528 research outputs found
Path integration and perturbation theory with complex Euclidean actions
The Euclidean path integral quite often involves an action that is not
completely real {\it i.e.} a complex action. This occurs when the Minkowski
action contains -odd CP-violating terms. Analytic continuation to Euclidean
time yields an imaginary term in the Euclidean action. In the presence of
imaginary terms in the Euclidean action, the usual method of perturbative
quantization can fail. Here the action is expanded about its critical points,
the quadratic part serving to define the Gaussian free theory and the higher
order terms defining the perturbative interactions. For a complex action, the
critical points are generically obtained at complex field configurations. Hence
the contour of path integration does not pass through the critical points and
the perturbative paradigm cannot be directly implemented. The contour of path
integration has to be deformed to pass through the complex critical point using
a generalized method of steepest descent, in order to do so. Typically, what is
done is that only the real part of the Euclidean action is considered, and its
critical points are used to define the perturbation theory. In this article we
present a simple 0+1-dimensional example, of scalar fields interacting with
a U(1) gauge field, in the presence of a Chern-Simons term, where
alternatively, the path integral can be done exactly, the procedure of
deformation of the contour of path integration can be done explicitly and the
standard method of only taking into account the real part of the action can be
followed. We show explicitly that the standard method does not give a correct
perturbative expansion.Comment: 11 pages, no figures, version to be published in PR
Problems With Complex Actions
We consider Euclidean functional integrals involving actions which are not
exclusively real. This situation arises, for example, when there are -odd
terms in the the Minkowski action. Writing the action in terms of only real
fields (which is always possible), such terms appear as explicitly imaginary
terms in the Euclidean action. The usual quanization procedure which involves
finding the critical points of the action and then quantizing the spectrum of
fluctuations about these critical points fails. In the case of complex actions,
there do not exist, in general, any critical points of the action on the space
of real fields, the critical points are in general complex. The proper
definition of the function integral then requires the analytic continuation of
the functional integration into the space of complex fields so as to pass
through the complex critical points according to the method of steepest
descent. We show a simple example where this procedure can be carried out
explicitly. The procedure of finding the critical points of the real part of
the action and quantizing the corresponding fluctuations, treating the
(exponential of the) complex part of the action as a bounded integrable
function is shown to fail in our explicit example, at least perturbatively.Comment: 6+epsilon pages, no figures, presented at Theory CANADA
Conformal Spinning Quantum Particles in Complex Minkowski Space as Constrained Nonlinear Sigma Models in U(2,2) and Born's Reciprocity
We revise the use of 8-dimensional conformal, complex (Cartan) domains as a
base for the construction of conformally invariant quantum (field) theory,
either as phase or configuration spaces. We follow a gauge-invariant Lagrangian
approach (of nonlinear sigma-model type) and use a generalized Dirac method for
the quantization of constrained systems, which resembles in some aspects the
standard approach to quantizing coadjoint orbits of a group G. Physical wave
functions, Haar measures, orthonormal basis and reproducing (Bergman) kernels
are explicitly calculated in and holomorphic picture in these Cartan domains
for both scalar and spinning quantum particles. Similarities and differences
with other results in the literature are also discussed and an extension of
Schwinger's Master Theorem is commented in connection with closure relations.
An adaptation of the Born's Reciprocity Principle (BRP) to the conformal
relativity, the replacement of space-time by the 8-dimensional conformal domain
at short distances and the existence of a maximal acceleration are also put
forward.Comment: 33 pages, no figures, LaTe
Seeking an Even-Parity Mass Term for 3-D Gauge Theory
Mass-gap calculations in three-dimensional gauge theories are discussed. Also
we present a Chern--Simons-like mass-generating mechanism which preserves
parity and is realized non-perturbatively.Comment: 11 pages, revte
Renormalization of the Hamiltonian and a geometric interpretation of asymptotic freedom
Using a novel approach to renormalization in the Hamiltonian formalism, we
study the connection between asymptotic freedom and the renormalization group
flow of the configuration space metric. It is argued that in asymptotically
free theories the effective distance between configuration decreases as high
momentum modes are integrated out.Comment: 22 pages, LaTeX, no figures; final version accepted in Phys.Rev.D;
added reference and appendix with comment on solution of eq. (9) in the tex
A Gauge-Invariant UV-IR Mixing and The Corresponding Phase Transition For U(1) Fields on the Fuzzy Sphere
From a string theory point of view the most natural gauge action on the fuzzy
sphere {\bf S}^2_L is the Alekseev-Recknagel-Schomerus action which is a
particular combination of the Yang-Mills action and the Chern-Simons term .
Since the differential calculus on the fuzzy sphere is 3-dimensional the field
content of this model consists naturally of a 2-dimensional gauge field
together with a scalar fluctuation normal to the sphere . For U(1) gauge theory
we compute the quadratic effective action and shows explicitly that the tadpole
diagrams and the vacuum polarization tensor contain a gauge-invariant UV-IR
mixing in the continuum limit L{\longrightarrow}{\infty} where L is the matrix
size of the fuzzy sphere. In other words the quantum U(1) effective action does
not vanish in the commutative limit and a noncommutative anomaly survives . We
compute the scalar effective potential and prove the gauge-fixing-independence
of the limiting model L={\infty} and then show explicitly that the one-loop
result predicts a first order phase transition which was observed recently in
simulation . The one-loop result for the U(1) theory is exact in this limit .
It is also argued that if we add a large mass term for the scalar mode the
UV-IR mixing will be completely removed from the gauge sector . It is found in
this case to be confined to the scalar sector only. This is in accordance with
the large L analysis of the model . Finally we show that the phase transition
becomes harder to reach starting from small couplings when we increase M .Comment: 41 pages, 4 figures . Introduction rewritten extensively to include a
summary of the main results of the pape
Remarks on Goldstone bosons and hard thermal loops
The hard thermal loop effective action for Goldstone bosons is deduced by symmetry arguments from the corresponding result for gauge bosons. Pseudoscalar mesons in chromodynamics and magnons in an antiferromagnet are discussed as special cases, including the hard thermal loop contribution to their scattering.Facultad de Ciencias Exacta
The magnetic mass of transverse gluon, the B-meson weak decay vertex and the triality symmetry of octonion
With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion
and a right-handed fermion both expressed as quaternion make an octonion which
possesses the triality symmetry, I calculate the magnetic mass of the
transverse self-dual gluon from three loop diagram, in which a heavy quark pair
is created and two self-dual gluons are interchanged.
The magnetic mass of the transverse gluon depends on the mass of the pair
created quarks, and in the case of charmed quark pair creation, the magnetic
mass becomes approximately equal to at MeV. A possible time-like magnetic gluon mass
from two self-dual gluon exchange is derived, and corrections in the B-meson
weak decay vertices from the two self-dual gluon exchange are also evaluated.Comment: 22 pages, 9 figure
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