclidean energies and whose form depends solely on the topology
of the graph.Comment: 9 pages, 1 figure, RevTe
An operator representation for Matsubara sums
In the context of the imaginary-time formalism for a scalar thermal field
theory, it is shown that the result of performing the sums over Matsubara
frequencies associated with loop Feynman diagrams can be written, for some
classes of diagrams, in terms of the action of a simple linear operator on the
corresponding energy integrals of the Euclidean theory at T=0. In its simplest
form the referred operator depends only on the number of internal propagators
of the graph.
More precisely, it is shown explicitly that this \emph{thermal operator
representation} holds for two generic classes of diagrams, namely, the
two-vertex diagram with an arbitrary number of internal propagators, and the
one-loop diagram with an arbitrary number of vertices.
The validity of the thermal operator representation for diagrams of more
complicated topologies remains an open problem. Its correctness is shown to be
equivalent to the correctness of some diagrammatic rules proposed a few years
ago.Comment: 4 figures; references added, minor changes in notation, final version
accepted for publicatio
Identity of the imaginary-time and real-time thermal propagators for scalar bound states in a one-generation Nambu-Jona-Lasinio model
By rigorous reanalysis of the results, we have proven that the propagators at
finite temperature for scalar bound states in one-generation fermion condensate
scheme of electroweak symmetry breaking are in fact identical in the
imaginary-time and the real-time formalism. This dismisses the doubt about
possible discrepancy between the two formalisms in this problem. Identity of
the derived thermal transformation matrices of the real-time matrix propagators
for scalar bound states without and with chemical potential and the ones for
corresponding elementary scalar particles shows similarity of thermodynamic
property between the two types of particles. Only one former inference is
modified, i.e. when the two flavors of fermions have unequal nonzero masses,
the amplitude of the composite Higgs particle will decay instead grow in time.Comment: 5 pages, revtex4, no figure
Shear viscosity in theory from an extended ladder resummation
We study shear viscosity in weakly coupled hot theory using the CTP
formalism . We show that the viscosity can be obtained as the integral of a
three-point function. Non-perturbative corrections to the bare one-loop result
can be obtained by solving a decoupled Schwinger-Dyson type integral equation
for this vertex. This integral equation represents the resummation of an
infinite series of ladder diagrams which contribute to the leading order
result. It can be shown that this integral equation has exactly the same form
as the Boltzmann equation. We show that the integral equation for the viscosity
can be reexpressed by writing the vertex as a combination of polarization
tensors. An expression for this polarization tensor can be obtained by solving
another Schwinger-Dyson type integral equation. This procedure results in an
expression for the viscosity that represents a non-perturbative resummation of
contributions to the viscosity which includes certain non-ladder graphs, as
well as the usual ladders. We discuss the motivation for this resummation. We
show that these resummations can also be obtained by writing the viscosity as
an integral equation involving a single four-point function. Finally, we show
that when the viscosity is expressed in terms of a four-point function, it is
possible to further extend the set of graphs included in the resummation by
treating vertex and propagator corrections self-consistently. We discuss the
significance of such a self-consistent resummation and show that the integral
equation contains cancellations between vertex and propagator corrections.Comment: Revtex 40 pages with 29 figures, version to appear in Phys. Rev.
Finite-temperature reaction-rate formula: Finite volume system, detailed balance, limit, and cutting rules
A complete derivation, from first principles, of the reaction-rate formula
for a generic process taking place in a heat bath of finite volume is given. It
is shown that the formula involves no finite-volume correction. Through
perturbative diagrammatic analysis of the resultant formula, the
detailed-balance formula is derived. The zero-temperature limit of the formula
is discussed. Thermal cutting rules, which are introduced in previous work, are
compared with those introduced by other authors.Comment: 35pages (text) plus 4pages (figures
Lattice Artefacts In The Non-Abelian Debye Screening Mass In One Loop Order
We compute the electric screening mass in lattice QCD with Wilson fermions at
finite temperature and chemical potential to one-loop order, and show that
lattice artefacts arising from a finite lattice spacing result in an
enhancement of the screening mass as compared to the continuum. We discuss the
magnitude of this enhancement as a function of the temperature and chemical
potential for lattices with different number of lattice sites in the temporal
direction that can be implemented in lattice simulations. Most of the
enhancement is found to be due to the fermion loop contribution.Comment: 23 pages, 8 figures, LaTe
The Finite-Temperature Feynman Propagator in Operator Form
In momentum space the Feynman propagator at non-zero temperature
is defined by a simple dispersion relation with the familiar property of being
an even function of and analytic for Re. The coordinate
space form of the propagator is expressed directly in terms of
matrix elements of the field operator and requires a new type of operator
ordering.Comment: 9 pages plain Te
Absorption of Electro-magnetic Waves in a Magnetized Medium
In continuation to our earlier work, in which the structure of the vacuum
polarisation tensor in a medium was analysed in presence of a background
electro-magnetic field, we discuss the absorptive part of the vacuum
polarization tensor. Using the real time formalism of finite temperature field
theory we calculate the absorptive part of 1-loop vacuum polarisation tensor in
the weak field limit (). Estimates of the absorption probability are
also made for different physical conditions of the background medium.Comment: 9 Pages. One figure. LaTe
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