146 research outputs found
Finite temperature formalism for nonabelian gauge theories in the physical phase space
We establish a new framework of finite temperature field theory for
Yang-Mills theories in the physical phase space eliminating all unphysical
degrees of freedoms. Relating our method to the imaginary time formalism of
James and Landshoff in temporal axial gauge, we calculate the two-loop pressure
and provide a systematic and unique method to construct the additional vertices
encountered in their approach.Comment: 18 pages, 5 postscript figures, uses revtex, eps
Wilson Loop and the Treatment of Axial Gauge Poles
We consider the question of gauge invariance of the Wilson loop in the light
of a new treatment of axial gauge propagator proposed recently based on a
finite field-dependent BRS (FFBRS) transformation. We remark that as under the
FFBRS transformation the vacuum expectation value of a gauge invariant
observable remains unchanged, our prescription automatically satisfies the
Wilson loop criterion. Further, we give an argument for {\it direct}
verification of the invariance of Wilson loop to O(g^4) using the earlier work
by Cheng and Tsai. We also note that our prescription preserves the thermal
Wilson loop to O(g^2).Comment: 8 pages, LaTex; some typos related to equation (18) correcte
Development Studies Working Paper, no. 47
This Working Paper contains the results of a pilot investigation undertaken in 1986/87 in selected areas of the Keiskammahoek District of Ciskei. The pilot study was undertaken in order to compile a comprehensive plan for a long-term study of the Keiskammahoek District as a whole. Such a study would be designed to analyse socio-economic and political changes which have taken place in the District, measured against the results of a major multidisciplinary research project (The Keiskammahoek Rural Survey) which was undertaken in the area between 1948 and 1950. The existence of the Keiskammahoek Rural Survey affords a unique opportunity for comparative social science research, particularly because it is well known that substantial changes have taken place in the District. However, the precise nature and scale of the changes were unknown; hence, the decision to conduct a pilot survey first. The results of the pilot survey, published here, have turned out to be extremely valuable in formulating proposals for a subsequent on-going research undertaking; and have fully justified the time and money devoted to the exploratory investigation which constituted the basis of the pilot project.Digitised by Rhodes University Library on behalf of the Institute of Social and Economic Research (ISER
Comparison of quantum field perturbation theory for the light front with the theory in lorentz coordinates
The relationship between the perturbation theory in light-front coordinates
and Lorentz-covariant perturbation theory is investigated. A method for finding
the difference between separate terms of the corresponding series without their
explicit evaluation is proposed. A procedure of constructing additional
counter-terms to the canonical Hamiltonian that compensate this difference at
any finite order is proposed. For the Yukawa model, the light-front Hamiltonian
with all of these counter-terms is obtained in a closed form. Possible
application of this approach to gauge theories is discussed.Comment: LaTex 2.09, 20 pages, 5 figure
Canonical Quantisation in n.A=0 gauges
We give a unified derivation of the propagator in the gauges for
timelike, spacelike or lightlike. We discuss the physical states and
other physical questions.Comment: 7 pages, DAMTP 93-33, ITP-SB-93-3
Similarity Renormalization, Hamiltonian Flow Equations, and Dyson's Intermediate Representation
A general framework is presented for the renormalization of Hamiltonians via
a similarity transformation. Divergences in the similarity flow equations may
be handled with dimensional regularization in this approach, and the resulting
effective Hamiltonian is finite since states well-separated in energy are
uncoupled. Specific schemes developed several years ago by Glazek and Wilson
and contemporaneously by Wegner correspond to particular choices within this
framework, and the relative merits of such choices are discussed from this
vantage point. It is shown that a scheme for the transformation of Hamiltonians
introduced by Dyson in the early 1950's also corresponds to a particular choice
within the similarity renormalization framework, and it is argued that Dyson's
scheme is preferable to the others for ease of computation. As an example, it
is shown how a logarithmically confining potential arises simply at second
order in light-front QCD within Dyson's scheme, a result found previously for
other similarity renormalization schemes. Steps toward higher order and
nonperturbative calculations are outlined. In particular, a set of equations
analogous to Dyson-Schwinger equations is developed.Comment: REVTex, 32 pages, 7 figures (corrected references
Renormalization of the mass gap
The full gluon propagator relevant for the description of the truly
non-perturbative QCD dynamics, the so-called intrinsically non-perturbative
gluon propagator has been derived in our previous work. It explicitly depends
on the regularized mass gap, which dominates its structure at small gluon
momentum. It is automatically transversal in a gauge invariant way. It is
characterized by the presence of severe infrared singularities at small gluon
momentum, so the gluons remain massless, and this does not depend on the gauge
choice. In this paper we have shown how precisely the renormalization program
for the regularized mass gap should be performed. We have also shown how
precisely severe infrared singularities should be correctly treated. This
allowed to analytically formulate the exact and gauge-invariant criteria of
gluon and quark confinement. After the renormalization program is completed,
one can derive the gluon propagator applicable for the calculation of physical
observables processes, etc., in low-energy QCD from first principles.Comment: 16 pages, no figures, no tables, some minor changes are introduce
Gauge-Independent Off-Shell Fermion Self-Energies at Two Loops: The Cases of QED and QCD
We use the pinch technique formalism to construct the gauge-independent
off-shell two-loop fermion self-energy, both for Abelian (QED) and non-Abelian
(QCD) gauge theories. The new key observation is that all contributions
originating from the longitudinal parts of gauge boson propagators, by virtue
of the elementary tree-level Ward identities they trigger, give rise to
effective vertices, which do not exist in the original Lagrangian; all such
vertices cancel diagrammatically inside physical quantities, such as current
correlation functions or S-matrix elements. We present two different, but
complementary derivations: First, we explicitly track down the aforementioned
cancellations inside two-loop diagrams, resorting to nothing more than basic
algebraic manipulations. Second, we present an absorptive derivation,
exploiting the unitarity of the S-matrix, and the Ward identities imposed on
tree-level and one-loop physical amplitudes by gauge invariance, in the case of
QED, or by the underlying Becchi-Rouet-Stora symmetry, in the case of QCD. The
propagator-like sub-amplitude defined by means of this latter construction
corresponds precisely to the imaginary parts of the effective self-energy
obtained in the former case; the real part may be obtained from a (twice
subtracted) dispersion relation. As in the one-loop case, the final two-loop
fermion self-energy constructed using either method coincides with the
conventional fermion self-energy computed in the Feynman gauge.Comment: 30 pages; uses axodraw (axodraw.sty included in the src); final
version to appear in Phys. Rev.
More on the relation between the two physically inequivalent decompositions of the nucleon spin and momentum
In a series of papers, we have established the existence of two
gauge-invariant decompositions of the nucleon spin, which are physically
nonequivalent. The orbital angular momenta of quarks and gluons appearing in
these two decompositions are gauge-invariant dynamical orbital angular momenta
and "generalized" canonical orbital angular momenta with gauge-invariance,
respectively. The key quantity, which characterizes the difference between
these two types of orbital angular momenta is what-we-call the {\it potential
angular momentum}. We argue that the physical meaning of the potential angular
momentum in the nucleon can be made more transparent, by investigating a
related but much simpler example from electrodynamics. We also make clear
several remaining issues in the spin and momentum decomposition problem of the
nucleon. We clarify the relationship between the evolution equations of orbital
angular momenta corresponding to the two different decompositions above. We
also try to answer the question whether the two different decompositions of the
nucleon momentum really lead to different evolution equations, thereby
predicting conflicting asymptotic values for the quark and gluon momentum
fractions in the nucleon.Comment: The version to appear in Physical Review D, LaTeX, 47 pages, 4
figure
Local well-posedness for membranes in the light cone gauge
In this paper we consider the classical initial value problem for the bosonic
membrane in light cone gauge. A Hamiltonian reduction gives a system with one
constraint, the area preserving constraint. The Hamiltonian evolution equations
corresponding to this system, however, fail to be hyperbolic. Making use of the
area preserving constraint, an equivalent system of evolution equations is
found, which is hyperbolic and has a well-posed initial value problem. We are
thus able to solve the initial value problem for the Hamiltonian evolution
equations by means of this equivalent system. We furthermore obtain a blowup
criterion for the membrane evolution equations, and show, making use of the
constraint, that one may achieve improved regularity estimates.Comment: 29 page
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